0.00/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.31	% Computer   : n014.cluster.edu
0.12/0.31	% Model      : x86_64 x86_64
0.12/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.31	% Memory     : 8042.1875MB
0.12/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.31	% CPULimit   : 1200
0.12/0.31	% DateTime   : Tue Jul 13 16:27:04 EDT 2021
0.12/0.31	% CPUTime    : 
1.14/1.45	============================== Prover9 ===============================
1.14/1.45	Prover9 (32) version 2009-11A, November 2009.
1.14/1.45	Process 11712 was started by sandbox2 on n014.cluster.edu,
1.14/1.45	Tue Jul 13 16:27:05 2021
1.14/1.45	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_11559_n014.cluster.edu".
1.14/1.45	============================== end of head ===========================
1.14/1.45	
1.14/1.45	============================== INPUT =================================
1.14/1.45	
1.14/1.45	% Reading from file /tmp/Prover9_11559_n014.cluster.edu
1.14/1.45	
1.14/1.45	set(prolog_style_variables).
1.14/1.45	set(auto2).
1.14/1.45	    % set(auto2) -> set(auto).
1.14/1.45	    % set(auto) -> set(auto_inference).
1.14/1.45	    % set(auto) -> set(auto_setup).
1.14/1.45	    % set(auto_setup) -> set(predicate_elim).
1.14/1.45	    % set(auto_setup) -> assign(eq_defs, unfold).
1.14/1.45	    % set(auto) -> set(auto_limits).
1.14/1.45	    % set(auto_limits) -> assign(max_weight, "100.000").
1.14/1.45	    % set(auto_limits) -> assign(sos_limit, 20000).
1.14/1.45	    % set(auto) -> set(auto_denials).
1.14/1.45	    % set(auto) -> set(auto_process).
1.14/1.45	    % set(auto2) -> assign(new_constants, 1).
1.14/1.45	    % set(auto2) -> assign(fold_denial_max, 3).
1.14/1.45	    % set(auto2) -> assign(max_weight, "200.000").
1.14/1.45	    % set(auto2) -> assign(max_hours, 1).
1.14/1.45	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.14/1.45	    % set(auto2) -> assign(max_seconds, 0).
1.14/1.45	    % set(auto2) -> assign(max_minutes, 5).
1.14/1.45	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.14/1.45	    % set(auto2) -> set(sort_initial_sos).
1.14/1.45	    % set(auto2) -> assign(sos_limit, -1).
1.14/1.45	    % set(auto2) -> assign(lrs_ticks, 3000).
1.14/1.45	    % set(auto2) -> assign(max_megs, 400).
1.14/1.45	    % set(auto2) -> assign(stats, some).
1.14/1.45	    % set(auto2) -> clear(echo_input).
1.14/1.45	    % set(auto2) -> set(quiet).
1.14/1.45	    % set(auto2) -> clear(print_initial_clauses).
1.14/1.45	    % set(auto2) -> clear(print_given).
1.14/1.45	assign(lrs_ticks,-1).
1.14/1.45	assign(sos_limit,10000).
1.14/1.45	assign(order,kbo).
1.14/1.45	set(lex_order_vars).
1.14/1.45	clear(print_given).
1.14/1.45	
1.14/1.45	% formulas(sos).  % not echoed (660 formulas)
1.14/1.45	
1.14/1.45	============================== end of input ==========================
1.14/1.45	
1.14/1.45	% From the command line: assign(max_seconds, 1200).
1.14/1.45	
1.14/1.45	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.14/1.45	
1.14/1.45	% Formulas that are not ordinary clauses:
1.14/1.45	1 (all P_1 all Ma all Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> ((Ma = Na -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))))) # label(fact_137_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	2 (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,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),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_331_power2__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	3 (all X_a (power(X_a) & semiring_0(X_a) -> (all N ((zero_zero(nat) != N -> hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N) = zero_zero(X_a)) & (zero_zero(nat) = N -> hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N) = one_one(X_a)))))) # label(fact_109_power__0__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	4 (all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))))) # label(fact_64_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	5 (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].
1.14/1.45	6 (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_431_not__leE) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	7 (all X_a (linordered_semidom(X_a) -> (all M_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)))))) # label(fact_279_zero__le__imp__of__nat) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	8 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)))) # label(fact_31_rel__simps_I17_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	9 (all I_2 all J_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),I_2))) # label(fact_117_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	10 (all X_a (order(X_a) -> (all Ya all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) -> (ti(X_a,Xa) = ti(X_a,Ya) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya))))))) # label(fact_396_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	11 (all K_2 all Ma all Na (Na = Ma <-> hAPP(nat,nat,plus_plus(nat,K_2),Ma) = hAPP(nat,nat,plus_plus(nat,K_2),Na))) # label(fact_124_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	12 (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(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))))) # label(fact_309_less__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	13 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a))) # label(fact_3_one__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	14 (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_273_not__one__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	15 (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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_335_sum__power2__ge__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	16 (all X_a all B_1_1 all B_2 all X_b (ord(X_b) -> hAPP(X_a,X_b,B_1_1,B_2) = ti(X_b,hAPP(X_a,X_b,B_1_1,B_2)))) # label(tsy_c_hAPP_0_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	17 (all M_1 all N (M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_352_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	18 (all K hAPP(int,int,succ,hAPP(int,int,bit1,K)) = hAPP(int,int,bit0,hAPP(int,int,succ,K))) # label(fact_316_succ__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	19 (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(hAPP(int,bool,P_1,X_1)))) <-> (all X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1)))))) # label(fact_291_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	20 (all P (fFalse = ti(bool,P) | ti(bool,P) = fTrue)) # label(help_If_3_1_T) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	21 (all B_1_1 all X_a (number(X_a) -> number_number_of(X_a,B_1_1) = number_number_of(X_a,ti(int,B_1_1)))) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	22 (all X_a (linorder(X_a) -> (all Xa all Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)))))) # label(fact_424_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	23 (all X_a (power(X_a) -> (all A_1 hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat)) = one_one(X_a)))) # label(fact_186_power__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	24 (all Wa all Z_2 ((exists N_1 Z_2 = hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z_2)))) # label(fact_294_zle__iff__zadd) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	25 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (zero_zero(X_a) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) <-> ti(X_a,Xa) = zero_zero(X_a) & ti(X_a,Ya) = zero_zero(X_a))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	26 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_5_zero__eq__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	27 (all X_a (number_ring(X_a) -> (all K hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,K)) = number_number_of(X_a,hAPP(int,int,succ,K))))) # label(fact_325_number__of__succ) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	28 (all X_a (linordered_semidom(X_a) -> (all Ma all Na 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)) -> (Na = Ma <-> hAPP(nat,X_a,power_power(X_a,A_2),Ma) = hAPP(nat,X_a,power_power(X_a,A_2),Na)))))) # label(fact_180_power__inject__exp) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	29 (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,power_power(X_a,number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_103_of__nat__less__two__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	30 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Ya))))))) # label(fact_50_less__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	31 (all B_1_1 all B_2 all X_a (power(X_a) -> ti(X_a,hAPP(nat,X_a,B_1_1,B_2)) = hAPP(nat,X_a,B_1_1,B_2))) # label(tsy_c_hAPP_1_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	32 (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_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	33 (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,plus_plus(int,one_one(int)),Z_1))))) # label(fact_324_le__imp__0__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	34 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)) -> W_1 = Z_1))) # label(fact_251_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	35 (all Va (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va))))) # label(fact_160_less__0__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.45	36 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))))))) # label(fact_222_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	37 (all P_1 all K_2 all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K_2),one_one(int)))) -> ((all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I_1)) -> (hBOOL(hAPP(int,bool,P_1,I_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I_1),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_112_int__gr__induct) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	38 (all K all I_2 all J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_2),J_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J_2),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_2),K))))) # label(fact_380_real__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	39 (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_280_of__nat__0__le__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	40 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2))))))) # label(fact_445_real__lbound__gt__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	41 (all N all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> N != M_1)) # label(fact_129_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	42 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1))))) # label(fact_243_rel__simps_I34_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	43 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> zero_zero(X_a) != hAPP(nat,X_a,power_power(X_a,A_1),N))))) # label(fact_164_field__power__not__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	44 (all X_a (linord20386208strict(X_a) -> (all A_1 all C_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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_1),B))))))) # label(fact_466_mult__right__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	45 (all X_a (one(X_a) -> (all Xa (one_one(X_a) = ti(X_a,Xa) <-> one_one(X_a) = ti(X_a,Xa))))) # label(fact_209_one__reorient) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	46 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)))))))) # label(fact_300_add__strict__increasing2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	47 (all P_2 all P_1 all Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(P_2) <-> hBOOL(P_1))) -> (hBOOL(P_2) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) & hBOOL(P_1)))) # label(fact_373_conj__le__cong) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	48 (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_423_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	49 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_128_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	50 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),hAPP(int,int,bit1,pls))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),number_number_of(X_a,Xa)),one_one(X_a))))))) # label(fact_263_le__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	51 (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_481_real__sqrt__gt__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	52 (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_388_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	53 (all Xa all Na (one_one(nat) = hAPP(nat,nat,power_power(nat,Xa),Na) <-> one_one(nat) = Xa | Na = zero_zero(nat))) # label(fact_192_exp__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	54 (all Ma all Na (zero_zero(nat) = Ma & zero_zero(nat) != Na <-> hAPP(nat,nat,power_power(nat,Ma),Na) = zero_zero(nat))) # label(fact_226_nat__power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	55 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_116_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	56 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1))))) # label(fact_308_rel__simps_I15_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	57 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)))))))) # label(fact_299_add__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	58 (all X_a (linorder(X_a) -> (all T_3 exists Z all X_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_eq(X_a),X_1),T_3)))))) # label(fact_449_pinf_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	59 (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,power_power(X_a,A_1),N)))))))) # label(fact_108_one__less__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	60 (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_410_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	61 (all M_1 all N (hAPP(nat,nat,plus_plus(nat,M_1),N) = M_1 -> zero_zero(nat) = N)) # label(fact_152_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	62 (all M_1 M_1 = hAPP(nat,nat,plus_plus(nat,M_1),zero_zero(nat))) # label(fact_154_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	63 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (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_1),B))))))) # label(fact_465_mult__left__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	64 (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_274_zero__le__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	65 (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,power_power(X_a,A_1),N))))))) # label(fact_178_zero__less__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	66 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	67 (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_402_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	68 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | X = Y | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)))) # label(fact_15_zless__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	69 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M hAPP(nat,int,semiring_1_of_nat(int),M) != Z_1))) # label(fact_376_nonneg__eq__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	70 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),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_eq(fun(X_a,X_b)),F),G)))))) # label(fact_447_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	71 (all Z1 all Z2 all Z3 hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3) = hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3))) # label(fact_45_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	72 (all X_a all B_1_1 all B_2 hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,ti(bool,B_2)) = hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2)) # label(tsy_c_hAPP_2_arg2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	73 (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,plus_plus(X_a,A_1),B)),zero_zero(X_a)))))))) # label(fact_302_add__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	74 (all X_b all X_a (order(X_b) & order(X_a) -> (all C 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),hAPP(X_a,X_b,F,B_1))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_454_xt7) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	75 (all X_a (linord581940658strict(X_a) -> (all Xa all Ya (zero_zero(X_a) != ti(X_a,Xa) | zero_zero(X_a) != ti(X_a,Ya) <-> 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,plus_plus(X_a,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya)))))))) # label(fact_477_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	76 (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_242_less__eq__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	77 (all Xa all Ya all P_1 ((hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Xa) = 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),Xa),Ya))) & (-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Ya) = 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),Xa),Ya))))) # label(fact_159_int__if__cong) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	78 (all K_2 all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_360_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	79 (all X_a (linordered_idom(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(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_95_zero__less__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	80 (all Va all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,Va)),number_number_of(nat,V))) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),V)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls))))) # label(fact_371_le__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	81 (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)))) # label(fact_147_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	82 (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,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_462_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	83 (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_390_order__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	84 (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].
1.14/1.46	85 (all X_a all B_1_1 all B_2 ti(fun(X_a,X_a),hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)) = hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)) # label(tsy_c_hAPP_3_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	86 (all Ma all K_2 all Na (Ma = Na <-> hAPP(nat,nat,plus_plus(nat,Na),K_2) = hAPP(nat,nat,plus_plus(nat,Ma),K_2))) # label(fact_125_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	87 (all X_b all X_a (order(X_a) & order(X_b) -> (all C 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),hAPP(X_a,X_b,F,B_1))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_451_xt5) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	88 (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_151_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	89 (all K_2 (pls = hAPP(int,int,bit0,K_2) <-> pls = K_2)) # label(fact_70_rel__simps_I44_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	90 (all X_a (number_semiring(X_a) -> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_1)) -> number_number_of(X_a,hAPP(int,int,succ,V_1)) = hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a)))))) # label(fact_296_semiring__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	91 (all X_a all B_1_1 all B_2 hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2) = ti(fun(X_a,fun(X_a,X_a)),hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2))) # label(tsy_c_hAPP_2_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	92 (all Na (Na != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_144_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	93 (all Va (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls)) <-> number_number_of(nat,Va) = zero_zero(nat))) # label(fact_305_eq__number__of__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	94 (all X_a (linorder(X_a) -> (all Xa all Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> ti(X_a,Xa) = ti(X_a,Ya) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)))))) # label(fact_421_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	95 (all Ma all K_2 all F ((all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M)),hAPP(nat,nat,F,N_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F,Ma)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,plus_plus(nat,Ma),K_2)))))) # label(fact_377_mono__nat__linear__lb) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	96 (all M_1 all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_23_zadd__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	97 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2)) -> (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,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))))))))) # label(fact_110_power__strict__decreasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	98 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_219_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	99 (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,plus_plus(X_a,A_1),B)))))))) # label(fact_298_add__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	100 (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,bit0,K1)),hAPP(int,int,bit0,K2))))) # label(fact_33_less__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	101 (all X_a (number_ring(X_a) -> one_one(X_a) = number_number_of(X_a,hAPP(int,int,bit1,pls)))) # label(fact_12_semiring__norm_I110_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	102 (all K_2 all L_1 (hAPP(int,int,bit1,K_2) = hAPP(int,int,bit1,L_1) <-> K_2 = L_1)) # label(fact_42_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	103 (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,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))) # label(fact_96_power2__less__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	104 (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),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_426_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	105 (all Wa all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,Wa),one_one(int))),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)))) # label(fact_318_add1__zle__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	106 (all X_a (ring_char_0(X_a) & number_ring(X_a) -> (all Xa all Ya (Xa = Ya <-> number_number_of(X_a,Xa) = number_number_of(X_a,Ya))))) # label(fact_40_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	107 (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_52_less__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	108 (all X_a (linordered_semidom(X_a) -> (all M_1 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,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))))) # label(fact_182_power__less__imp__less__exp) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	109 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_215_add__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	110 (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_433_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	111 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (B = C_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C_1))))))) # label(fact_393_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	112 (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),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,plus_plus(X_a,A_2),A_2)),zero_zero(X_a))))))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	113 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	114 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1))))))) # label(fact_409_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	115 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Ya)))))) # label(fact_63_less__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	116 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> 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),Na))))) # label(fact_370_zle__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	117 (all X_a (mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) & power(X_a) -> (all A_2 all Na (hAPP(nat,X_a,power_power(X_a,A_2),Na) = zero_zero(X_a) <-> zero_zero(nat) != Na & ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_184_power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	118 (all X_a (order(X_a) -> (all C_1 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_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_1))))))) # label(fact_394_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	119 (all W_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1))) # label(fact_248_zle__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	120 (all X_a (zero(X_a) -> (all Xa (zero_zero(X_a) = ti(X_a,Xa) <-> ti(X_a,Xa) = zero_zero(X_a))))) # label(fact_196_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	121 (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_441_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	122 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,power_power(X_a,A_1),N) = hAPP(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,A_1) = ti(X_a,B)))))))) # label(fact_321_power__eq__imp__eq__base) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	123 (all K hAPP(int,int,plus_plus(int,K),one_one(int)) = hAPP(int,int,succ,K)) # label(fact_320_succ__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	124 (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,plus_plus(X_a,one_one(X_a)),one_one(X_a)))))) # label(fact_111_zero__less__two) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	125 (all X_a (ordere236663937imp_le(X_a) -> (all C 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,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1))))))) # label(fact_235_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	126 (all K_2 all L_1 (hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1) <-> K_2 = L_1)) # label(fact_43_rel__simps_I48_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	127 (all X_a (semiring_1(X_a) -> (all M_1 all N hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),N) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,power_power(nat,M_1),N))))) # label(fact_171_of__nat__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	128 (all X_a (linordered_semidom(X_a) -> (all X all Y (hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,power_power(X_a,X),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_332_power2__eq__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	129 (all X_a (number_ring(X_a) -> (all V_1 all W_1 number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1)) = hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1))))) # label(fact_89_number__of__add) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	130 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 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,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_240_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	131 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))))) # label(fact_485_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	132 (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,plus_plus(X_a,A_1),one_one(X_a))))))) # label(fact_179_less__add__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	133 (all X_a all B_1_1 all B_2 hAPP(X_a,fun(X_a,X_a),B_1_1,ti(X_a,B_2)) = hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)) # label(tsy_c_hAPP_3_arg2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	134 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))))) # label(fact_213_add__0__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	135 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_472_mult__less__le__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	136 (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,plus_plus(int,X),Y)))))) # label(fact_287_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	137 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_283_less__eq__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	138 (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_415_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	139 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_345_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	140 (all B_1_1 all X_a (power(X_a) -> power_power(X_a,ti(X_a,B_1_1)) = power_power(X_a,B_1_1))) # label(tsy_c_Power_Opower__class_Opower_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	141 (all X_a (linorder(X_a) -> (all Ya all Xa (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) -> (ti(X_a,Ya) = ti(X_a,Xa) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))))))) # label(fact_419_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
1.14/1.46	142 (all X_a (ordere223160158up_add(X_a) -> (all C_1 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_1),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)))))))) # label(fact_220_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	143 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C_1 all D hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	144 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (zero_zero(X_a) = ti(X_a,Ya) & zero_zero(X_a) = ti(X_a,Xa) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))))))) # label(fact_336_sum__power2__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	145 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2)) -> (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,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2)))))))) # label(fact_183_power__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	146 (all P_1 all K_2 all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),I)) -> (hBOOL(hAPP(int,bool,P_1,K_2)) -> ((all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),I_1)) -> (hBOOL(hAPP(int,bool,P_1,I_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I_1),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_382_int__ge__induct) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	147 (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_404_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	148 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),B) = hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1) -> ti(X_a,B) = ti(X_a,C_1))))) # label(fact_198_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	149 (all X_a all X_b (order(X_a) & order(X_b) -> (all C 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)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))))))))) # label(fact_459_order__less__le__subst1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	150 (all X_a (number_ring(X_a) -> (all W_1 hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1)) = number_number_of(X_a,hAPP(int,int,bit0,W_1))))) # label(fact_99_number__of__Bit0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	151 (all I all J all F ((all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_1)),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_384_less__mono__imp__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	152 (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_386_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	153 (all Z_1 all W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),Z_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W_1)))) # label(fact_379_real__le__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	154 (all X_a (monoid_mult(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N)))) # label(fact_165_power__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	155 (all X_a (order(X_a) -> (all Xa all Ya (ti(X_a,Ya) = ti(X_a,Xa) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)))))) # label(fact_399_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	156 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_145_not__less0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	157 (all N all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,plus_plus(nat,M_1),N)))) # label(fact_357_le__add2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	158 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> T_3 != S)) # label(fact_130_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	159 (all X_a (linordered_semiring(X_a) -> (all A_1 all C_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1),B))))))) # label(fact_470_mult__right__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	160 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),number_number_of(X_a,Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Ya)))))) # label(fact_262_le__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	161 (all B_1_1 all X_a (ab_semigroup_add(X_a) -> plus_plus(X_a,ti(X_a,B_1_1)) = plus_plus(X_a,B_1_1))) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	162 (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,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_478_not__sum__squares__lt__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	163 (all X_a (ordere216010020id_add(X_a) -> (all Ya all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ya)) -> (ti(X_a,Xa) = zero_zero(X_a) & ti(X_a,Ya) = zero_zero(X_a) <-> hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya) = zero_zero(X_a))))))) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	164 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_342_le0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	165 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)))) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	166 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))))))) # label(fact_237_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	167 (all B_1_1 all X_a (number(X_a) -> number_number_of(X_a,B_1_1) = ti(X_a,number_number_of(X_a,B_1_1)))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	168 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)))) # label(fact_34_rel__simps_I14_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	169 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_448_le__funI) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	170 (all M_1 all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1))))) # label(fact_131_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	171 (all K_2 all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_126_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	172 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)))) # label(fact_249_zle__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	173 (all P_2 all P_1 all Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(P_2) <-> hBOOL(P_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hBOOL(P_2)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hBOOL(P_1))))) # label(fact_374_imp__le__cong) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	174 (all P_1 ((exists X_1 (hBOOL(hAPP(int,bool,P_1,X_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) <-> (exists X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1)))))) # label(fact_290_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	175 (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_492_mult__neg__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	176 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (exists N_1 K = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_340_zero__le__imp__eq__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	177 (all M_1 all N all K hAPP(nat,nat,plus_plus(nat,M_1),hAPP(nat,nat,plus_plus(nat,N),K)) = hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M_1),N)),K)) # label(fact_123_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	178 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_1 all C (ti(X_a,C) = ti(X_a,B_1) <-> hAPP(X_a,X_a,plus_plus(X_a,A_2),C) = hAPP(X_a,X_a,plus_plus(X_a,A_2),B_1))))) # label(fact_202_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	179 (all A_1 all B hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),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),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_463_zadd__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	180 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K_2))))) # label(fact_281_rel__simps_I22_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	181 (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,plus_plus(X_a,A_2),A_2))))))) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	182 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)))) # label(fact_484_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	183 (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_403_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	184 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)))) # label(fact_53_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	185 (all X_a (linord20386208strict(X_a) -> (all A_1 all C_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1),B))))))) # label(fact_469_mult__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	186 (all X_a (number_ring(X_a) -> number_number_of(X_a,pls) = zero_zero(X_a))) # label(fact_83_semiring__norm_I112_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	187 (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,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),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_334_power2__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	188 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_214_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	189 (all K all L hAPP(int,int,bit0,K) != hAPP(int,int,bit1,L)) # label(fact_69_rel__simps_I49_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	190 (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,power_power(int,X),N))))) # label(fact_293_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	191 (all X_a (order(X_a) -> (all C_1 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_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1))))))) # label(fact_406_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	192 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_2 all C (ti(X_a,C) = ti(X_a,B_1) <-> hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2) = hAPP(X_a,X_a,plus_plus(X_a,C),A_2))))) # label(fact_201_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	193 (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_493_mult__neg__pos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	194 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))))) # label(fact_58_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	195 (all X_a all B_1_1 all B_2 all X_b (ord(X_b) -> hAPP(X_a,X_b,ti(fun(X_a,X_b),B_1_1),B_2) = hAPP(X_a,X_b,B_1_1,B_2))) # label(tsy_c_hAPP_0_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	196 (all K all L all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L)))))) # label(fact_134_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	197 (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_495_zero__less__mult__pos2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	198 (all K all L hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),L)) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) # label(fact_77_add__Bit0__Bit0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	199 (all X_a (order(X_a) -> (all C_1 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_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_1))))))) # label(fact_392_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	200 (all B_1_1 all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,X_a),plus_plus(X_a,B_1_1)) = plus_plus(X_a,B_1_1))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	201 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),hAPP(int,int,bit1,pls))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),one_one(X_a))))))) # label(fact_62_less__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	202 (all K all L all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L)))))) # label(fact_364_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	203 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_471_mult__le__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	204 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),pls)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),number_number_of(X_a,Xa)),zero_zero(X_a))))))) # label(fact_258_le__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	205 (all X_a (linordered_semidom(X_a) -> (all Xa all Ya 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_eq(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Xa),Ya))))))) # label(fact_260_power__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	206 (all L_1 (pls = L_1 <-> pls = hAPP(int,int,bit0,L_1))) # label(fact_71_rel__simps_I38_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	207 (all X_a (number_semiring(X_a) -> hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a)) = number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_9_semiring__one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	208 (all X_a (number_ring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_82_number__of__Pls) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	209 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,power_power(X_a,X),one_one(nat)) = ti(X_a,X)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	210 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) & Ma != Na)) # label(fact_349_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	211 (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_435_leD) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	212 (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,bit1,K2))))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	213 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))))) # label(fact_156_power__one__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	214 (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 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_450_dense__le__bounded) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	215 (all Va all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V)))) # label(fact_150_less__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	216 (all B_1_1 all X_a (monoid_add(X_a) -> plus_plus(X_a,ti(X_a,B_1_1)) = plus_plus(X_a,B_1_1))) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	217 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C 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,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C))))))) # label(fact_234_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	218 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_434_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	219 (all B_1_1 (hBOOL(B_1_1) <-> hBOOL(ti(bool,B_1_1)))) # label(tsy_c_hBOOL_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	220 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K_2)),number_number_of(int,L_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)))) # label(fact_16_less__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	221 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,K_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K_2)))) # label(fact_284_rel__simps_I21_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	222 (all X_a all X_b (order(X_a) & order(X_b) -> (all F all C 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)) -> ((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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> 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)))))))) # label(fact_455_order__less__le__subst2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	223 (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_385_order__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	224 (all X_a (ordere236663937imp_le(X_a) -> (all C 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,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1))))))) # label(fact_223_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	225 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),B)))) # label(fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	226 (all K hAPP(int,int,bit0,K) = hAPP(int,int,plus_plus(int,K),K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	227 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)))))) # label(fact_18_less__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	228 (all X_a (linordered_semidom(X_a) -> (all M_1 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,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N))))))) # label(fact_261_power__le__imp__le__exp) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	229 (all X_a all B_1_1 all B_2 all X_b (ord(X_b) -> hAPP(X_a,X_b,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_b,B_1_1,B_2))) # label(tsy_c_hAPP_0_arg2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	230 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) -> (ti(X_a,Ya) = ti(X_a,Xa) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))))))) # label(fact_437_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.47	231 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_114_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	232 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_162_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	233 (all X_a (linordered_semiring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	234 (all Na all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,Na)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),Na)) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,plus_plus(nat,K_1),one_one(nat)))) & (all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_1))))))))) # label(fact_375_ex__least__nat__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	235 (all X_a (semiring_1(X_a) -> zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_4_zero__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	236 (all K all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K))))) # label(fact_133_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	237 (all Na (hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) <-> zero_zero(nat) = Na)) # label(fact_27_int__eq__0__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	238 (all Ma all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_149_zless__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	239 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_347_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	240 (all X_a (linorder(X_a) -> (all Xa all Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) -> (ti(X_a,Xa) = ti(X_a,Ya) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya))))))) # label(fact_432_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	241 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> Ma != Na)) # label(fact_120_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	242 (all X_a (number_semiring(X_a) -> (all V_2 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_2)) -> number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),V_2)) = hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,V_2))))))) # label(fact_322_semiring__add__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	243 (all X_a (number_ring(X_a) -> (all W_1 hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1)) = number_number_of(X_a,hAPP(int,int,bit1,W_1))))) # label(fact_100_number__of__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	244 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_65_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	245 (all M_1 all N hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N))) # label(fact_20_zpower__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	246 (all X_b all X_a (order(X_a) & order(X_b) -> (all C 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),B_1)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)))))))) # label(fact_460_xt4) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	247 (all X_a (number_ring(X_a) -> (all V_1 hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a)) = number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),hAPP(int,int,bit1,pls)))))) # label(fact_7_add__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	248 (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_414_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	249 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C 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),B_1)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)))))))) # label(fact_457_xt6) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	250 (all Xa all Ya (Ya != Xa & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)))) # label(fact_356_real__less__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	251 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_138_gr0I) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	252 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)))) # label(fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	253 (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,plus_plus(X_a,A_1),B)))))))) # label(fact_228_add__pos__pos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	254 (all X_a (number_semiring(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = number_number_of(X_a,hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_94_number__of__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	255 (all X_a (semiring_1(X_a) -> (all M_1 all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,plus_plus(nat,M_1),N)) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_169_of__nat__add) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	256 (all X_a (number_ring(X_a) -> (all W_1 number_number_of(X_a,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),W_1)) = hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))))) # label(fact_6_add__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	257 (all M_1 all N hAPP(nat,nat,plus_plus(nat,M_1),N) = hAPP(nat,nat,plus_plus(nat,N),M_1)) # label(fact_121_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	258 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))))))) # label(fact_236_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	259 (all K all L hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L))) # label(fact_90_add__Bit1__Bit0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	260 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)))) # label(fact_486_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	261 (all K -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))) # label(fact_61_int__less__0__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	262 (all X_a (semiri456707255roduct(X_a) -> (all B_1 all A_2 (ti(X_a,B_1) = hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_210_add__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	263 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & K = hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_190_zero__less__imp__eq__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	264 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_224_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	265 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all Wa (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa)) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a) & number_number_of(nat,Wa) != zero_zero(nat))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	266 (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_436_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	267 (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,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_330_zero__le__power2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	268 (all Va (zero_zero(nat) = number_number_of(nat,Va) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls)))) # label(fact_304_eq__0__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	269 (all X_a all X_b (ord(X_b) -> (all Xa 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,Xa)),hAPP(X_a,X_b,G,Xa))))))) # label(fact_397_le__funD) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	270 (all X_a (number_semiring(X_a) -> one_one(X_a) = number_number_of(X_a,hAPP(int,int,bit1,pls)))) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	271 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	272 (all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_329_power2__ge__self) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	273 (all X_a (number_semiring(X_a) -> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_1)) -> number_number_of(X_a,hAPP(int,int,succ,V_1)) = hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,V_1)))))) # label(fact_295_semiring__1__add__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	274 (all X_a (linordered_semidom(X_a) -> (all M_1 all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_168_of__nat__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	275 (all X_a (linordered_semidom(X_a) -> (all Xa all Ya 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(nat),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))))))) # label(fact_181_power__strict__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	276 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_372_two__realpow__ge__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	277 (all K all L hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L)) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))) # label(fact_91_add__Bit0__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	278 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))))) # label(fact_85_add__numeral__0__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	279 (all Wa all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int)))))) # label(fact_317_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	280 (all M_1 all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)))) # label(fact_365_add__leD2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	281 (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,plus_plus(X_a,A_1),B)),zero_zero(X_a)))))))) # label(fact_227_add__neg__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	282 (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_444_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	283 (all I_2 all J_2 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K)))) # label(fact_136_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	284 (all X_a (linord581940658strict(X_a) -> (all C_1 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_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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_487_mult__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	285 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K_2)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)))) # label(fact_307_rel__simps_I29_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	286 (all B_1_1 all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,X_a),plus_plus(X_a,B_1_1)) = plus_plus(X_a,B_1_1))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	287 (all L hAPP(int,int,bit1,L) != pls) # label(fact_67_rel__simps_I39_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	288 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_391_order__antisym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	289 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K_2)),pls)))) # label(fact_285_rel__simps_I27_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	290 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (ti(X_a,Xa) != zero_zero(X_a) | zero_zero(X_a) != ti(X_a,Ya) <-> 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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	291 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (C_1 = B -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1))))))) # label(fact_407_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	292 (all K all L hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),hAPP(int,int,succ,L))) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) # label(fact_326_add__Bit1__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	293 (all X_a (linordered_semidom(X_a) -> (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> 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),Na))))))) # label(fact_253_of__nat__le__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	294 (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,bit0,K2))))) # label(fact_245_less__eq__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	295 (all X_a (preorder(X_a) -> (all P_1 all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) -> hBOOL(P_1)))))) # label(fact_412_order__less__imp__triv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	296 (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,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N))))))))) # label(fact_327_power__strict__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	297 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 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,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_218_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	298 (all X_a (order(X_a) -> (all C_1 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_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1))))))) # label(fact_408_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	299 (all K all L hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),L))),L) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K)),L)) # label(fact_464_mult__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	300 (all X_a (semiring_char_0(X_a) -> (all Ma all Na (hAPP(nat,X_a,semiring_1_of_nat(X_a),Na) = hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma) <-> Na = Ma)))) # label(fact_157_of__nat__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	301 (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,power_power(X_a,A_1),N)),hAPP(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_303_power__less__imp__less__base) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	302 (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_176_not__one__less__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	303 (all V_2 all V_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2)) = number_number_of(nat,V_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> number_number_of(nat,hAPP(int,int,plus_plus(int,V_1),V_2)) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2)) = number_number_of(nat,V_2)))) # label(fact_36_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	304 (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_430_leI) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	305 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,K_2)),number_number_of(int,L_1))))) # label(fact_256_less__eq__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	306 (all K hAPP(int,int,succ,hAPP(int,int,bit0,K)) = hAPP(int,int,bit1,K)) # label(fact_315_succ__Bit0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	307 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)))))) # label(fact_49_less__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	308 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_490_mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	309 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1),B))))))) # label(fact_467_mult__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	310 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))))))) # label(fact_221_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	311 (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].
1.14/1.48	312 (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),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_400_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	313 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))))) # label(fact_211_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	314 (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_413_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	315 (all Z_1 all W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),Z_1)) -> Z_1 = W_1))) # label(fact_381_real__le__antisym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	316 (all X_a (preorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)))))) # label(fact_428_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	317 (all Na (zero_zero(nat) = Na <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))))) # label(fact_313_int__le__0__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	318 (all X_a all X_b (order(X_a) & order(X_b) -> (all F all C 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)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C)))))))) # label(fact_458_order__le__less__subst2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	319 (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(X_a),Y),X)) | ti(X_a,Y) = ti(X_a,X))))) # label(fact_420_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	320 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a))) # label(fact_187_of__nat__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	321 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C_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,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_239_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	322 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) | 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)),hAPP(nat,nat,plus_plus(nat,Ma),Na))))) # label(fact_143_add__gr__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	323 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_446_dense__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	324 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	325 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all 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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),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_476_mult__le__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	326 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_425_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	327 (all X all Y hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X),Y))) # label(fact_173_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	328 (all X_a (preorder(X_a) -> (all X all Y (Y = X -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_398_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	329 (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_418_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	330 (all X_a (ordere223160158up_add(X_a) -> (all C_1 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_1),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)))))))) # label(fact_271_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	331 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)))) # label(fact_217_add__0__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	332 (all Ma all Na (Na = Ma | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_348_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	333 (all X_a all B_1_1 all B_2 hAPP(X_a,fun(X_a,X_a),ti(fun(X_a,fun(X_a,X_a)),B_1_1),B_2) = hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)) # label(tsy_c_hAPP_3_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	334 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)))) # label(fact_246_rel__simps_I31_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	335 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_474_mult__strict__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	336 (all X_a (ordere223160158up_add(X_a) -> (all C_1 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_1),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)))))))) # label(fact_272_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	337 (all X_a (linord581940658strict(X_a) -> (all C_1 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_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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_488_mult__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	338 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	339 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_127_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	340 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))))) # label(fact_483_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	341 (all K all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K))))) # label(fact_363_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	342 (all X_a (linord20386208strict(X_a) -> (all C_1 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_1),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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_473_mult__strict__mono_H) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	343 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_350_le__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	344 (all Ma all Na (hAPP(nat,nat,plus_plus(nat,Ma),Na) = zero_zero(nat) <-> zero_zero(nat) = Na & Ma = zero_zero(nat))) # label(fact_153_add__is__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	345 (all B_1_1 all B_2 all X_a (power(X_a) -> hAPP(nat,X_a,B_1_1,ti(nat,B_2)) = hAPP(nat,X_a,B_1_1,B_2))) # label(tsy_c_hAPP_1_arg2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.48	346 (all M_1 all N all K all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) -> (hAPP(nat,nat,plus_plus(nat,M_1),L) = hAPP(nat,nat,plus_plus(nat,K),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))) # label(fact_135_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	347 (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 (A_1 = hAPP(nat,real,power_power(real,R),N) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R))))))) # label(fact_230_realpow__pos__nth) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	348 (all Xa all Ya (Ya = zero_zero(real) & zero_zero(real) = Xa <-> zero_zero(real) = hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_106_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	349 (all X_a all B_1_1 all B_2 ti(X_a,hAPP(X_a,X_a,B_1_1,B_2)) = hAPP(X_a,X_a,B_1_1,B_2)) # label(tsy_c_hAPP_4_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	350 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> zero_zero(real) != hAPP(real,real,sqrt,X))) # label(fact_482_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	351 (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_311_less__eq__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	352 (all X_a (linorder(X_a) -> (all Xa all Ya (ti(X_a,Ya) != ti(X_a,Xa) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)))))) # label(fact_422_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	353 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C_1))))))) # label(fact_395_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	354 (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,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_44_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	355 (all J_2 all I_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_2),I_2)),I_2))) # label(fact_118_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	356 (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_442_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	357 (all X_a (number_ring(X_a) -> (all V_1 all W_1 number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1)) = hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1))))) # label(fact_88_add__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	358 (all M_1 all N all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_2),M_1)),hAPP(nat,nat,power_power(nat,I_2),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))) # label(fact_140_nat__power__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	359 (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,power_power(X_a,A_1),N))))))) # label(fact_278_one__le__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	360 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na))))) # label(fact_161_zero__less__int__conv) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	361 (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_177_zero__less__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	362 (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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))) # label(fact_98_not__sum__power2__lt__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	363 (all B_1_1 all X_a (power(X_a) -> power_power(X_a,B_1_1) = ti(fun(nat,X_a),power_power(X_a,B_1_1)))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	364 (all X_a (number_semiring(X_a) -> number_number_of(X_a,pls) = zero_zero(X_a))) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	365 (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,plus_plus(X_a,A_1),B)))))))) # label(fact_297_add__pos__nonneg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	366 (all X_a (ordere779506340up_add(X_a) -> (all C_1 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_1),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)))))))) # label(fact_238_add__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	367 (all Na all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,Na)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),Na)) & (all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_1)))) & hBOOL(hAPP(nat,bool,P_1,K_1))))))) # label(fact_383_ex__least__nat__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	368 (all Ma all Na (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(nat,int,semiring_1_of_nat(int),Na) <-> Na = Ma)) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	369 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C (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_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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))))))) # label(fact_475_mult__le__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	370 (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_411_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	371 (all Z_3 all Z_1 all W_2 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_3),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W_1),Z_1)))))) # label(fact_288_zadd__zless__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	372 (all K all I_2 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_2),K)),hAPP(int,int,plus_plus(int,J_2),K))))) # label(fact_35_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	373 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),pls)))) # label(fact_51_rel__simps_I12_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	374 (all X_a (linorder(X_a) & number(X_a) -> (all Va all Wa (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),number_number_of(X_a,Va)),number_number_of(X_a,Wa))))))) # label(fact_275_le__number__of__eq__not__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	375 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))))) # label(fact_204_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	376 (all X_a (linordered_semidom(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)))))))) # label(fact_175_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	377 (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].
1.14/1.49	378 (all M_1 all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_366_add__leD1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	379 (all K K = hAPP(int,int,plus_plus(int,K),pls)) # label(fact_75_add__Pls__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	380 (all X_a (linorder(X_a) -> (all T_3 exists Z all X_1 (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_eq(X_a),T_3),X_1)))))) # label(fact_456_minf_I8_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	381 (all X_a (number_ring(X_a) -> (all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,V_1))) -> number_number_of(X_a,V_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,V_1))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1)) = zero_zero(X_a)))))) # label(fact_333_of__nat__number__of__lemma) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	382 (all M_1 all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2))))) # label(fact_362_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	383 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_343_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	384 (all M_1 all N all Z_1 hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N))),Z_1) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1))) # label(fact_22_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	385 (all B_1_1 all X_a (cancel_semigroup_add(X_a) -> plus_plus(X_a,ti(X_a,B_1_1)) = plus_plus(X_a,B_1_1))) # label(tsy_c_Groups_Oplus__class_Oplus_2_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	386 (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,plus_plus(X_a,A_1),B)))))))) # label(fact_266_add__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	387 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),number_number_of(X_a,Ya))))))) # label(fact_257_le__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	388 (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)),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,plus_plus(X_a,A_2),A_2))))))) # label(fact_194_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	389 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_2)) -> (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,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))))))))) # label(fact_259_power__decreasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	390 (all K hAPP(int,int,plus_plus(int,pls),K) = K) # label(fact_76_add__Pls) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	391 (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,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N)))))))) # label(fact_277_power__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	392 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> -(all N_1 hAPP(nat,int,semiring_1_of_nat(int),N_1) != K))) # label(fact_341_nonneg__int__cases) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	393 (all X_a all B_1_1 all B_2 hAPP(X_a,X_a,B_1_1,B_2) = hAPP(X_a,X_a,B_1_1,ti(X_a,B_2))) # label(tsy_c_hAPP_4_arg2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	394 (all X_a (number_ring(X_a) -> one_one(X_a) = number_number_of(X_a,hAPP(int,int,bit1,pls)))) # label(fact_13_numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	395 (all Xa all Ya (Ya = Xa <-> hAPP(nat,int,semiring_1_of_nat(int),Ya) = hAPP(nat,int,semiring_1_of_nat(int),Xa))) # label(fact_158_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	396 (all K all I_2 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_2),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K))))) # label(fact_250_zle__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	397 (all W_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_1)))) # label(fact_319_zless__imp__add1__zle) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	398 (all M_1 all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N)) = hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N)) # label(fact_21_int__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	399 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))))) # label(fact_56_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	400 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_351_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	401 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a)) = number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_8_one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	402 (all K all L hAPP(int,int,bit1,K) != hAPP(int,int,bit0,L)) # label(fact_68_rel__simps_I50_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	403 (all X_a (linordered_semidom(X_a) -> (all Na (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))))) # label(fact_107_of__nat__0__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	404 (all X all Y all Z_1 hAPP(nat,nat,plus_plus(nat,X),hAPP(nat,nat,plus_plus(nat,Y),Z_1)) = hAPP(nat,nat,plus_plus(nat,Y),hAPP(nat,nat,plus_plus(nat,X),Z_1))) # label(fact_122_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	405 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> N != zero_zero(nat))) # label(fact_139_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	406 (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,power_power(X_a,A_1),N)))))))) # label(fact_480_power__gt1__lemma) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	407 (all M_1 all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2))))) # label(fact_132_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	408 (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,plus_plus(real,Z_1),X)),hAPP(real,real,plus_plus(real,Z_1),Y))))) # label(fact_368_real__add__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	409 (all X_a (number_ring(X_a) -> (all V_1 all W_1 all Z_1 hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W_1)),Z_1)) = hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))),Z_1)))) # label(fact_87_add__number__of__left) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	410 (all X_a (semiring_0(X_a) & power(X_a) -> (all W_1 ((zero_zero(nat) = number_number_of(nat,W_1) -> one_one(X_a) = hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))) & (zero_zero(nat) != number_number_of(nat,W_1) -> zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))))))) # label(fact_11_power__0__left__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	411 (all K all I_2 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,K),I_2)),hAPP(int,int,plus_plus(int,K),J_2))))) # label(fact_255_zadd__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	412 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_163_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	413 (all V_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> number_number_of(nat,hAPP(int,int,succ,V_1)) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> one_one(nat) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))))) # label(fact_232_nat__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	414 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_440_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	415 (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_438_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	416 (all X_a (linordered_semidom(X_a) -> (all M_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),zero_zero(X_a)))))) # label(fact_185_of__nat__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	417 (all K hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K)),K) = hAPP(int,int,bit1,K)) # label(fact_92_Bit1__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	418 (all V_1 all W_1 hAPP(int,int,plus_plus(int,number_number_of(int,V_1)),number_number_of(int,W_1)) = number_number_of(int,hAPP(int,int,plus_plus(int,V_1),W_1))) # label(fact_17_plus__numeral__code_I9_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	419 (all M_1 all K all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))))) # label(fact_367_add__leE) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	420 (all K K = number_number_of(int,K)) # label(fact_119_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	421 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K_2)))) # label(fact_306_rel__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	422 (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].
1.14/1.49	423 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1))))) # label(fact_282_rel__simps_I32_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	424 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K_2))))) # label(fact_55_rel__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	425 (all X_a (linorder(X_a) -> (all T_3 exists Z all X_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_eq(X_a),T_3),X_1)))))) # label(fact_453_pinf_I8_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	426 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	427 (all B_1_1 all X_a (monoid_add(X_a) -> plus_plus(X_a,B_1_1) = ti(fun(X_a,X_a),plus_plus(X_a,B_1_1)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	428 (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,Y) = ti(X_a,X)))))) # label(fact_389_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	429 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 all D hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D)) = hAPP(X_a,X_a,plus_plus(X_a,C_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),D))))) # label(fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	430 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M_1)) -> M_1 = N))) # label(fact_354_le__antisym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	431 (all Z_1 all W_1 hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1)) # label(fact_47_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	432 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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),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,plus_plus(X_a,A_1),C_1)))))))) # label(fact_269_add__increasing2) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	433 (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,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,power_power(X_a,A_1),N)))))))) # label(fact_479_power__less__power__Suc) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	434 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)))))))) # label(fact_268_add__increasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	435 (all Z_1 Z_1 = hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))) # label(fact_79_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	436 (all X_a (linordered_semidom(X_a) -> (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> 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),Na))))))) # label(fact_166_of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	437 (all X_a (linorder(X_a) -> (all T_3 exists Z all X_1 (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_eq(X_a),X_1),T_3)))))) # label(fact_452_minf_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	438 (all X_a (order(X_a) -> (all Xa all Ya (ti(X_a,Ya) = ti(X_a,Xa) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_429_order__le__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	439 (all Z_1 zero_zero(int) != hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)) # label(fact_93_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	440 (all W_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),W_1))) # label(fact_378_real__le__refl) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	441 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_491_mult__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	442 (all X_a (linord893533164strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_489_comm__mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	443 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))))))) # label(fact_401_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	444 (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,plus_plus(X_a,A_1),B)),zero_zero(X_a)))))))) # label(fact_270_add__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	445 (all K all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K))))) # label(fact_353_le__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	446 (all N N = hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N)) # label(fact_155_plus__nat_Oadd__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	447 (all Xa all Wa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa)))) <-> zero_zero(nat) = number_number_of(nat,Wa) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)))) # label(fact_148_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	448 (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),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> one_one(int) = X | zero_zero(int) = X))) # label(fact_337_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	449 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na))) <-> Na = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)))) # label(fact_146_zero__less__power__nat__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	450 (all K hAPP(int,int,bit1,K) != pls) # label(fact_66_rel__simps_I46_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	451 (all Wa all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)) | Z_2 = Wa)) # label(fact_60_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	452 (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_417_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	453 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C_1 (hAPP(X_a,X_a,plus_plus(X_a,B),A_1) = hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1) -> ti(X_a,C_1) = ti(X_a,B))))) # label(fact_197_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	454 (all X_a all X_b (order(X_b) & order(X_a) -> (all C 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)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))))))))) # label(fact_461_order__le__less__subst1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	455 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)))) # label(fact_54_rel__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	456 (all X all N hAPP(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,power_power(nat,X),N))) # label(fact_174_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	457 (all Z_1 Z_1 = hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)) # label(fact_80_zadd__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	458 (all K_2 all L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1))))) # label(fact_310_rel__simps_I33_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	459 (all X_a all B_1_1 all B_2 hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2) = hAPP(bool,fun(X_a,fun(X_a,X_a)),ti(fun(bool,fun(X_a,fun(X_a,X_a))),B_1_1),B_2)) # label(tsy_c_hAPP_2_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	460 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_141_less__nat__zero__code) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	461 (all B_1_1 all B_2 all X_a (power(X_a) -> hAPP(nat,X_a,B_1_1,B_2) = hAPP(nat,X_a,ti(fun(nat,X_a),B_1_1),B_2))) # label(tsy_c_hAPP_1_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	462 (all Z_2 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa)) & Z_2 != Wa <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)))) # label(fact_254_zless__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	463 (all Ma all Na ((exists K_1 Na = hAPP(nat,nat,plus_plus(nat,Ma),K_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_359_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	464 (all X_a (number(X_a) -> (all Wa all Xa (number_number_of(X_a,Wa) = ti(X_a,Xa) <-> ti(X_a,Xa) = number_number_of(X_a,Wa))))) # label(fact_41_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	465 (all X all Y all Z_1 hAPP(int,int,plus_plus(int,Y),hAPP(int,int,plus_plus(int,X),Z_1)) = hAPP(int,int,plus_plus(int,X),hAPP(int,int,plus_plus(int,Y),Z_1))) # label(fact_46_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	466 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) | Ya = Xa)) # label(fact_355_less__eq__real__def) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	467 (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_416_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	468 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na))) <-> Na = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)))) # label(fact_142_nat__zero__less__power__iff) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	469 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_2)) -> (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,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2)))))))) # label(fact_241_power__increasing) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	470 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))))) # label(fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	471 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat)) = one_one(X_a)))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	472 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Xa),Ya)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))))) # label(fact_369_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.49	473 (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_443_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	474 (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,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_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	475 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C (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),B_1),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),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))))))) # label(fact_494_mult__less__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	476 (all V_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1)) = number_number_of(nat,hAPP(int,int,succ,V_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1)) = one_one(nat)))) # label(fact_233_nat__1__add__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	477 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,N)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,N)))))) # label(fact_338_number__of1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	478 (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_405_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	479 (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_170_of__nat__1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	480 (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_439_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	481 (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,plus_plus(X_a,A_1),B)),zero_zero(X_a)))))))) # label(fact_301_add__neg__nonpos) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	482 (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_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) & (all Y_1 (A_1 = hAPP(nat,real,power_power(real,Y_1),N) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> X_1 = Y_1)) & hAPP(nat,real,power_power(real,X_1),N) = A_1))))) # label(fact_229_realpow__pos__nth__unique) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	483 (all M_1 all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1))))) # label(fact_361_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	484 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 all D hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D)) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),D)))) # label(fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	485 (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_292_zero__zle__int) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	486 (all X_a all B_1_1 all B_2 hAPP(X_a,X_a,B_1_1,B_2) = hAPP(X_a,X_a,ti(fun(X_a,X_a),B_1_1),B_2)) # label(tsy_c_hAPP_4_arg1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	487 (all N all M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,plus_plus(nat,N),M_1)))) # label(fact_358_le__add1) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	488 (all X_a (order(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> ti(X_a,Xa) != ti(X_a,Ya) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_427_order__less__le) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	489 (all X_a (linordered_semiring(X_a) -> (all C_1 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1),B))))))) # label(fact_468_mult__left__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	490 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)) = hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)))) # label(fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	491 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1) = ti(X_a,A_1)))) # label(fact_84_add__numeral__0) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	492 (all X hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_10_quartic__square__square) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	493 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya))))))) # label(fact_252_le__number__of) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	494 (all X_a all X_b (ord(X_b) -> (all Xa 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,Xa)),hAPP(X_a,X_b,G,Xa))))))) # label(fact_387_le__funE) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	495 (all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z_2)))) # label(fact_312_int__one__le__iff__zero__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	496 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> (N != M_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))) # label(fact_346_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	497 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),B) = hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1) -> ti(X_a,C_1) = ti(X_a,B))))) # label(fact_199_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	498 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	499 (all X_a (linordered_semidom(X_a) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))))) # label(fact_167_less__imp__of__nat__less) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	500 (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,power_power(X_a,A_1),N))))))) # label(fact_276_zero__le__power) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	501 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	502 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))) <-> zero_zero(nat) = Na)) # label(fact_344_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	503 (all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> (exists K_1 (J_2 = hAPP(nat,nat,plus_plus(nat,I_2),K_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)))))) # label(fact_191_less__imp__add__positive) # label(axiom) # label(non_clause).  [assumption].
1.14/1.50	504 -(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
1.14/1.50	
1.14/1.50	============================== end of process non-clausal formulas ===
1.14/1.50	
1.14/1.50	============================== PROCESS INITIAL CLAUSES ===============
1.14/1.50	
1.14/1.50	============================== PREDICATE ELIMINATION =================
1.14/1.50	505 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.14/1.50	506 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_331_power2__le__imp__le) # label(axiom).  [clausify(2)].
1.14/1.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,power_power(nat,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(505,a,506,a)].
1.14/1.50	507 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_279_zero__le__imp__of__nat) # label(axiom).  [clausify(7)].
1.14/1.50	508 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_273_not__one__le__zero) # label(axiom).  [clausify(14)].
1.14/1.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))).  [resolve(508,a,505,a)].
1.14/1.50	509 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C != D | hAPP(nat,A,power_power(A,B),C) = hAPP(nat,A,power_power(A,B),D) # label(fact_180_power__inject__exp) # label(axiom).  [clausify(28)].
1.14/1.50	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B != C | hAPP(nat,nat,power_power(nat,A),B) = hAPP(nat,nat,power_power(nat,A),C).  [resolve(509,a,505,a)].
1.14/1.50	510 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C = D | hAPP(nat,A,power_power(A,B),C) != hAPP(nat,A,power_power(A,B),D) # label(fact_180_power__inject__exp) # label(axiom).  [clausify(28)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B = C | hAPP(nat,nat,power_power(nat,A),B) != hAPP(nat,nat,power_power(nat,A),C).  [resolve(510,a,505,a)].
1.14/1.51	511 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_280_of__nat__0__le__iff) # label(axiom).  [clausify(39)].
1.14/1.51	512 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))) # label(fact_108_one__less__power) # label(axiom).  [clausify(59)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,power_power(nat,A),B))).  [resolve(512,a,505,a)].
1.14/1.51	513 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_274_zero__le__one) # label(axiom).  [clausify(64)].
1.14/1.51	514 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))) # label(fact_178_zero__less__power) # label(axiom).  [clausify(65)].
1.14/1.51	515 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))) # label(fact_110_power__strict__decreasing) # label(axiom).  [clausify(97)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,C),B)),hAPP(nat,nat,power_power(nat,C),A))).  [resolve(515,a,505,a)].
1.14/1.51	516 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_182_power__less__imp__less__exp) # label(axiom).  [clausify(108)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(516,a,505,a)].
1.14/1.51	517 -linordered_semidom(A) | hAPP(nat,A,power_power(A,B),C) != hAPP(nat,A,power_power(A,D),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_321_power__eq__imp__eq__base) # label(axiom).  [clausify(122)].
1.14/1.51	Derived: hAPP(nat,nat,power_power(nat,A),B) != hAPP(nat,nat,power_power(nat,C),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C).  [resolve(517,a,505,a)].
1.14/1.51	518 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,one_one(A)),one_one(A)))) # label(fact_111_zero__less__two) # label(axiom).  [clausify(124)].
1.14/1.51	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))).  [resolve(518,a,505,a)].
1.14/1.51	519 -linordered_semidom(A) | hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = ti(A,C) # label(fact_332_power2__eq__imp__eq) # label(axiom).  [clausify(128)].
1.14/1.51	Derived: hAPP(nat,nat,power_power(nat,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,nat,power_power(nat,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | ti(nat,A) = ti(nat,B).  [resolve(519,a,505,a)].
1.14/1.51	520 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,plus_plus(A,B),one_one(A)))) # label(fact_179_less__add__one) # label(axiom).  [clausify(132)].
1.14/1.51	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,plus_plus(nat,A),one_one(nat)))).  [resolve(520,a,505,a)].
1.14/1.51	521 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))) # label(fact_183_power__strict__increasing) # label(axiom).  [clausify(145)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,C),A)),hAPP(nat,nat,power_power(nat,C),B))).  [resolve(521,a,505,a)].
1.14/1.51	522 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_334_power2__less__imp__less) # label(axiom).  [clausify(187)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,power_power(nat,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(522,a,505,a)].
1.14/1.51	523 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_260_power__increasing__iff) # label(axiom).  [clausify(205)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(523,a,505,a)].
1.14/1.51	524 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_260_power__increasing__iff) # label(axiom).  [clausify(205)].
1.14/1.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(524,a,505,a)].
1.14/1.52	525 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_261_power__le__imp__le__exp) # label(axiom).  [clausify(228)].
1.14/1.52	526 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_168_of__nat__less__imp__less) # label(axiom).  [clausify(274)].
1.14/1.52	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(526,a,505,a)].
1.14/1.52	527 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) # label(fact_181_power__strict__increasing__iff) # label(axiom).  [clausify(275)].
1.14/1.52	528 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D))) # label(fact_181_power__strict__increasing__iff) # label(axiom).  [clausify(275)].
1.14/1.52	529 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_253_of__nat__le__iff) # label(axiom).  [clausify(293)].
1.14/1.52	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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(529,a,505,a)].
1.14/1.52	530 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_253_of__nat__le__iff) # label(axiom).  [clausify(293)].
1.14/1.52	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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(530,a,505,a)].
1.14/1.52	531 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))) # label(fact_327_power__strict__mono) # label(axiom).  [clausify(296)].
1.14/1.52	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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,power_power(nat,A),C)),hAPP(nat,nat,power_power(nat,B),C))).  [resolve(531,a,505,a)].
1.14/1.52	532 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_303_power__less__imp__less__base) # label(axiom).  [clausify(301)].
1.14/1.53	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(532,a,505,a)].
1.14/1.53	533 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_176_not__one__less__zero) # label(axiom).  [clausify(302)].
1.14/1.53	534 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))) # label(fact_278_one__le__power) # label(axiom).  [clausify(359)].
1.14/1.53	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,power_power(nat,A),B))).  [resolve(534,a,505,a)].
1.14/1.53	535 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_177_zero__less__one) # label(axiom).  [clausify(361)].
1.14/1.53	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))).  [resolve(535,a,505,a)].
1.14/1.53	536 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,plus_plus(A,B),D))) # label(fact_175_pos__add__strict) # label(axiom).  [clausify(376)].
1.14/1.53	537 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))) # label(fact_259_power__decreasing) # label(axiom).  [clausify(389)].
1.14/1.53	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,C),B)),hAPP(nat,nat,power_power(nat,C),A))).  [resolve(537,a,505,a)].
1.14/1.53	538 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))) # label(fact_277_power__mono) # label(axiom).  [clausify(391)].
1.14/1.53	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,A),C)),hAPP(nat,nat,power_power(nat,B),C))).  [resolve(538,a,505,a)].
1.14/1.53	539 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_107_of__nat__0__less__iff) # label(axiom).  [clausify(403)].
1.14/1.53	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(539,a,505,a)].
1.14/1.53	540 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_107_of__nat__0__less__iff) # label(axiom).  [clausify(403)].
1.14/1.53	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(540,a,505,a)].
1.14/1.54	541 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,power_power(A,B),C)))) # label(fact_480_power__gt1__lemma) # label(axiom).  [clausify(406)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,power_power(nat,A),B)))).  [resolve(541,a,505,a)].
1.14/1.54	542 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),zero_zero(A))) # label(fact_185_of__nat__less__0__iff) # label(axiom).  [clausify(416)].
1.14/1.54	543 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,power_power(A,B),C)))) # label(fact_479_power__less__power__Suc) # label(axiom).  [clausify(433)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,power_power(nat,A),B)))).  [resolve(543,a,505,a)].
1.14/1.54	544 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_166_of__nat__less__iff) # label(axiom).  [clausify(436)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))).  [resolve(544,a,505,a)].
1.14/1.54	545 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_166_of__nat__less__iff) # label(axiom).  [clausify(436)].
1.14/1.54	546 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))) # label(fact_241_power__increasing) # label(axiom).  [clausify(469)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,power_power(nat,C),A)),hAPP(nat,nat,power_power(nat,C),B))).  [resolve(546,a,505,a)].
1.14/1.54	547 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(547,a,506,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))).  [resolve(547,a,508,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B != C | hAPP(nat,int,power_power(int,A),B) = hAPP(nat,int,power_power(int,A),C).  [resolve(547,a,509,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B = C | hAPP(nat,int,power_power(int,A),B) != hAPP(nat,int,power_power(int,A),C).  [resolve(547,a,510,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(nat,int,power_power(int,A),B))).  [resolve(547,a,512,a)].
1.14/1.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))).  [resolve(547,a,513,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),B))).  [resolve(547,a,514,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,C),B)),hAPP(nat,int,power_power(int,C),A))).  [resolve(547,a,515,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),B)),hAPP(nat,int,power_power(int,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(547,a,516,a)].
1.14/1.54	Derived: hAPP(nat,int,power_power(int,A),B) != hAPP(nat,int,power_power(int,C),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C).  [resolve(547,a,517,a)].
1.14/1.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),one_one(int)))).  [resolve(547,a,518,a)].
1.14/1.54	Derived: hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | ti(int,A) = ti(int,B).  [resolve(547,a,519,a)].
1.14/1.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,A),one_one(int)))).  [resolve(547,a,520,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,C),A)),hAPP(nat,int,power_power(int,C),B))).  [resolve(547,a,521,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(547,a,522,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,A),B)),hAPP(nat,int,power_power(int,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(547,a,523,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,A),B)),hAPP(nat,int,power_power(int,A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(547,a,524,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(547,a,526,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))).  [resolve(547,a,529,a)].
1.14/1.54	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))).  [resolve(547,a,530,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),C)),hAPP(nat,int,power_power(int,B),C))).  [resolve(547,a,531,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),B)),hAPP(nat,int,power_power(int,C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(547,a,532,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))).  [resolve(547,a,533,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(nat,int,power_power(int,A),B))).  [resolve(547,a,534,a)].
1.14/1.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).  [resolve(547,a,535,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,plus_plus(int,A),C))).  [resolve(547,a,536,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,C),B)),hAPP(nat,int,power_power(int,C),A))).  [resolve(547,a,537,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,A),C)),hAPP(nat,int,power_power(int,B),C))).  [resolve(547,a,538,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(547,a,539,a)].
1.14/1.54	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(547,a,540,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,power_power(int,A),B)))).  [resolve(547,a,541,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))).  [resolve(547,a,542,a)].
1.14/1.54	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,power_power(int,A),B)))).  [resolve(547,a,543,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))).  [resolve(547,a,544,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,power_power(int,C),A)),hAPP(nat,int,power_power(int,C),B))).  [resolve(547,a,546,a)].
1.14/1.54	548 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_167_less__imp__of__nat__less) # label(axiom).  [clausify(499)].
1.14/1.54	549 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(549,a,506,a)].
1.14/1.54	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))).  [resolve(549,a,507,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))).  [resolve(549,a,508,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B != C | hAPP(nat,real,power_power(real,A),B) = hAPP(nat,real,power_power(real,A),C).  [resolve(549,a,509,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B = C | hAPP(nat,real,power_power(real,A),B) != hAPP(nat,real,power_power(real,A),C).  [resolve(549,a,510,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(nat,real,power_power(real,A),B))).  [resolve(549,a,512,a)].
1.14/1.54	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))).  [resolve(549,a,513,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,power_power(real,A),B))).  [resolve(549,a,514,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,C),B)),hAPP(nat,real,power_power(real,C),A))).  [resolve(549,a,515,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),B)),hAPP(nat,real,power_power(real,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(549,a,516,a)].
1.14/1.54	Derived: hAPP(nat,real,power_power(real,A),B) != hAPP(nat,real,power_power(real,C),B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(real,A) = ti(real,C).  [resolve(549,a,517,a)].
1.14/1.54	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,one_one(real)),one_one(real)))).  [resolve(549,a,518,a)].
1.14/1.54	Derived: hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = ti(real,B).  [resolve(549,a,519,a)].
1.14/1.54	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,plus_plus(real,A),one_one(real)))).  [resolve(549,a,520,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,C),A)),hAPP(nat,real,power_power(real,C),B))).  [resolve(549,a,521,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(549,a,522,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,A),B)),hAPP(nat,real,power_power(real,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(549,a,523,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,A),B)),hAPP(nat,real,power_power(real,A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(549,a,524,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(549,a,526,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))).  [resolve(549,a,529,a)].
1.14/1.54	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))).  [resolve(549,a,530,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),C)),hAPP(nat,real,power_power(real,B),C))).  [resolve(549,a,531,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),B)),hAPP(nat,real,power_power(real,C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(549,a,532,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))).  [resolve(549,a,533,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,A),B))).  [resolve(549,a,534,a)].
1.14/1.54	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))).  [resolve(549,a,535,a)].
1.14/1.54	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,plus_plus(real,A),C))).  [resolve(549,a,536,a)].
1.14/1.54	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,C),B)),hAPP(nat,real,power_power(real,C),A))).  [resolve(549,a,537,a)].
1.14/1.56	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)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,A),C)),hAPP(nat,real,power_power(real,B),C))).  [resolve(549,a,538,a)].
1.14/1.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(549,a,539,a)].
1.14/1.56	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(549,a,540,a)].
1.14/1.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,power_power(real,A),B)))).  [resolve(549,a,541,a)].
1.14/1.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),zero_zero(real))).  [resolve(549,a,542,a)].
1.14/1.56	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,power_power(real,A),B)))).  [resolve(549,a,543,a)].
1.14/1.56	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))).  [resolve(549,a,544,a)].
1.14/1.56	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,power_power(real,C),A)),hAPP(nat,real,power_power(real,C),B))).  [resolve(549,a,546,a)].
1.14/1.56	550 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))) # label(fact_276_zero__le__power) # label(axiom).  [clausify(500)].
1.14/1.56	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B))).  [resolve(550,a,505,a)].
1.14/1.56	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),B))).  [resolve(550,a,547,a)].
1.14/1.56	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)),hAPP(nat,real,power_power(real,A),B))).  [resolve(550,a,549,a)].
1.14/1.56	551 power(real) # label(arity_RealDef_Oreal___Power_Opower) # label(axiom).  [assumption].
1.14/1.56	552 -power(A) | -semiring_0(A) | zero_zero(nat) = B | zero_zero(A) = hAPP(nat,A,power_power(A,zero_zero(A)),B) # label(fact_109_power__0__left) # label(axiom).  [clausify(3)].
1.14/1.56	553 -power(A) | -semiring_0(A) | zero_zero(nat) != B | one_one(A) = hAPP(nat,A,power_power(A,zero_zero(A)),B) # label(fact_109_power__0__left) # label(axiom).  [clausify(3)].
1.14/1.56	554 -power(A) | one_one(A) = hAPP(nat,A,power_power(A,B),zero_zero(nat)) # label(fact_186_power__0) # label(axiom).  [clausify(23)].
1.14/1.56	Derived: -semiring_0(real) | zero_zero(nat) = A | zero_zero(real) = hAPP(nat,real,power_power(real,zero_zero(real)),A).  [resolve(551,a,552,a)].
1.14/1.57	Derived: -semiring_0(real) | zero_zero(nat) != A | one_one(real) = hAPP(nat,real,power_power(real,zero_zero(real)),A).  [resolve(551,a,553,a)].
1.14/1.57	Derived: one_one(real) = hAPP(nat,real,power_power(real,A),zero_zero(nat)).  [resolve(551,a,554,a)].
1.14/1.57	555 -power(A) | ti(A,hAPP(nat,A,B,C)) = hAPP(nat,A,B,C) # label(tsy_c_hAPP_1_res) # label(axiom).  [clausify(31)].
1.14/1.57	Derived: ti(real,hAPP(nat,real,A,B)) = hAPP(nat,real,A,B).  [resolve(555,a,551,a)].
1.14/1.57	556 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) | zero_zero(nat) != C # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(117)].
1.14/1.57	Derived: -mult_zero(real) | -no_zero_divisors(real) | -zero_neq_one(real) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B) | zero_zero(nat) != B.  [resolve(556,d,551,a)].
1.14/1.57	557 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) | ti(A,B) = zero_zero(A) # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(117)].
1.14/1.57	Derived: -mult_zero(real) | -no_zero_divisors(real) | -zero_neq_one(real) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B) | ti(real,A) = zero_zero(real).  [resolve(557,d,551,a)].
1.14/1.57	558 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | zero_zero(A) = hAPP(nat,A,power_power(A,B),C) | zero_zero(nat) = C | ti(A,B) != zero_zero(A) # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(117)].
1.14/1.57	Derived: -mult_zero(real) | -no_zero_divisors(real) | -zero_neq_one(real) | zero_zero(real) = hAPP(nat,real,power_power(real,A),B) | zero_zero(nat) = B | ti(real,A) != zero_zero(real).  [resolve(558,d,551,a)].
1.14/1.57	559 -power(A) | power_power(A,ti(A,B)) = power_power(A,B) # label(tsy_c_Power_Opower__class_Opower_arg1) # label(axiom).  [clausify(140)].
1.14/1.57	Derived: power_power(real,ti(real,A)) = power_power(real,A).  [resolve(559,a,551,a)].
1.14/1.57	560 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
1.14/1.57	Derived: -semiring_0(int) | zero_zero(nat) = A | zero_zero(int) = hAPP(nat,int,power_power(int,zero_zero(int)),A).  [resolve(560,a,552,a)].
1.14/1.57	Derived: -semiring_0(int) | zero_zero(nat) != A | one_one(int) = hAPP(nat,int,power_power(int,zero_zero(int)),A).  [resolve(560,a,553,a)].
1.14/1.57	Derived: one_one(int) = hAPP(nat,int,power_power(int,A),zero_zero(nat)).  [resolve(560,a,554,a)].
1.14/1.57	Derived: ti(int,hAPP(nat,int,A,B)) = hAPP(nat,int,A,B).  [resolve(560,a,555,a)].
1.14/1.57	Derived: -mult_zero(int) | -no_zero_divisors(int) | -zero_neq_one(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B) | zero_zero(nat) != B.  [resolve(560,a,556,d)].
1.14/1.57	Derived: -mult_zero(int) | -no_zero_divisors(int) | -zero_neq_one(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B) | ti(int,A) = zero_zero(int).  [resolve(560,a,557,d)].
1.14/1.57	Derived: -mult_zero(int) | -no_zero_divisors(int) | -zero_neq_one(int) | zero_zero(int) = hAPP(nat,int,power_power(int,A),B) | zero_zero(nat) = B | ti(int,A) != zero_zero(int).  [resolve(560,a,558,d)].
1.14/1.57	Derived: power_power(int,ti(int,A)) = power_power(int,A).  [resolve(560,a,559,a)].
1.14/1.57	561 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),number_number_of(nat,C)) | ti(A,B) = zero_zero(A) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(265)].
1.14/1.57	562 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),number_number_of(nat,C)) | zero_zero(nat) != number_number_of(nat,C) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(265)].
1.14/1.57	563 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) = hAPP(nat,A,power_power(A,B),number_number_of(nat,C)) | ti(A,B) != zero_zero(A) | zero_zero(nat) = number_number_of(nat,C) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(265)].
1.14/1.57	564 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom).  [assumption].
1.14/1.57	Derived: -semiring_0(nat) | zero_zero(nat) = A | zero_zero(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),A).  [resolve(564,a,552,a)].
1.14/1.61	Derived: -semiring_0(nat) | zero_zero(nat) != A | one_one(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),A).  [resolve(564,a,553,a)].
1.14/1.61	Derived: one_one(nat) = hAPP(nat,nat,power_power(nat,A),zero_zero(nat)).  [resolve(564,a,554,a)].
1.14/1.61	Derived: -mult_zero(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | zero_zero(nat) != hAPP(nat,nat,power_power(nat,A),B) | zero_zero(nat) != B.  [resolve(564,a,556,d)].
1.14/1.61	Derived: -mult_zero(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | zero_zero(nat) != hAPP(nat,nat,power_power(nat,A),B) | ti(nat,A) = zero_zero(nat).  [resolve(564,a,557,d)].
1.14/1.61	Derived: -mult_zero(nat) | -no_zero_divisors(nat) | -zero_neq_one(nat) | zero_zero(nat) = hAPP(nat,nat,power_power(nat,A),B) | zero_zero(nat) = B | ti(nat,A) != zero_zero(nat).  [resolve(564,a,558,d)].
1.14/1.61	Derived: power_power(nat,ti(nat,A)) = power_power(nat,A).  [resolve(564,a,559,a)].
1.14/1.61	565 -power(A) | hAPP(nat,A,B,ti(nat,C)) = hAPP(nat,A,B,C) # label(tsy_c_hAPP_1_arg2) # label(axiom).  [clausify(345)].
1.14/1.61	Derived: hAPP(nat,real,A,ti(nat,B)) = hAPP(nat,real,A,B).  [resolve(565,a,551,a)].
1.14/1.61	Derived: hAPP(nat,int,A,ti(nat,B)) = hAPP(nat,int,A,B).  [resolve(565,a,560,a)].
1.14/1.61	566 -power(A) | ti(fun(nat,A),power_power(A,B)) = power_power(A,B) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom).  [clausify(363)].
1.14/1.61	Derived: ti(fun(nat,real),power_power(real,A)) = power_power(real,A).  [resolve(566,a,551,a)].
1.14/1.61	Derived: ti(fun(nat,int),power_power(int,A)) = power_power(int,A).  [resolve(566,a,560,a)].
1.14/1.61	Derived: ti(fun(nat,nat),power_power(nat,A)) = power_power(nat,A).  [resolve(566,a,564,a)].
1.14/1.61	567 -semiring_0(A) | -power(A) | zero_zero(nat) != number_number_of(nat,B) | one_one(A) = hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B)) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(410)].
1.14/1.61	568 -semiring_0(A) | -power(A) | zero_zero(nat) = number_number_of(nat,B) | zero_zero(A) = hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B)) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(410)].
1.14/1.61	569 -power(A) | hAPP(nat,A,ti(fun(nat,A),B),C) = hAPP(nat,A,B,C) # label(tsy_c_hAPP_1_arg1) # label(axiom).  [clausify(461)].
1.14/1.61	Derived: hAPP(nat,real,ti(fun(nat,real),A),B) = hAPP(nat,real,A,B).  [resolve(569,a,551,a)].
1.14/1.61	Derived: hAPP(nat,int,ti(fun(nat,int),A),B) = hAPP(nat,int,A,B).  [resolve(569,a,560,a)].
1.14/1.61	570 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom).  [assumption].
1.14/1.61	571 -semiring_1(A) | ti(fun(nat,A),semiring_1_of_nat(A)) = semiring_1_of_nat(A) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom).  [clausify(5)].
1.14/1.61	572 -semiring_1(A) | one_one(A) = hAPP(nat,A,power_power(A,one_one(A)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_3_one__power2) # label(axiom).  [clausify(13)].
1.14/1.61	Derived: ti(fun(nat,nat),semiring_1_of_nat(nat)) = semiring_1_of_nat(nat).  [resolve(570,a,571,a)].
1.14/1.61	Derived: one_one(nat) = hAPP(nat,nat,power_power(nat,one_one(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(570,a,572,a)].
1.14/1.61	573 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,power_power(nat,B),C)) = hAPP(nat,A,power_power(A,hAPP(nat,A,semiring_1_of_nat(A),B)),C) # label(fact_171_of__nat__power) # label(axiom).  [clausify(127)].
1.14/1.61	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,power_power(nat,A),B)) = hAPP(nat,nat,power_power(nat,hAPP(nat,nat,semiring_1_of_nat(nat),A)),B).  [resolve(573,a,570,a)].
1.14/1.61	574 semiring_1(real) # label(arity_RealDef_Oreal___Rings_Osemiring__1) # label(axiom).  [assumption].
1.14/1.61	Derived: ti(fun(nat,real),semiring_1_of_nat(real)) = semiring_1_of_nat(real).  [resolve(574,a,571,a)].
1.14/1.61	Derived: one_one(real) = hAPP(nat,real,power_power(real,one_one(real)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(574,a,572,a)].
1.14/1.61	Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,power_power(nat,A),B)) = hAPP(nat,real,power_power(real,hAPP(nat,real,semiring_1_of_nat(real),A)),B).  [resolve(574,a,573,a)].
1.14/1.65	575 -semiring_1(A) | zero_zero(A) = hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_4_zero__power2) # label(axiom).  [clausify(235)].
1.14/1.65	Derived: zero_zero(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(575,a,570,a)].
1.14/1.65	Derived: zero_zero(real) = hAPP(nat,real,power_power(real,zero_zero(real)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(575,a,574,a)].
1.14/1.65	576 -semiring_1(A) | hAPP(A,A,plus_plus(A,hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,plus_plus(nat,B),C)) # label(fact_169_of__nat__add) # label(axiom).  [clausify(255)].
1.14/1.65	Derived: hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,plus_plus(nat,A),B)).  [resolve(576,a,570,a)].
1.14/1.65	Derived: hAPP(real,real,plus_plus(real,hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,plus_plus(nat,A),B)).  [resolve(576,a,574,a)].
1.14/1.65	577 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom).  [assumption].
1.14/1.65	Derived: ti(fun(nat,int),semiring_1_of_nat(int)) = semiring_1_of_nat(int).  [resolve(577,a,571,a)].
1.14/1.65	Derived: one_one(int) = hAPP(nat,int,power_power(int,one_one(int)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(577,a,572,a)].
1.14/1.65	Derived: zero_zero(int) = hAPP(nat,int,power_power(int,zero_zero(int)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(577,a,575,a)].
1.14/1.65	578 -semiring_1(A) | zero_zero(A) = hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat)) # label(fact_187_of__nat__0) # label(axiom).  [clausify(320)].
1.14/1.65	Derived: zero_zero(nat) = hAPP(nat,nat,semiring_1_of_nat(nat),zero_zero(nat)).  [resolve(578,a,570,a)].
1.14/1.65	Derived: zero_zero(real) = hAPP(nat,real,semiring_1_of_nat(real),zero_zero(nat)).  [resolve(578,a,574,a)].
1.14/1.65	Derived: zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).  [resolve(578,a,577,a)].
1.14/1.65	579 -semiring_1(A) | one_one(A) = hAPP(nat,A,semiring_1_of_nat(A),one_one(nat)) # label(fact_170_of__nat__1) # label(axiom).  [clausify(479)].
1.14/1.65	Derived: one_one(nat) = hAPP(nat,nat,semiring_1_of_nat(nat),one_one(nat)).  [resolve(579,a,570,a)].
1.14/1.65	Derived: one_one(real) = hAPP(nat,real,semiring_1_of_nat(real),one_one(nat)).  [resolve(579,a,574,a)].
1.14/1.65	Derived: one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).  [resolve(579,a,577,a)].
1.14/1.65	580 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom).  [assumption].
1.14/1.65	581 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_431_not__leE) # label(axiom).  [clausify(6)].
1.14/1.65	582 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_424_linorder__not__less) # label(axiom).  [clausify(22)].
1.14/1.65	583 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_424_linorder__not__less) # label(axiom).  [clausify(22)].
1.14/1.65	584 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f6(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_449_pinf_I6_J) # label(axiom).  [clausify(58)].
1.14/1.65	585 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_402_linorder__cases) # label(axiom).  [clausify(67)].
1.14/1.65	586 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_421_not__less__iff__gr__or__eq) # label(axiom).  [clausify(94)].
1.14/1.65	587 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_421_not__less__iff__gr__or__eq) # label(axiom).  [clausify(94)].
1.14/1.66	588 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_421_not__less__iff__gr__or__eq) # label(axiom).  [clausify(94)].
1.14/1.66	589 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_426_linorder__le__less__linear) # label(axiom).  [clausify(104)].
1.14/1.66	590 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_419_linorder__antisym__conv3) # label(axiom).  [clausify(141)].
1.14/1.66	591 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_419_linorder__antisym__conv3) # label(axiom).  [clausify(141)].
1.14/1.66	592 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_386_linorder__le__cases) # label(axiom).  [clausify(152)].
1.14/1.66	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),A)).  [resolve(580,a,581,a)].
1.14/1.66	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),B),A)).  [resolve(580,a,583,a)].
1.14/1.66	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f6(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(580,a,584,a)].
1.14/1.66	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(580,a,585,a)].
1.14/1.66	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) != ti(real,B).  [resolve(580,a,587,a)].
1.14/1.66	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),A)).  [resolve(580,a,588,a)].
1.14/1.66	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)).  [resolve(580,a,592,a)].
1.14/1.66	593 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_435_leD) # label(axiom).  [clausify(211)].
1.14/1.66	594 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_437_linorder__antisym__conv2) # label(axiom).  [clausify(230)].
1.14/1.66	595 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_437_linorder__antisym__conv2) # label(axiom).  [clausify(230)].
1.14/1.66	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,A) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)).  [resolve(595,a,580,a)].
1.14/1.66	596 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_432_linorder__antisym__conv1) # label(axiom).  [clausify(240)].
1.14/1.66	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) != ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(596,a,580,a)].
1.14/1.66	597 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_432_linorder__antisym__conv1) # label(axiom).  [clausify(240)].
1.14/1.66	598 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_430_leI) # label(axiom).  [clausify(304)].
1.14/1.66	599 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_400_linorder__linear) # label(axiom).  [clausify(312)].
1.14/1.66	600 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_420_linorder__less__linear) # label(axiom).  [clausify(319)].
1.14/1.66	601 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_425_linorder__not__le) # label(axiom).  [clausify(326)].
1.14/1.66	602 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_425_linorder__not__le) # label(axiom).  [clausify(326)].
1.14/1.66	603 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_418_linorder__neqE) # label(axiom).  [clausify(329)].
1.14/1.66	604 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom).  [assumption].
1.14/1.66	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(604,a,581,a)].
1.14/1.66	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(604,a,583,a)].
1.14/1.66	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f6(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(604,a,584,a)].
1.14/1.66	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(604,a,585,a)].
1.14/1.66	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B).  [resolve(604,a,587,a)].
1.14/1.66	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(604,a,588,a)].
1.14/1.66	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(604,a,592,a)].
1.14/1.66	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(604,a,595,a)].
1.14/1.66	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(604,a,596,a)].
1.14/1.66	605 -linorder(A) | ti(A,B) = ti(A,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),C),B)) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(352)].
1.14/1.66	606 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(352)].
1.14/1.66	607 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(352)].
1.14/1.66	Derived: ti(real,A) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(607,a,580,a)].
1.14/1.66	Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)).  [resolve(607,a,604,a)].
1.14/1.66	608 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom).  [assumption].
1.14/1.66	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),B),A)).  [resolve(608,a,581,a)].
1.14/1.66	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(608,a,583,a)].
1.14/1.66	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f6(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(608,a,584,a)].
1.14/1.70	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).  [resolve(608,a,585,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B).  [resolve(608,a,587,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).  [resolve(608,a,588,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).  [resolve(608,a,595,a)].
1.14/1.70	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(608,a,596,a)].
1.14/1.70	Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).  [resolve(608,a,607,a)].
1.14/1.70	609 -linorder(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,C)),number_number_of(A,B))) # label(fact_275_le__number__of__eq__not__less) # label(axiom).  [clausify(374)].
1.14/1.70	610 -linorder(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,C)),number_number_of(A,B))) # label(fact_275_le__number__of__eq__not__less) # label(axiom).  [clausify(374)].
1.14/1.70	611 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f37(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_456_minf_I8_J) # label(axiom).  [clausify(380)].
1.14/1.70	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f37(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(611,a,580,a)].
1.14/1.70	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f37(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(611,a,604,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f37(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(611,a,608,a)].
1.14/1.70	612 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f39(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_453_pinf_I8_J) # label(axiom).  [clausify(425)].
1.14/1.70	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f39(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(612,a,580,a)].
1.14/1.70	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f39(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(612,a,604,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f39(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(612,a,608,a)].
1.14/1.70	613 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f40(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_452_minf_I6_J) # label(axiom).  [clausify(437)].
1.14/1.70	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f40(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(613,a,580,a)].
1.14/1.70	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f40(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(613,a,604,a)].
1.14/1.70	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f40(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(613,a,608,a)].
1.14/1.70	614 -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),f23(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_450_dense__le__bounded) # label(axiom).  [clausify(214)].
1.49/1.80	615 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom).  [assumption].
1.49/1.80	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),f23(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(614,a,615,a)].
1.49/1.80	616 -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),f23(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_450_dense__le__bounded) # label(axiom).  [clausify(214)].
1.49/1.80	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),f23(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(616,a,615,a)].
1.49/1.80	617 -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),f23(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_450_dense__le__bounded) # label(axiom).  [clausify(214)].
1.49/1.80	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),f23(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(617,a,615,a)].
1.49/1.80	618 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f34(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_446_dense__le) # label(axiom).  [clausify(323)].
1.49/1.80	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f34(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(618,a,615,a)].
1.49/1.80	619 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f34(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_446_dense__le) # label(axiom).  [clausify(323)].
1.49/1.80	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f34(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(619,a,615,a)].
1.49/1.80	620 -cancel146912293up_add(A) | hAPP(A,A,plus_plus(A,B),C) != hAPP(A,A,plus_plus(A,B),D) | ti(A,C) = ti(A,D) # label(fact_198_add__imp__eq) # label(axiom).  [clausify(148)].
1.49/1.80	621 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
1.49/1.80	Derived: hAPP(nat,nat,plus_plus(nat,A),B) != hAPP(nat,nat,plus_plus(nat,A),C) | ti(nat,B) = ti(nat,C).  [resolve(620,a,621,a)].
1.49/1.80	622 cancel146912293up_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
1.49/1.80	Derived: hAPP(real,real,plus_plus(real,A),B) != hAPP(real,real,plus_plus(real,A),C) | ti(real,B) = ti(real,C).  [resolve(622,a,620,a)].
1.49/1.80	623 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
1.49/1.80	Derived: hAPP(int,int,plus_plus(int,A),B) != hAPP(int,int,plus_plus(int,A),C) | ti(int,B) = ti(int,C).  [resolve(623,a,620,a)].
1.49/1.80	624 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
1.49/1.80	625 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_335_sum__power2__ge__zero) # label(axiom).  [clausify(15)].
1.49/1.80	626 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(A,B) = zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(25)].
1.49/1.80	627 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(A,C) = zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(25)].
1.49/1.80	628 -linordered_idom(A) | zero_zero(A) = hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(25)].
1.49/1.80	629 -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,power_power(A,number_number_of(A,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_103_of__nat__less__two__power) # label(axiom).  [clausify(29)].
1.49/1.80	630 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B))) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(30)].
1.49/1.80	631 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B))) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(30)].
1.49/1.80	632 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),one_one(A))) # label(fact_263_le__special_I4_J) # label(axiom).  [clausify(50)].
1.49/1.80	633 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),one_one(A))) # label(fact_263_le__special_I4_J) # label(axiom).  [clausify(50)].
1.49/1.80	634 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(79)].
1.49/1.80	635 -linordered_idom(A) | ti(A,B) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(79)].
1.49/1.80	636 -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_151_linorder__neqE__linordered__idom) # label(axiom).  [clausify(88)].
1.49/1.80	637 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))) # label(fact_96_power2__less__0) # label(axiom).  [clausify(103)].
1.49/1.80	638 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(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_63_less__special_I2_J) # label(axiom).  [clausify(115)].
1.49/1.80	639 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(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_63_less__special_I2_J) # label(axiom).  [clausify(115)].
1.49/1.80	640 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_336_sum__power2__le__zero__iff) # label(axiom).  [clausify(144)].
1.49/1.81	641 -linordered_idom(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_336_sum__power2__le__zero__iff) # label(axiom).  [clausify(144)].
1.49/1.81	642 -linordered_idom(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_336_sum__power2__le__zero__iff) # label(axiom).  [clausify(144)].
1.49/1.81	643 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),number_number_of(A,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_262_le__special_I2_J) # label(axiom).  [clausify(160)].
1.49/1.81	644 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),number_number_of(A,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_262_le__special_I2_J) # label(axiom).  [clausify(160)].
1.49/1.81	645 -number_ring(A) | -linordered_idom(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),number_number_of(A,B)),one_one(A))) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(201)].
1.49/1.81	646 -number_ring(A) | -linordered_idom(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),number_number_of(A,B)),one_one(A))) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(201)].
1.49/1.81	647 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),zero_zero(A))) # label(fact_258_le__special_I3_J) # label(axiom).  [clausify(204)].
1.49/1.81	648 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),zero_zero(A))) # label(fact_258_le__special_I3_J) # label(axiom).  [clausify(204)].
1.49/1.81	649 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_18_less__number__of) # label(axiom).  [clausify(227)].
1.49/1.81	650 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_18_less__number__of) # label(axiom).  [clausify(227)].
1.49/1.81	651 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_330_zero__le__power2) # label(axiom).  [clausify(267)].
1.49/1.81	652 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(290)].
1.49/1.81	653 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(290)].
1.49/1.81	654 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(290)].
1.49/1.81	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(624,a,625,a)].
1.49/1.81	Derived: zero_zero(int) != hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(int,A) = zero_zero(int).  [resolve(624,a,626,a)].
1.49/1.81	Derived: zero_zero(int) != hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(int,B) = zero_zero(int).  [resolve(624,a,627,a)].
1.49/1.81	Derived: zero_zero(int) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int).  [resolve(624,a,628,a)].
1.49/1.81	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,power_power(int,number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(624,a,629,a)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),number_number_of(int,A))).  [resolve(624,a,630,a)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),number_number_of(int,A))).  [resolve(624,a,631,a)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,A)),one_one(int))).  [resolve(624,a,632,b)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,A)),one_one(int))).  [resolve(624,a,633,b)].
1.49/1.81	Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(624,a,634,a)].
1.49/1.81	Derived: ti(int,A) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(624,a,635,a)].
1.49/1.81	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(int))).  [resolve(624,a,637,a)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(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(624,a,638,b)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(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(624,a,639,b)].
1.49/1.81	Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))).  [resolve(624,a,640,a)].
1.49/1.81	Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))).  [resolve(624,a,641,a)].
1.49/1.81	Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))).  [resolve(624,a,642,a)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),number_number_of(int,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)).  [resolve(624,a,643,b)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),number_number_of(int,A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)).  [resolve(624,a,644,b)].
1.49/1.81	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),number_number_of(int,A)),one_one(int))).  [resolve(624,a,645,b)].
1.49/1.81	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),number_number_of(int,A)),one_one(int))).  [resolve(624,a,646,b)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,A)),zero_zero(int))).  [resolve(624,a,647,a)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,A)),zero_zero(int))).  [resolve(624,a,648,a)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(624,a,649,a)].
1.49/1.81	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(624,a,650,a)].
1.49/1.81	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(624,a,651,a)].
1.49/1.81	Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(624,a,652,a)].
1.49/1.81	Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(624,a,653,a)].
1.49/1.81	Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(624,a,654,a)].
1.49/1.81	655 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(307)].
1.49/1.81	Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).  [resolve(655,b,624,a)].
1.49/1.82	656 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(307)].
1.49/1.82	Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).  [resolve(656,b,624,a)].
1.49/1.82	657 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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_44_even__less__0__iff) # label(axiom).  [clausify(354)].
1.49/1.82	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(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(657,a,624,a)].
1.49/1.82	658 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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_44_even__less__0__iff) # label(axiom).  [clausify(354)].
1.49/1.82	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(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(658,a,624,a)].
1.49/1.82	659 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_98_not__sum__power2__lt__zero) # label(axiom).  [clausify(362)].
1.49/1.82	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))).  [resolve(659,a,624,a)].
1.49/1.82	660 -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)),number_number_of(A,B))) # label(fact_257_le__special_I1_J) # label(axiom).  [clausify(387)].
1.49/1.82	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)),number_number_of(int,A))).  [resolve(660,b,624,a)].
1.49/1.82	661 -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)),number_number_of(A,B))) # label(fact_257_le__special_I1_J) # label(axiom).  [clausify(387)].
1.49/1.82	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)),number_number_of(int,A))).  [resolve(661,b,624,a)].
1.49/1.82	662 linordered_idom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__idom) # label(axiom).  [assumption].
1.49/1.82	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(662,a,625,a)].
1.49/1.82	Derived: zero_zero(real) != hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(real,A) = zero_zero(real).  [resolve(662,a,626,a)].
1.49/1.82	Derived: zero_zero(real) != hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(real,B) = zero_zero(real).  [resolve(662,a,627,a)].
1.49/1.82	Derived: zero_zero(real) = hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real).  [resolve(662,a,628,a)].
1.49/1.82	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,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))).  [resolve(662,a,629,a)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),number_number_of(real,A))).  [resolve(662,a,630,a)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),number_number_of(real,A))).  [resolve(662,a,631,a)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),one_one(real))).  [resolve(662,a,632,b)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),one_one(real))).  [resolve(662,a,633,b)].
1.49/1.82	Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(662,a,634,a)].
1.49/1.82	Derived: ti(real,A) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(662,a,635,a)].
1.49/1.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(real))).  [resolve(662,a,637,a)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(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(662,a,638,b)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(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(662,a,639,b)].
1.49/1.82	Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))).  [resolve(662,a,640,a)].
1.49/1.82	Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))).  [resolve(662,a,641,a)].
1.49/1.82	Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))).  [resolve(662,a,642,a)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),number_number_of(real,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)).  [resolve(662,a,643,b)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),number_number_of(real,A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)).  [resolve(662,a,644,b)].
1.49/1.82	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),number_number_of(real,A)),one_one(real))).  [resolve(662,a,645,b)].
1.49/1.82	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),number_number_of(real,A)),one_one(real))).  [resolve(662,a,646,b)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),zero_zero(real))).  [resolve(662,a,647,a)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),zero_zero(real))).  [resolve(662,a,648,a)].
1.49/1.82	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),number_number_of(real,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(662,a,649,a)].
1.49/1.82	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),number_number_of(real,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)).  [resolve(662,a,650,a)].
1.49/1.82	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))).  [resolve(662,a,651,a)].
1.49/1.82	Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(662,a,652,a)].
1.49/1.82	Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(662,a,653,a)].
1.49/1.82	Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))).  [resolve(662,a,654,a)].
1.58/1.85	Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).  [resolve(662,a,655,b)].
1.58/1.85	Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)).  [resolve(662,a,656,b)].
1.58/1.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(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(662,a,657,a)].
1.58/1.85	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(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(662,a,658,a)].
1.58/1.85	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))).  [resolve(662,a,659,a)].
1.58/1.85	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)),number_number_of(real,A))).  [resolve(662,a,660,b)].
1.58/1.85	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)),number_number_of(real,A))).  [resolve(662,a,661,b)].
1.58/1.85	663 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),number_number_of(A,C))) # label(fact_252_le__number__of) # label(axiom).  [clausify(493)].
1.58/1.85	Derived: -number_ring(int) | -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),number_number_of(int,A)),number_number_of(int,B))).  [resolve(663,b,624,a)].
1.58/1.85	Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),number_number_of(real,B))).  [resolve(663,b,662,a)].
1.58/1.85	664 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),number_number_of(A,C))) # label(fact_252_le__number__of) # label(axiom).  [clausify(493)].
1.58/1.85	Derived: -number_ring(int) | 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),number_number_of(int,A)),number_number_of(int,B))).  [resolve(664,b,624,a)].
1.58/1.85	Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),number_number_of(real,B))).  [resolve(664,b,662,a)].
1.58/1.85	665 -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,plus_plus(A,B),D))) # label(fact_300_add__strict__increasing2) # label(axiom).  [clausify(46)].
1.58/1.85	666 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.58/1.85	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,plus_plus(real,A),C))).  [resolve(665,a,666,a)].
1.58/1.86	667 -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,plus_plus(A,B),D))) # label(fact_299_add__strict__increasing) # label(axiom).  [clausify(57)].
1.58/1.86	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,plus_plus(real,A),C))).  [resolve(667,a,666,a)].
1.58/1.86	668 -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,plus_plus(A,B),C)),zero_zero(A))) # label(fact_302_add__nonpos__neg) # label(axiom).  [clausify(73)].
1.58/1.86	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,plus_plus(real,A),B)),zero_zero(real))).  [resolve(668,a,666,a)].
1.58/1.86	669 -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,plus_plus(A,B),C))) # label(fact_298_add__nonneg__pos) # label(axiom).  [clausify(99)].
1.58/1.86	670 -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)) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(163)].
1.58/1.86	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)) | ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | zero_zero(real) = hAPP(real,real,plus_plus(real,A),B).  [resolve(670,a,666,a)].
1.58/1.86	671 -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)) | ti(A,B) = zero_zero(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(163)].
1.58/1.86	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)) | ti(real,A) = zero_zero(real) | zero_zero(real) != hAPP(real,real,plus_plus(real,A),B).  [resolve(671,a,666,a)].
1.58/1.86	672 -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)) | ti(A,C) = zero_zero(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(163)].
1.58/1.86	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)) | ti(real,B) = zero_zero(real) | zero_zero(real) != hAPP(real,real,plus_plus(real,A),B).  [resolve(672,a,666,a)].
1.58/1.86	673 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.58/1.86	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,plus_plus(int,A),C))).  [resolve(673,a,665,a)].
1.58/1.86	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,plus_plus(int,A),C))).  [resolve(673,a,667,a)].
1.58/1.86	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,plus_plus(int,A),B)),zero_zero(int))).  [resolve(673,a,668,a)].
1.58/1.86	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)) | ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | zero_zero(int) = hAPP(int,int,plus_plus(int,A),B).  [resolve(673,a,670,a)].
1.58/1.86	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)) | ti(int,A) = zero_zero(int) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),B).  [resolve(673,a,671,a)].
1.58/1.86	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)) | ti(int,B) = zero_zero(int) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),B).  [resolve(673,a,672,a)].
1.58/1.86	674 -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,plus_plus(A,B),C))) # label(fact_228_add__pos__pos) # label(axiom).  [clausify(253)].
1.58/1.86	675 -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,plus_plus(A,B),C)),zero_zero(A))) # label(fact_227_add__neg__neg) # label(axiom).  [clausify(281)].
1.58/1.86	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,plus_plus(real,A),B)),zero_zero(real))).  [resolve(675,a,666,a)].
1.58/1.86	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,plus_plus(int,A),B)),zero_zero(int))).  [resolve(675,a,673,a)].
1.58/1.86	676 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.58/1.86	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,plus_plus(nat,A),C))).  [resolve(676,a,667,a)].
1.58/1.86	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)) | ti(nat,A) != zero_zero(nat) | ti(nat,B) != zero_zero(nat) | zero_zero(nat) = hAPP(nat,nat,plus_plus(nat,A),B).  [resolve(676,a,670,a)].
1.58/1.86	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)) | ti(nat,A) = zero_zero(nat) | zero_zero(nat) != hAPP(nat,nat,plus_plus(nat,A),B).  [resolve(676,a,671,a)].
1.58/1.86	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)) | ti(nat,B) = zero_zero(nat) | zero_zero(nat) != hAPP(nat,nat,plus_plus(nat,A),B).  [resolve(676,a,672,a)].
1.58/1.86	677 -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,plus_plus(A,B),C))) # label(fact_297_add__pos__nonneg) # label(axiom).  [clausify(365)].
1.58/1.86	678 -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,plus_plus(A,B),C))) # label(fact_266_add__nonneg__nonneg) # label(axiom).  [clausify(386)].
1.58/1.86	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,plus_plus(real,A),B))).  [resolve(678,a,666,a)].
1.58/1.86	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,plus_plus(int,A),B))).  [resolve(678,a,673,a)].
1.58/1.86	679 -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,plus_plus(A,D),B))) # label(fact_269_add__increasing2) # label(axiom).  [clausify(432)].
1.58/1.86	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,plus_plus(real,C),A))).  [resolve(679,a,666,a)].
1.58/1.86	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,plus_plus(int,C),A))).  [resolve(679,a,673,a)].
1.58/1.86	680 -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,plus_plus(A,B),D))) # label(fact_268_add__increasing) # label(axiom).  [clausify(434)].
1.58/1.86	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,plus_plus(real,A),C))).  [resolve(680,a,666,a)].
1.58/1.86	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,plus_plus(int,A),C))).  [resolve(680,a,673,a)].
1.58/1.86	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,plus_plus(nat,A),C))).  [resolve(680,a,676,a)].
1.58/1.86	681 -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,plus_plus(A,B),C)),zero_zero(A))) # label(fact_270_add__nonpos__nonpos) # label(axiom).  [clausify(444)].
1.58/1.86	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,plus_plus(real,A),B)),zero_zero(real))).  [resolve(681,a,666,a)].
1.58/1.86	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,plus_plus(int,A),B)),zero_zero(int))).  [resolve(681,a,673,a)].
1.64/1.92	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,plus_plus(nat,A),B)),zero_zero(nat))).  [resolve(681,a,676,a)].
1.64/1.92	682 -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,plus_plus(A,B),C)),zero_zero(A))) # label(fact_301_add__neg__nonpos) # label(axiom).  [clausify(481)].
1.64/1.92	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,plus_plus(real,A),B)),zero_zero(real))).  [resolve(682,a,666,a)].
1.64/1.92	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,plus_plus(int,A),B)),zero_zero(int))).  [resolve(682,a,673,a)].
1.64/1.92	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,plus_plus(nat,A),B)),zero_zero(nat))).  [resolve(682,a,676,a)].
1.64/1.92	683 -zero(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom).  [clausify(422)].
1.64/1.92	684 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom).  [assumption].
1.64/1.92	685 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom).  [assumption].
1.64/1.92	Derived: ti(real,zero_zero(real)) = zero_zero(real).  [resolve(683,a,684,a)].
1.64/1.92	Derived: ti(nat,zero_zero(nat)) = zero_zero(nat).  [resolve(683,a,685,a)].
1.64/1.92	686 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom).  [assumption].
1.64/1.92	Derived: ti(int,zero_zero(int)) = zero_zero(int).  [resolve(686,a,683,a)].
1.64/1.92	687 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | number_number_of(A,hAPP(int,int,succ,B)) = hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A)) # label(fact_296_semiring__number__of__add__1) # label(axiom).  [clausify(90)].
1.64/1.92	688 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom).  [assumption].
1.64/1.92	689 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom).  [assumption].
1.64/1.92	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(real,hAPP(int,int,succ,A)) = hAPP(real,real,plus_plus(real,number_number_of(real,A)),one_one(real)).  [resolve(687,a,688,a)].
1.64/1.92	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(nat,hAPP(int,int,succ,A)) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),one_one(nat)).  [resolve(687,a,689,a)].
1.64/1.92	690 -number_semiring(A) | number_number_of(A,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(A,A,plus_plus(A,one_one(A)),one_one(A)) # label(fact_9_semiring__one__add__one__is__two) # label(axiom).  [clausify(207)].
1.64/1.92	Derived: number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(real,real,plus_plus(real,one_one(real)),one_one(real)).  [resolve(690,a,688,a)].
1.64/1.92	Derived: number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)).  [resolve(690,a,689,a)].
1.64/1.92	691 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
1.64/1.92	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(int,hAPP(int,int,succ,A)) = hAPP(int,int,plus_plus(int,number_number_of(int,A)),one_one(int)).  [resolve(691,a,687,a)].
1.70/1.95	Derived: number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,plus_plus(int,one_one(int)),one_one(int)).  [resolve(691,a,690,a)].
1.70/1.95	692 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | number_number_of(A,hAPP(int,int,plus_plus(int,B),C)) = hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C)) # label(fact_322_semiring__add__number__of) # label(axiom).  [clausify(242)].
1.70/1.95	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | number_number_of(real,hAPP(int,int,plus_plus(int,A),B)) = hAPP(real,real,plus_plus(real,number_number_of(real,A)),number_number_of(real,B)).  [resolve(692,a,688,a)].
1.70/1.95	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | number_number_of(nat,hAPP(int,int,plus_plus(int,A),B)) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B)).  [resolve(692,a,689,a)].
1.70/1.95	693 -number_semiring(A) | number_number_of(A,hAPP(nat,int,semiring_1_of_nat(int),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_94_number__of__int) # label(axiom).  [clausify(254)].
1.70/1.95	Derived: number_number_of(real,hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,real,semiring_1_of_nat(real),A).  [resolve(693,a,688,a)].
1.70/1.95	Derived: number_number_of(nat,hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,nat,semiring_1_of_nat(nat),A).  [resolve(693,a,689,a)].
1.70/1.95	694 -number_semiring(A) | one_one(A) = number_number_of(A,hAPP(int,int,bit1,pls)) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom).  [clausify(270)].
1.70/1.95	Derived: one_one(real) = number_number_of(real,hAPP(int,int,bit1,pls)).  [resolve(694,a,688,a)].
1.70/1.95	Derived: one_one(nat) = number_number_of(nat,hAPP(int,int,bit1,pls)).  [resolve(694,a,689,a)].
1.70/1.95	Derived: one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)).  [resolve(694,a,691,a)].
1.70/1.95	695 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | number_number_of(A,hAPP(int,int,succ,B)) = hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B)) # label(fact_295_semiring__1__add__number__of) # label(axiom).  [clausify(273)].
1.70/1.95	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(real,hAPP(int,int,succ,A)) = hAPP(real,real,plus_plus(real,one_one(real)),number_number_of(real,A)).  [resolve(695,a,688,a)].
1.70/1.95	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(nat,hAPP(int,int,succ,A)) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,A)).  [resolve(695,a,689,a)].
1.70/1.95	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | number_number_of(int,hAPP(int,int,succ,A)) = hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,A)).  [resolve(695,a,691,a)].
1.70/1.95	696 -number_semiring(A) | zero_zero(A) = number_number_of(A,pls) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom).  [clausify(364)].
1.70/1.95	Derived: zero_zero(real) = number_number_of(real,pls).  [resolve(696,a,688,a)].
1.70/1.95	Derived: zero_zero(nat) = number_number_of(nat,pls).  [resolve(696,a,689,a)].
1.70/1.95	697 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom).  [assumption].
1.70/1.95	698 -number(A) | number_number_of(A,ti(int,B)) = number_number_of(A,B) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom).  [clausify(21)].
1.70/1.95	699 -number(A) | ti(A,number_number_of(A,B)) = number_number_of(A,B) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom).  [clausify(167)].
1.70/1.95	Derived: number_number_of(int,ti(int,A)) = number_number_of(int,A).  [resolve(697,a,698,a)].
1.70/1.95	Derived: ti(int,number_number_of(int,A)) = number_number_of(int,A).  [resolve(697,a,699,a)].
1.70/1.95	700 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom).  [assumption].
1.75/2.04	Derived: number_number_of(nat,ti(int,A)) = number_number_of(nat,A).  [resolve(700,a,698,a)].
1.75/2.04	Derived: ti(nat,number_number_of(nat,A)) = number_number_of(nat,A).  [resolve(700,a,699,a)].
1.75/2.04	701 number(real) # label(arity_RealDef_Oreal___Int_Onumber) # label(axiom).  [assumption].
1.75/2.04	Derived: number_number_of(real,ti(int,A)) = number_number_of(real,A).  [resolve(701,a,698,a)].
1.75/2.04	Derived: ti(real,number_number_of(real,A)) = number_number_of(real,A).  [resolve(701,a,699,a)].
1.75/2.04	702 -semiri456707255roduct(A) | ti(A,B) != hAPP(A,A,plus_plus(A,B),C) | ti(A,C) = zero_zero(A) # label(fact_210_add__0__iff) # label(axiom).  [clausify(262)].
1.75/2.04	703 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom).  [assumption].
1.75/2.04	704 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
1.75/2.04	705 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
1.75/2.04	Derived: ti(real,A) != hAPP(real,real,plus_plus(real,A),B) | ti(real,B) = zero_zero(real).  [resolve(702,a,703,a)].
1.75/2.04	Derived: ti(nat,A) != hAPP(nat,nat,plus_plus(nat,A),B) | ti(nat,B) = zero_zero(nat).  [resolve(702,a,704,a)].
1.75/2.04	Derived: ti(int,A) != hAPP(int,int,plus_plus(int,A),B) | ti(int,B) = zero_zero(int).  [resolve(702,a,705,a)].
1.75/2.04	706 -semiri456707255roduct(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),C) | ti(A,C) != zero_zero(A) # label(fact_210_add__0__iff) # label(axiom).  [clausify(262)].
1.75/2.04	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,A),B) | ti(real,B) != zero_zero(real).  [resolve(706,a,703,a)].
1.75/2.04	Derived: ti(nat,A) = hAPP(nat,nat,plus_plus(nat,A),B) | ti(nat,B) != zero_zero(nat).  [resolve(706,a,704,a)].
1.75/2.04	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,A),B) | ti(int,B) != zero_zero(int).  [resolve(706,a,705,a)].
1.75/2.04	707 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
1.75/2.04	708 -ring_11004092258visors(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(A,B) = zero_zero(A) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(26)].
1.75/2.04	709 -ring_11004092258visors(A) | zero_zero(A) = hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(A,B) != zero_zero(A) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(26)].
1.75/2.04	710 -ring_11004092258visors(A) | ti(A,B) = zero_zero(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) # label(fact_164_field__power__not__zero) # label(axiom).  [clausify(43)].
1.75/2.04	Derived: zero_zero(int) != hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(int,A) = zero_zero(int).  [resolve(707,a,708,a)].
1.75/2.04	Derived: zero_zero(int) = hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(int,A) != zero_zero(int).  [resolve(707,a,709,a)].
1.75/2.04	Derived: ti(int,A) = zero_zero(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B).  [resolve(707,a,710,a)].
1.75/2.04	711 ring_11004092258visors(real) # label(arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
1.75/2.04	Derived: zero_zero(real) != hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(real,A) = zero_zero(real).  [resolve(711,a,708,a)].
1.75/2.04	Derived: zero_zero(real) = hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | ti(real,A) != zero_zero(real).  [resolve(711,a,709,a)].
1.75/2.04	Derived: ti(real,A) = zero_zero(real) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B).  [resolve(711,a,710,a)].
1.75/2.04	712 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_489_comm__mult__strict__left__mono) # label(axiom).  [clausify(442)].
1.80/2.07	713 linord893533164strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
1.80/2.07	714 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
1.80/2.07	715 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
1.80/2.07	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(712,a,713,a)].
1.80/2.07	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))).  [resolve(712,a,714,a)].
1.80/2.07	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))).  [resolve(712,a,715,a)].
1.80/2.07	716 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
1.80/2.07	717 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_222_add__strict__right__mono) # label(axiom).  [clausify(36)].
1.80/2.07	718 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
1.80/2.07	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,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),C))).  [resolve(718,a,717,a)].
1.80/2.07	719 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))) # label(fact_220_add__strict__mono) # label(axiom).  [clausify(142)].
1.80/2.07	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),D))).  [resolve(719,a,718,a)].
1.80/2.07	720 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
1.80/2.07	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))).  [resolve(720,a,719,a)].
1.80/2.07	721 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_221_add__strict__left__mono) # label(axiom).  [clausify(310)].
1.80/2.07	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,C),A)),hAPP(nat,nat,plus_plus(nat,C),B))).  [resolve(721,a,716,a)].
1.80/2.07	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,plus_plus(real,C),A)),hAPP(real,real,plus_plus(real,C),B))).  [resolve(721,a,718,a)].
1.80/2.10	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,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))).  [resolve(721,a,720,a)].
1.80/2.10	722 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))) # label(fact_271_add__less__le__mono) # label(axiom).  [clausify(330)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D))).  [resolve(722,a,716,a)].
1.80/2.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),D))).  [resolve(722,a,718,a)].
1.80/2.10	723 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))) # label(fact_272_add__le__less__mono) # label(axiom).  [clausify(336)].
1.80/2.10	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),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D))).  [resolve(723,a,716,a)].
1.80/2.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),D))).  [resolve(723,a,718,a)].
1.80/2.10	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))).  [resolve(723,a,720,a)].
1.80/2.10	724 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.80/2.10	725 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_466_mult__right__le__imp__le) # label(axiom).  [clausify(44)].
1.80/2.10	726 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_465_mult__left__le__imp__le) # label(axiom).  [clausify(63)].
1.80/2.10	727 -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_472_mult__less__le__imp__less) # label(axiom).  [clausify(135)].
1.80/2.10	728 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_469_mult__less__imp__less__right) # label(axiom).  [clausify(185)].
1.80/2.10	729 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_493_mult__neg__pos) # label(axiom).  [clausify(193)].
1.80/2.10	730 -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_495_zero__less__mult__pos2) # label(axiom).  [clausify(197)].
1.80/2.10	731 -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_471_mult__le__less__imp__less) # label(axiom).  [clausify(203)].
1.80/2.10	732 -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_490_mult__strict__left__mono) # label(axiom).  [clausify(308)].
1.80/2.10	733 -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_467_mult__less__imp__less__left) # label(axiom).  [clausify(309)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)).  [resolve(724,a,725,a)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(724,a,726,a)].
1.80/2.10	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(724,a,727,a)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(724,a,728,a)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).  [resolve(724,a,730,a)].
1.80/2.10	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(724,a,731,a)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(724,a,733,a)].
1.80/2.10	734 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_474_mult__strict__mono) # label(axiom).  [clausify(335)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))).  [resolve(734,a,724,a)].
1.80/2.10	735 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_473_mult__strict__mono_H) # label(axiom).  [clausify(342)].
1.80/2.10	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))).  [resolve(735,a,724,a)].
1.80/2.10	736 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.80/2.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)).  [resolve(736,a,725,a)].
1.80/2.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(736,a,726,a)].
1.80/2.10	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(736,a,727,a)].
1.80/2.11	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(736,a,728,a)].
1.80/2.11	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)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))).  [resolve(736,a,729,a)].
1.80/2.11	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(736,a,730,a)].
1.80/2.11	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(736,a,731,a)].
1.80/2.11	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(736,a,733,a)].
1.80/2.11	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(736,a,734,a)].
1.80/2.11	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))).  [resolve(736,a,735,a)].
1.80/2.11	737 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_491_mult__strict__right__mono) # label(axiom).  [clausify(441)].
1.80/2.11	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))).  [resolve(737,a,724,a)].
1.80/2.11	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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),C))).  [resolve(737,a,736,a)].
1.80/2.11	738 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)).  [resolve(738,a,725,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(738,a,726,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))).  [resolve(738,a,727,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(738,a,728,a)].
1.80/2.11	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)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))).  [resolve(738,a,729,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)).  [resolve(738,a,730,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))).  [resolve(738,a,731,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(738,a,733,a)].
1.80/2.11	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))).  [resolve(738,a,734,a)].
1.89/2.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))).  [resolve(738,a,735,a)].
1.89/2.17	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),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))).  [resolve(738,a,737,a)].
1.89/2.17	739 -comm_monoid_add(A) | ti(A,B) = hAPP(A,A,plus_plus(A,zero_zero(A)),B) # label(fact_215_add__0) # label(axiom).  [clausify(109)].
1.89/2.17	740 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
1.89/2.17	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,zero_zero(int)),A).  [resolve(739,a,740,a)].
1.89/2.17	741 comm_monoid_add(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
1.89/2.17	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,zero_zero(real)),A).  [resolve(741,a,739,a)].
1.89/2.17	742 -comm_monoid_add(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),zero_zero(A)) # label(fact_211_add_Ocomm__neutral) # label(axiom).  [clausify(313)].
1.89/2.17	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,A),zero_zero(int)).  [resolve(742,a,740,a)].
1.89/2.17	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,A),zero_zero(real)).  [resolve(742,a,741,a)].
1.89/2.17	743 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
1.89/2.17	Derived: ti(nat,A) = hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),A).  [resolve(743,a,739,a)].
1.89/2.17	Derived: ti(nat,A) = hAPP(nat,nat,plus_plus(nat,A),zero_zero(nat)).  [resolve(743,a,742,a)].
1.89/2.17	744 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
1.89/2.17	745 -linord581940658strict(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) # label(fact_477_sum__squares__gt__zero__iff) # label(axiom).  [clausify(75)].
1.89/2.17	746 -linord581940658strict(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)))) # label(fact_477_sum__squares__gt__zero__iff) # label(axiom).  [clausify(75)].
1.89/2.17	747 -linord581940658strict(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) # label(fact_477_sum__squares__gt__zero__iff) # label(axiom).  [clausify(75)].
1.89/2.17	748 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_492_mult__neg__neg) # label(axiom).  [clausify(175)].
1.89/2.17	Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))).  [resolve(744,a,745,a)].
1.89/2.17	Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)))).  [resolve(744,a,746,a)].
1.89/2.17	Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))).  [resolve(744,a,747,a)].
1.89/2.17	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))).  [resolve(744,a,748,a)].
1.89/2.17	749 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_487_mult__strict__left__mono__neg) # label(axiom).  [clausify(284)].
1.89/2.17	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),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))).  [resolve(749,a,744,a)].
1.89/2.17	750 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_476_mult__le__cancel__left__pos) # label(axiom).  [clausify(325)].
1.89/2.17	751 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_476_mult__le__cancel__left__pos) # label(axiom).  [clausify(325)].
1.89/2.17	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(751,a,744,a)].
1.89/2.17	752 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_488_mult__strict__right__mono__neg) # label(axiom).  [clausify(337)].
1.89/2.17	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),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))).  [resolve(752,a,744,a)].
1.89/2.17	753 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_475_mult__le__cancel__left__neg) # label(axiom).  [clausify(369)].
1.89/2.17	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),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))).  [resolve(753,a,744,a)].
1.89/2.17	754 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_475_mult__le__cancel__left__neg) # label(axiom).  [clausify(369)].
1.89/2.17	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),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))).  [resolve(754,a,744,a)].
1.89/2.17	755 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
1.89/2.17	Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))).  [resolve(755,a,745,a)].
1.89/2.17	Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)))).  [resolve(755,a,746,a)].
1.89/2.17	Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))).  [resolve(755,a,747,a)].
1.89/2.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(755,a,748,a)].
1.89/2.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))).  [resolve(755,a,749,a)].
1.89/2.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(755,a,751,a)].
1.89/2.17	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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),times_times(int),A),C))).  [resolve(755,a,752,a)].
1.89/2.17	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),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(755,a,753,a)].
1.89/2.17	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),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(755,a,754,a)].
2.00/2.29	756 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),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),B),C))) # label(fact_494_mult__less__cancel__left__neg) # label(axiom).  [clausify(475)].
2.00/2.29	757 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),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),B),C))) # label(fact_494_mult__less__cancel__left__neg) # label(axiom).  [clausify(475)].
2.00/2.29	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),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),A),B))).  [resolve(757,a,744,a)].
2.00/2.29	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))).  [resolve(757,a,755,a)].
2.00/2.29	758 -ring_char_0(A) | -number_ring(A) | B != C | number_number_of(A,B) = number_number_of(A,C) # label(fact_40_eq__number__of) # label(axiom).  [clausify(106)].
2.00/2.29	759 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom).  [assumption].
2.00/2.29	Derived: -number_ring(int) | A != B | number_number_of(int,A) = number_number_of(int,B).  [resolve(758,a,759,a)].
2.00/2.29	760 -ring_char_0(A) | -number_ring(A) | B = C | number_number_of(A,B) != number_number_of(A,C) # label(fact_40_eq__number__of) # label(axiom).  [clausify(106)].
2.00/2.29	Derived: -number_ring(int) | A = B | number_number_of(int,A) != number_number_of(int,B).  [resolve(760,a,759,a)].
2.00/2.29	761 ring_char_0(real) # label(arity_RealDef_Oreal___Int_Oring__char__0) # label(axiom).  [assumption].
2.00/2.29	Derived: -number_ring(real) | A != B | number_number_of(real,A) = number_number_of(real,B).  [resolve(761,a,758,a)].
2.00/2.29	Derived: -number_ring(real) | A = B | number_number_of(real,A) != number_number_of(real,B).  [resolve(761,a,760,a)].
2.00/2.29	762 -monoid_mult(A) | one_one(A) = hAPP(nat,A,power_power(A,one_one(A)),B) # label(fact_165_power__one) # label(axiom).  [clausify(154)].
2.00/2.29	763 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom).  [assumption].
2.00/2.29	Derived: one_one(real) = hAPP(nat,real,power_power(real,one_one(real)),A).  [resolve(762,a,763,a)].
2.00/2.29	764 -monoid_mult(A) | ti(A,B) = hAPP(nat,A,power_power(A,B),one_one(nat)) # label(fact_156_power__one__right) # label(axiom).  [clausify(213)].
2.00/2.29	Derived: ti(real,A) = hAPP(nat,real,power_power(real,A),one_one(nat)).  [resolve(764,a,763,a)].
2.00/2.29	765 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom).  [assumption].
2.00/2.29	Derived: one_one(nat) = hAPP(nat,nat,power_power(nat,one_one(nat)),A).  [resolve(765,a,762,a)].
2.00/2.29	Derived: ti(nat,A) = hAPP(nat,nat,power_power(nat,A),one_one(nat)).  [resolve(765,a,764,a)].
2.00/2.29	766 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom).  [assumption].
2.00/2.29	Derived: one_one(int) = hAPP(nat,int,power_power(int,one_one(int)),A).  [resolve(766,a,762,a)].
2.00/2.29	Derived: ti(int,A) = hAPP(nat,int,power_power(int,A),one_one(nat)).  [resolve(766,a,764,a)].
2.00/2.29	767 -linordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_470_mult__right__less__imp__less) # label(axiom).  [clausify(159)].
2.00/2.29	768 linordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.11/2.37	769 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.11/2.37	770 -linordered_semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom).  [clausify(233)].
2.11/2.37	Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)).  [resolve(770,a,768,a)].
2.11/2.37	Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)).  [resolve(770,a,769,a)].
2.11/2.37	771 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.11/2.37	Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)).  [resolve(771,a,770,a)].
2.11/2.37	772 -linordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_468_mult__left__less__imp__less) # label(axiom).  [clausify(489)].
2.11/2.37	773 ordere236663937imp_le(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.11/2.37	774 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_219_add__less__imp__less__right) # label(axiom).  [clausify(98)].
2.11/2.37	775 -ordere236663937imp_le(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,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_235_add__le__cancel__left) # label(axiom).  [clausify(125)].
2.11/2.37	776 -ordere236663937imp_le(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,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_235_add__le__cancel__left) # label(axiom).  [clausify(125)].
2.11/2.37	777 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_240_add__le__imp__le__left) # label(axiom).  [clausify(130)].
2.11/2.37	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,A),B)),hAPP(real,real,plus_plus(real,C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)).  [resolve(773,a,774,a)].
2.11/2.37	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,plus_plus(real,C),A)),hAPP(real,real,plus_plus(real,C),B))).  [resolve(773,a,776,a)].
2.11/2.37	778 -ordere236663937imp_le(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,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_234_add__le__cancel__right) # label(axiom).  [clausify(217)].
2.11/2.37	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,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),C))).  [resolve(778,a,773,a)].
2.11/2.37	779 -ordere236663937imp_le(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,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_234_add__le__cancel__right) # label(axiom).  [clausify(217)].
2.11/2.37	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,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),C))).  [resolve(779,a,773,a)].
2.11/2.37	780 -ordere236663937imp_le(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,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_223_add__less__cancel__left) # label(axiom).  [clausify(224)].
2.11/2.38	781 -ordere236663937imp_le(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,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_223_add__less__cancel__left) # label(axiom).  [clausify(224)].
2.11/2.38	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,plus_plus(real,C),A)),hAPP(real,real,plus_plus(real,C),B))).  [resolve(781,a,773,a)].
2.11/2.38	782 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_224_add__less__cancel__right) # label(axiom).  [clausify(264)].
2.11/2.38	783 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_224_add__less__cancel__right) # label(axiom).  [clausify(264)].
2.11/2.38	784 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_218_add__less__imp__less__left) # label(axiom).  [clausify(297)].
2.11/2.38	785 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_239_add__le__imp__le__right) # label(axiom).  [clausify(321)].
2.11/2.38	786 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.11/2.38	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),B)),hAPP(int,int,plus_plus(int,C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)).  [resolve(786,a,774,a)].
2.11/2.38	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))).  [resolve(786,a,776,a)].
2.11/2.38	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),C))).  [resolve(786,a,778,a)].
2.11/2.38	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),C))).  [resolve(786,a,779,a)].
2.11/2.38	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,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))).  [resolve(786,a,781,a)].
2.11/2.38	787 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.11/2.38	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(787,a,774,a)].
2.11/2.38	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,C),A)),hAPP(nat,nat,plus_plus(nat,C),B))).  [resolve(787,a,775,a)].
2.11/2.38	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,C),A)),hAPP(nat,nat,plus_plus(nat,C),B))).  [resolve(787,a,776,a)].
2.11/2.38	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))).  [resolve(787,a,778,a)].
2.11/2.43	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))).  [resolve(787,a,779,a)].
2.11/2.43	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,C),A)),hAPP(nat,nat,plus_plus(nat,C),B))).  [resolve(787,a,781,a)].
2.11/2.43	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).  [resolve(787,a,783,a)].
2.11/2.43	788 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
2.11/2.43	789 -linord219039673up_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),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(112)].
2.11/2.43	790 -linord219039673up_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),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(112)].
2.11/2.43	791 -linord219039673up_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)),hAPP(A,A,plus_plus(A,B),B))) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(181)].
2.11/2.43	792 -linord219039673up_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)),hAPP(A,A,plus_plus(A,B),B))) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(181)].
2.11/2.43	793 -linord219039673up_add(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),B) | ti(A,B) = zero_zero(A) # label(fact_214_double__zero__sym) # label(axiom).  [clausify(188)].
2.11/2.43	794 -linord219039673up_add(A) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),B) | ti(A,B) != zero_zero(A) # label(fact_214_double__zero__sym) # label(axiom).  [clausify(188)].
2.11/2.43	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,plus_plus(int,A),A)),zero_zero(int))).  [resolve(788,a,790,a)].
2.11/2.43	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)),hAPP(int,int,plus_plus(int,A),A))).  [resolve(788,a,792,a)].
2.11/2.43	Derived: zero_zero(int) != hAPP(int,int,plus_plus(int,A),A) | ti(int,A) = zero_zero(int).  [resolve(788,a,793,a)].
2.11/2.43	Derived: zero_zero(int) = hAPP(int,int,plus_plus(int,A),A) | ti(int,A) != zero_zero(int).  [resolve(788,a,794,a)].
2.11/2.43	795 -linord219039673up_add(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),B) | ti(A,B) = zero_zero(A) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(244)].
2.11/2.43	796 -linord219039673up_add(A) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),B) | ti(A,B) != zero_zero(A) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(244)].
2.11/2.43	797 -linord219039673up_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)),hAPP(A,A,plus_plus(A,B),B))) # label(fact_194_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(388)].
2.11/2.43	798 -linord219039673up_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)),hAPP(A,A,plus_plus(A,B),B))) # label(fact_194_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(388)].
2.11/2.43	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),A))).  [resolve(798,a,788,a)].
2.27/2.55	799 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(474)].
2.27/2.55	800 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(474)].
2.27/2.55	801 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
2.27/2.55	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,plus_plus(real,A),A)),zero_zero(real))).  [resolve(801,a,790,a)].
2.27/2.55	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)),hAPP(real,real,plus_plus(real,A),A))).  [resolve(801,a,792,a)].
2.27/2.55	Derived: zero_zero(real) != hAPP(real,real,plus_plus(real,A),A) | ti(real,A) = zero_zero(real).  [resolve(801,a,793,a)].
2.27/2.55	Derived: zero_zero(real) = hAPP(real,real,plus_plus(real,A),A) | ti(real,A) != zero_zero(real).  [resolve(801,a,794,a)].
2.27/2.55	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,plus_plus(real,A),A))).  [resolve(801,a,798,a)].
2.27/2.55	802 -one(A) | ti(A,one_one(A)) = one_one(A) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(377)].
2.27/2.55	803 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom).  [assumption].
2.27/2.55	Derived: ti(nat,one_one(nat)) = one_one(nat).  [resolve(802,a,803,a)].
2.27/2.55	804 one(real) # label(arity_RealDef_Oreal___Groups_Oone) # label(axiom).  [assumption].
2.27/2.55	Derived: ti(real,one_one(real)) = one_one(real).  [resolve(804,a,802,a)].
2.27/2.55	805 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom).  [assumption].
2.27/2.55	Derived: ti(int,one_one(int)) = one_one(int).  [resolve(805,a,802,a)].
2.27/2.55	806 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom).  [assumption].
2.27/2.55	807 -monoid_add(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),zero_zero(A)) # label(fact_213_add__0__right) # label(axiom).  [clausify(134)].
2.27/2.55	808 -monoid_add(A) | plus_plus(A,ti(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg1) # label(axiom).  [clausify(216)].
2.27/2.55	Derived: plus_plus(int,ti(int,A)) = plus_plus(int,A).  [resolve(808,a,806,a)].
2.27/2.55	809 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom).  [assumption].
2.27/2.55	Derived: plus_plus(nat,ti(nat,A)) = plus_plus(nat,A).  [resolve(809,a,808,a)].
2.27/2.55	810 -monoid_add(A) | ti(A,B) = hAPP(A,A,plus_plus(A,zero_zero(A)),B) # label(fact_217_add__0__left) # label(axiom).  [clausify(331)].
2.27/2.55	811 monoid_add(real) # label(arity_RealDef_Oreal___Groups_Omonoid__add) # label(axiom).  [assumption].
2.27/2.55	Derived: plus_plus(real,ti(real,A)) = plus_plus(real,A).  [resolve(811,a,808,a)].
2.27/2.55	812 -monoid_add(A) | ti(fun(A,A),plus_plus(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(427)].
2.27/2.55	Derived: ti(fun(int,int),plus_plus(int,A)) = plus_plus(int,A).  [resolve(812,a,806,a)].
2.27/2.55	Derived: ti(fun(nat,nat),plus_plus(nat,A)) = plus_plus(nat,A).  [resolve(812,a,809,a)].
2.27/2.55	Derived: ti(fun(real,real),plus_plus(real,A)) = plus_plus(real,A).  [resolve(812,a,811,a)].
2.27/2.55	813 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.27/2.55	814 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),E)) = hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E)) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom).  [clausify(143)].
2.29/2.56	Derived: hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,A),B)),hAPP(real,real,plus_plus(real,C),D)) = hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),D)).  [resolve(813,a,814,a)].
2.29/2.56	815 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,plus_plus(A,zero_zero(A)),B) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom).  [clausify(165)].
2.29/2.56	816 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,power_power(A,B),one_one(nat)) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom).  [clausify(209)].
2.29/2.56	817 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D) = hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),C) # label(fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom).  [clausify(225)].
2.29/2.56	Derived: hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,A),B)),C) = hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,A),C)),B).  [resolve(817,a,813,a)].
2.29/2.56	818 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,B),C) = hAPP(A,A,plus_plus(A,C),B) # label(fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom).  [clausify(252)].
2.29/2.56	Derived: hAPP(real,real,plus_plus(real,A),B) = hAPP(real,real,plus_plus(real,B),A).  [resolve(818,a,813,a)].
2.29/2.56	819 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.29/2.56	Derived: hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,A),B)),hAPP(int,int,plus_plus(int,C),D)) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D)).  [resolve(819,a,814,a)].
2.29/2.56	Derived: hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,A),B)),C) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,A),C)),B).  [resolve(819,a,817,a)].
2.29/2.56	820 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.29/2.56	Derived: hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,C),D)) = hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D)).  [resolve(820,a,814,a)].
2.29/2.56	Derived: hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,A),B)),C) = hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,A),C)),B).  [resolve(820,a,817,a)].
2.29/2.56	Derived: hAPP(nat,nat,plus_plus(nat,A),B) = hAPP(nat,nat,plus_plus(nat,B),A).  [resolve(820,a,818,a)].
2.29/2.56	821 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)) = hAPP(A,A,plus_plus(A,C),hAPP(A,A,plus_plus(A,B),D)) # label(fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom).  [clausify(429)].
2.29/2.56	Derived: hAPP(real,real,plus_plus(real,A),hAPP(real,real,plus_plus(real,B),C)) = hAPP(real,real,plus_plus(real,B),hAPP(real,real,plus_plus(real,A),C)).  [resolve(821,a,813,a)].
2.29/2.56	Derived: hAPP(nat,nat,plus_plus(nat,A),hAPP(nat,nat,plus_plus(nat,B),C)) = hAPP(nat,nat,plus_plus(nat,B),hAPP(nat,nat,plus_plus(nat,A),C)).  [resolve(821,a,820,a)].
2.29/2.56	822 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),zero_zero(A)) # label(fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom).  [clausify(470)].
2.29/2.56	823 -comm_semiring_1(A) | one_one(A) = hAPP(nat,A,power_power(A,B),zero_zero(nat)) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom).  [clausify(471)].
2.29/2.56	824 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D) = hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)) # label(fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom).  [clausify(484)].
2.29/2.56	Derived: hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,A),B)),C) = hAPP(real,real,plus_plus(real,A),hAPP(real,real,plus_plus(real,B),C)).  [resolve(824,a,813,a)].
2.29/2.56	Derived: hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,A),B)),C) = hAPP(int,int,plus_plus(int,A),hAPP(int,int,plus_plus(int,B),C)).  [resolve(824,a,819,a)].
2.29/2.56	Derived: hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,A),B)),C) = hAPP(nat,nat,plus_plus(nat,A),hAPP(nat,nat,plus_plus(nat,B),C)).  [resolve(824,a,820,a)].
2.41/2.68	825 -comm_semiring_1(A) | hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D) = hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)) # label(fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom).  [clausify(490)].
2.41/2.68	826 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.41/2.68	827 -ab_semigroup_add(A) | plus_plus(A,ti(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg1) # label(axiom).  [clausify(161)].
2.41/2.68	828 -ab_semigroup_add(A) | ti(fun(A,A),plus_plus(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(200)].
2.41/2.68	829 ab_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.41/2.68	830 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.41/2.68	831 -ab_semigroup_add(A) | hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D) = hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)) # label(fact_204_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom).  [clausify(375)].
2.41/2.68	832 linordered_ring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring) # label(axiom).  [assumption].
2.41/2.68	833 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) # label(fact_478_not__sum__squares__lt__zero) # label(axiom).  [clausify(162)].
2.41/2.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))).  [resolve(832,a,833,a)].
2.41/2.68	834 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom).  [assumption].
2.41/2.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))).  [resolve(834,a,833,a)].
2.41/2.68	835 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
2.41/2.68	836 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))) # label(fact_237_add__left__mono) # label(axiom).  [clausify(166)].
2.41/2.68	837 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_236_add__right__mono) # label(axiom).  [clausify(258)].
2.41/2.68	838 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))) # label(fact_238_add__mono) # label(axiom).  [clausify(366)].
2.41/2.68	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))).  [resolve(835,a,838,a)].
2.41/2.68	839 ordere779506340up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
2.41/2.68	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,plus_plus(real,C),A)),hAPP(real,real,plus_plus(real,C),B))).  [resolve(839,a,836,a)].
2.41/2.68	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),D))).  [resolve(839,a,838,a)].
2.48/2.76	840 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
2.48/2.76	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),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D))).  [resolve(840,a,838,a)].
2.48/2.76	841 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) | B = C # label(fact_157_of__nat__eq__iff) # label(axiom).  [clausify(300)].
2.48/2.76	842 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.48/2.76	843 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.48/2.76	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B.  [resolve(841,a,842,a)].
2.48/2.76	Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B.  [resolve(841,a,843,a)].
2.48/2.76	844 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) | B != C # label(fact_157_of__nat__eq__iff) # label(axiom).  [clausify(300)].
2.48/2.76	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B.  [resolve(844,a,842,a)].
2.48/2.76	Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B.  [resolve(844,a,843,a)].
2.48/2.76	845 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.48/2.76	846 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
2.48/2.76	847 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,plus_plus(A,D),B) = hAPP(A,A,plus_plus(A,D),C) # label(fact_202_add__left__cancel) # label(axiom).  [clausify(178)].
2.48/2.76	848 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,plus_plus(A,D),B) != hAPP(A,A,plus_plus(A,D),C) # label(fact_202_add__left__cancel) # label(axiom).  [clausify(178)].
2.48/2.76	849 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,plus_plus(A,B),D) = hAPP(A,A,plus_plus(A,C),D) # label(fact_201_add__right__cancel) # label(axiom).  [clausify(192)].
2.48/2.76	850 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,plus_plus(A,B),D) != hAPP(A,A,plus_plus(A,C),D) # label(fact_201_add__right__cancel) # label(axiom).  [clausify(192)].
2.48/2.76	Derived: ti(real,A) != ti(real,B) | hAPP(real,real,plus_plus(real,C),A) = hAPP(real,real,plus_plus(real,C),B).  [resolve(846,a,847,a)].
2.48/2.76	Derived: ti(real,A) != ti(real,B) | hAPP(real,real,plus_plus(real,A),C) = hAPP(real,real,plus_plus(real,B),C).  [resolve(846,a,849,a)].
2.48/2.76	Derived: ti(real,A) = ti(real,B) | hAPP(real,real,plus_plus(real,A),C) != hAPP(real,real,plus_plus(real,B),C).  [resolve(846,a,850,a)].
2.48/2.76	851 -cancel_semigroup_add(A) | ti(fun(A,A),plus_plus(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom).  [clausify(286)].
2.48/2.76	852 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
2.48/2.76	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,plus_plus(int,C),A) = hAPP(int,int,plus_plus(int,C),B).  [resolve(852,a,847,a)].
2.48/2.76	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,plus_plus(int,A),C) = hAPP(int,int,plus_plus(int,B),C).  [resolve(852,a,849,a)].
2.48/2.76	Derived: ti(int,A) = ti(int,B) | hAPP(int,int,plus_plus(int,A),C) != hAPP(int,int,plus_plus(int,B),C).  [resolve(852,a,850,a)].
2.48/2.76	853 -cancel_semigroup_add(A) | plus_plus(A,ti(A,B)) = plus_plus(A,B) # label(tsy_c_Groups_Oplus__class_Oplus_2_arg1) # label(axiom).  [clausify(385)].
2.48/2.76	854 -cancel_semigroup_add(A) | hAPP(A,A,plus_plus(A,B),C) != hAPP(A,A,plus_plus(A,D),C) | ti(A,B) = ti(A,D) # label(fact_197_add__right__imp__eq) # label(axiom).  [clausify(453)].
2.48/2.76	855 -cancel_semigroup_add(A) | hAPP(A,A,plus_plus(A,B),C) != hAPP(A,A,plus_plus(A,B),D) | ti(A,C) = ti(A,D) # label(fact_199_add__left__imp__eq) # label(axiom).  [clausify(497)].
9.71/10.00	856 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
9.71/10.00	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,plus_plus(nat,C),A) = hAPP(nat,nat,plus_plus(nat,C),B).  [resolve(856,a,847,a)].
9.71/10.00	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,plus_plus(nat,A),C) = hAPP(nat,nat,plus_plus(nat,B),C).  [resolve(856,a,849,a)].
9.71/10.00	Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,nat,plus_plus(nat,A),C) != hAPP(nat,nat,plus_plus(nat,B),C).  [resolve(856,a,850,a)].
9.71/10.00	
9.71/10.00	============================== end predicate elimination =============
9.71/10.00	
9.71/10.00	Auto_denials:  (non-Horn, no changes).
9.71/10.00	
9.71/10.00	Term ordering decisions:
9.71/10.00	Function symbol KB weights:  int=1. nat=1. bool=1. real=1. pls=1. bit1=1. bit0=1. succ=1. sqrt=1. n=1. fFalse=1. fTrue=1. t=1. m1=1. tn=1. fun=1. plus_plus=1. number_number_of=1. power_power=1. ti=1. f3=1. f5=1. f6=1. f26=1. f35=1. f36=1. f37=1. f39=1. f40=1. f44=1. f45=1. f46=1. ord_less=1. ord_less_eq=1. zero_zero=1. one_one=1. semiring_1_of_nat=1. times_times=1. if=1. undefined=1. f1=1. f2=1. f7=1. f20=1. f21=1. f22=1. f31=1. f38=1. f4=1. f12=1. f13=1. f14=1. f17=1. f18=1. f34=1. hAPP=1. f19=1. f23=1. f41=1. f8=1. f9=1. f10=1. f11=1. f15=1. f16=1. f24=1. f25=1. f27=1. f28=1. f29=1. f30=1. f32=1. f33=1. f42=1. f43=1.
9.71/10.00	
9.71/10.00	============================== end of process initial clauses ========
9.71/10.00	
9.71/10.00	============================== CLAUSES FOR SEARCH ====================
9.71/10.00	
9.71/10.00	============================== end of clauses for search =============
9.71/10.00	
9.71/10.00	============================== SEARCH ================================
9.71/10.00	
9.71/10.00	% Starting search at 1.48 seconds.
9.71/10.00	
9.71/10.00	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 1.80 sec).
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9.71/10.00	Low Water (displace): id=22728, wt=17.000
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9.71/10.00	Low Water (keep): wt=24.000, iters=3393
71.64/71.94	
71.64/71.94	Low Water (displace): id=24563, wt=16.000
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71.64/71.94	Low Water (displace): id=27914, wt=15.000
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71.64/71.94	Low Water (keep): wt=23.000, iters=3367
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71.64/71.94	Low Water (keep): wt=22.000, iters=3333
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71.64/71.94	Low Water (keep): wt=21.000, iters=3378
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71.64/71.94	Low Water (displace): id=51733, wt=14.000
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71.64/71.94	Low Water (displace): id=51791, wt=13.000
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71.64/71.94	Low Water (displace): id=52248, wt=12.000
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71.64/71.94	Low Water (keep): wt=20.000, iters=3335
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71.64/71.94	Low Water (keep): wt=19.000, iters=3333
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71.64/71.94	Low Water (keep): wt=18.000, iters=3333
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71.64/71.94	Low Water (keep): wt=17.000, iters=3333
71.64/71.94	
71.64/71.94	============================== PROOF =================================
71.64/71.94	% SZS status Theorem
71.64/71.94	% SZS output start Refutation
71.64/71.94	
71.64/71.94	% Proof 1 at 68.81 (+ 1.71) seconds.
71.64/71.94	% Length of proof is 61.
71.64/71.94	% Level of proof is 8.
71.64/71.94	% Maximum clause weight is 44.000.
71.64/71.94	% Given clauses 13511.
71.64/71.94	
71.64/71.94	21 (all B_1_1 all X_a (number(X_a) -> number_number_of(X_a,B_1_1) = number_number_of(X_a,ti(int,B_1_1)))) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	24 (all Wa all Z_2 ((exists N_1 Z_2 = hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z_2)))) # label(fact_294_zle__iff__zadd) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	32 (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_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	43 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> zero_zero(X_a) != hAPP(nat,X_a,power_power(X_a,A_1),N))))) # label(fact_164_field__power__not__zero) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	69 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M hAPP(nat,int,semiring_1_of_nat(int),M) != Z_1))) # label(fact_376_nonneg__eq__int) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	123 (all K hAPP(int,int,plus_plus(int,K),one_one(int)) = hAPP(int,int,succ,K)) # label(fact_320_succ__def) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	163 (all X_a (ordere216010020id_add(X_a) -> (all Ya all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ya)) -> (ti(X_a,Xa) = zero_zero(X_a) & ti(X_a,Ya) = zero_zero(X_a) <-> hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya) = zero_zero(X_a))))))) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	270 (all X_a (number_semiring(X_a) -> one_one(X_a) = number_number_of(X_a,hAPP(int,int,bit1,pls)))) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	368 (all Ma all Na (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(nat,int,semiring_1_of_nat(int),Na) <-> Na = Ma)) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	390 (all K hAPP(int,int,plus_plus(int,pls),K) = K) # label(fact_76_add__Pls) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	420 (all K K = number_number_of(int,K)) # label(fact_119_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	431 (all Z_1 all W_1 hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1)) # label(fact_47_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
71.64/71.94	504 -(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
71.64/71.94	672 -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)) | ti(A,C) = zero_zero(A) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(163)].
71.64/71.94	673 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
71.64/71.94	691 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
71.64/71.94	694 -number_semiring(A) | one_one(A) = number_number_of(A,hAPP(int,int,bit1,pls)) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom).  [clausify(270)].
71.64/71.94	697 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom).  [assumption].
71.64/71.94	698 -number(A) | number_number_of(A,ti(int,B)) = number_number_of(A,B) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom).  [clausify(21)].
71.64/71.94	707 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
71.64/71.94	710 -ring_11004092258visors(A) | ti(A,B) = zero_zero(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) # label(fact_164_field__power__not__zero) # label(axiom).  [clausify(43)].
71.64/71.94	861 number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_104_transfer__int__nat__numerals_I3_J) # label(axiom).  [assumption].
71.64/71.94	862 hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))).  [copy(861),flip(a)].
71.64/71.94	883 hAPP(int,int,plus_plus(int,A),hAPP(nat,int,semiring_1_of_nat(int),B)) != C | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) # label(fact_294_zle__iff__zadd) # label(axiom).  [clausify(24)].
71.64/71.94	888 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) # label(fact_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom).  [clausify(32)].
71.64/71.94	936 -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),f7(A)) = A # label(fact_376_nonneg__eq__int) # label(axiom).  [clausify(69)].
71.64/71.94	998 hAPP(int,int,plus_plus(int,A),one_one(int)) = hAPP(int,int,succ,A) # label(fact_320_succ__def) # label(axiom).  [clausify(123)].
71.64/71.94	1088 pls = zero_zero(int) # label(fact_73_Pls__def) # label(axiom).  [assumption].
71.64/71.94	1227 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))) # label(fact_286_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) # label(axiom).  [assumption].
71.64/71.94	1249 hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B # label(fact_48_int__int__eq) # label(axiom).  [clausify(368)].
71.64/71.94	1271 hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) # label(fact_29_nat__1__add__1) # label(axiom).  [assumption].
71.64/71.94	1272 number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,zero_zero(int)))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)).  [copy(1271),rewrite([1088(17)]),flip(a)].
71.64/71.94	1273 hAPP(int,int,plus_plus(int,pls),A) = A # label(fact_76_add__Pls) # label(axiom).  [clausify(390)].
71.64/71.94	1274 hAPP(int,int,plus_plus(int,zero_zero(int)),A) = A.  [copy(1273),rewrite([1088(4)])].
71.64/71.94	1279 one_one(int) != zero_zero(int) # label(fact_74_int__0__neq__1) # label(axiom).  [assumption].
71.64/71.94	1307 number_number_of(int,A) = A # label(fact_119_number__of__is__id) # label(axiom).  [clausify(420)].
71.64/71.94	1320 hAPP(int,int,plus_plus(int,A),B) = hAPP(int,int,plus_plus(int,B),A) # label(fact_47_zadd__commute) # label(axiom).  [clausify(431)].
71.64/71.94	1401 zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(conj_0) # label(negated_conjecture).  [clausify(504)].
71.64/71.94	1402 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) = zero_zero(int).  [copy(1401),rewrite([1088(27),1272(31)]),flip(a)].
71.64/71.94	1786 -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)) | ti(int,B) = zero_zero(int) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),B).  [resolve(673,a,672,a)].
71.64/71.95	1787 -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)) | ti(int,B) = zero_zero(int) | hAPP(int,int,plus_plus(int,A),B) != zero_zero(int).  [copy(1786),flip(d)].
71.64/71.95	1832 one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)).  [resolve(694,a,691,a)].
71.64/71.95	1833 hAPP(int,int,bit1,zero_zero(int)) = one_one(int).  [copy(1832),rewrite([1088(7),1307(10)]),flip(a)].
71.64/71.95	1843 number_number_of(int,ti(int,A)) = number_number_of(int,A).  [resolve(697,a,698,a)].
71.64/71.95	1844 ti(int,A) = A.  [copy(1843),rewrite([1307(4),1307(4)])].
71.64/71.95	1866 ti(int,A) = zero_zero(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B).  [resolve(707,a,710,a)].
71.64/71.95	1867 zero_zero(int) = A | hAPP(nat,int,power_power(int,A),B) != zero_zero(int).  [copy(1866),rewrite([1844(2)]),flip(a),flip(b)].
71.64/71.95	2084 hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = hAPP(int,int,bit0,one_one(int)).  [back_rewrite(862),rewrite([1088(12),1833(14),1088(21),1833(23),1307(21)])].
71.64/71.95	2132 hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))).  [back_rewrite(1272),rewrite([1833(10)]),flip(a)].
71.64/71.95	2147 -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) = B | hAPP(int,int,plus_plus(int,A),B) != zero_zero(int).  [back_rewrite(1787),rewrite([1844(28)]),flip(c)].
71.64/71.95	2272 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = zero_zero(int).  [back_rewrite(1402),rewrite([2132(26)])].
71.64/71.95	2286 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,plus_plus(int,A),hAPP(nat,int,semiring_1_of_nat(int),B)))).  [xx_res(883,a)].
71.64/71.95	2312 hAPP(nat,int,semiring_1_of_nat(int),f7(hAPP(nat,int,semiring_1_of_nat(int),A))) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(936,a,888,a)].
71.64/71.95	3190 hAPP(int,int,plus_plus(int,one_one(int)),A) = hAPP(int,int,succ,A).  [para(1320(a,1),998(a,1))].
71.64/71.95	3210 hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = zero_zero(int).  [back_rewrite(2272),rewrite([3190(16)])].
71.64/71.95	6419 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,succ,A) != zero_zero(int).  [resolve(2147,b,1227,a),rewrite([998(25)]),flip(b),unit_del(b,1279)].
71.64/71.95	8173 hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),A)) != zero_zero(int).  [resolve(6419,a,2286,a),rewrite([1274(15)])].
71.64/71.95	8665 f7(hAPP(nat,int,semiring_1_of_nat(int),A)) = A.  [resolve(2312,a,1249,a)].
71.64/71.95	8677 number_number_of(nat,hAPP(int,int,bit0,one_one(int))) = f7(hAPP(int,int,bit0,one_one(int))).  [para(2084(a,1),8665(a,1,1)),flip(a)].
71.64/71.95	8996 hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),f7(hAPP(int,int,bit0,one_one(int)))) = zero_zero(int).  [back_rewrite(3210),rewrite([8677(22)])].
71.64/71.95	92063 $F.  [resolve(8996,a,1867,b),flip(a),unit_del(a,8173)].
71.64/71.95	
71.64/71.95	% SZS output end Refutation
71.64/71.95	============================== end of proof ==========================
71.64/71.95	
71.64/71.95	============================== STATISTICS ============================
71.64/71.95	
71.64/71.95	Given=13511. Generated=3094565. Kept=90868. proofs=1.
71.64/71.95	Usable=12839. Sos=9999. Demods=555. Limbo=0, Disabled=69394. Hints=0.
71.64/71.95	Megabytes=128.63.
71.64/71.95	User_CPU=68.82, System_CPU=1.71, Wall_clock=70.
71.64/71.95	
71.64/71.95	============================== end of statistics =====================
71.64/71.95	
71.64/71.95	============================== end of search =========================
71.64/71.95	
71.64/71.95	THEOREM PROVED
71.64/71.95	% SZS status Theorem
71.64/71.95	
71.64/71.95	Exiting with 1 proof.
71.64/71.95	
71.64/71.95	Process 11712 exit (max_proofs) Tue Jul 13 16:28:15 2021
71.64/71.95	Prover9 interrupted
71.64/71.95	EOF