0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n008.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 960
0.13/0.34	% DateTime   : Thu Jul  2 06:42:29 EDT 2020
0.13/0.34	% CPUTime    : 
1.41/1.72	============================== Prover9 ===============================
1.41/1.72	Prover9 (32) version 2009-11A, November 2009.
1.41/1.72	Process 25054 was started by sandbox2 on n008.cluster.edu,
1.41/1.72	Thu Jul  2 06:42:30 2020
1.41/1.72	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_24855_n008.cluster.edu".
1.41/1.72	============================== end of head ===========================
1.41/1.72	
1.41/1.72	============================== INPUT =================================
1.41/1.72	
1.41/1.72	% Reading from file /tmp/Prover9_24855_n008.cluster.edu
1.41/1.72	
1.41/1.72	set(prolog_style_variables).
1.41/1.72	set(auto2).
1.41/1.72	    % set(auto2) -> set(auto).
1.41/1.72	    % set(auto) -> set(auto_inference).
1.41/1.72	    % set(auto) -> set(auto_setup).
1.41/1.72	    % set(auto_setup) -> set(predicate_elim).
1.41/1.72	    % set(auto_setup) -> assign(eq_defs, unfold).
1.41/1.72	    % set(auto) -> set(auto_limits).
1.41/1.72	    % set(auto_limits) -> assign(max_weight, "100.000").
1.41/1.72	    % set(auto_limits) -> assign(sos_limit, 20000).
1.41/1.72	    % set(auto) -> set(auto_denials).
1.41/1.72	    % set(auto) -> set(auto_process).
1.41/1.72	    % set(auto2) -> assign(new_constants, 1).
1.41/1.72	    % set(auto2) -> assign(fold_denial_max, 3).
1.41/1.72	    % set(auto2) -> assign(max_weight, "200.000").
1.41/1.72	    % set(auto2) -> assign(max_hours, 1).
1.41/1.72	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.41/1.72	    % set(auto2) -> assign(max_seconds, 0).
1.41/1.72	    % set(auto2) -> assign(max_minutes, 5).
1.41/1.72	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.41/1.72	    % set(auto2) -> set(sort_initial_sos).
1.41/1.72	    % set(auto2) -> assign(sos_limit, -1).
1.41/1.72	    % set(auto2) -> assign(lrs_ticks, 3000).
1.41/1.72	    % set(auto2) -> assign(max_megs, 400).
1.41/1.72	    % set(auto2) -> assign(stats, some).
1.41/1.72	    % set(auto2) -> clear(echo_input).
1.41/1.72	    % set(auto2) -> set(quiet).
1.41/1.72	    % set(auto2) -> clear(print_initial_clauses).
1.41/1.72	    % set(auto2) -> clear(print_given).
1.41/1.72	assign(lrs_ticks,-1).
1.41/1.72	assign(sos_limit,10000).
1.41/1.72	assign(order,kbo).
1.41/1.72	set(lex_order_vars).
1.41/1.72	clear(print_given).
1.41/1.72	
1.41/1.72	% formulas(sos).  % not echoed (660 formulas)
1.41/1.72	
1.41/1.72	============================== end of input ==========================
1.41/1.72	
1.41/1.72	% From the command line: assign(max_seconds, 960).
1.41/1.72	
1.41/1.72	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.41/1.72	
1.41/1.72	% Formulas that are not ordinary clauses:
1.41/1.72	1 (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(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1))))) # label(fact_53_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	2 (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].
1.41/1.72	3 (all X_a if(X_a) = ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))) # label(tsy_c_If_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	4 (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].
1.41/1.72	5 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),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))))))) # label(fact_18_less__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	6 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))))) # label(fact_283_less__eq__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	7 (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].
1.41/1.72	8 (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].
1.41/1.72	9 (all N (zero_zero(nat) != N -> 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].
1.41/1.72	10 (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].
1.41/1.72	11 (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 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hAPP(nat,nat,plus_plus(nat,I_2),K_1) = J_2)))) # label(fact_191_less__imp__add__positive) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	12 (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].
1.41/1.72	13 (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),C_1) = hAPP(X_a,X_a,plus_plus(X_a,A_1),B) -> ti(X_a,B) = ti(X_a,C_1))))) # label(fact_199_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	14 (all Ma all Na (Ma = Na <-> hAPP(nat,int,semiring_1_of_nat(int),Na) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	15 (all K number_number_of(int,K) = K) # label(fact_119_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	16 (all X_a all B_1_1 all B_2 hAPP(X_a,X_a,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_a,B_1_1,B_2)) # label(tsy_c_hAPP_4_arg2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	17 (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].
1.41/1.72	18 (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].
1.41/1.72	19 (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].
1.41/1.72	20 (all Ma all Na (hAPP(nat,nat,plus_plus(nat,Ma),Na) = zero_zero(nat) <-> zero_zero(nat) = Ma & Na = zero_zero(nat))) # label(fact_153_add__is__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	21 (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,C),A_2) = hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2))))) # label(fact_201_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	22 (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].
1.41/1.72	23 (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),pls)) <-> 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))))))) # label(fact_49_less__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	24 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> zero_zero(nat) != N)) # label(fact_139_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	25 (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].
1.41/1.72	26 (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].
1.41/1.72	27 (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].
1.41/1.72	28 (all K_2 all 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))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_2),L_1)))) # label(fact_256_less__eq__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	29 (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].
1.41/1.72	30 (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)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) <-> ti(X_a,Xa) = ti(X_a,Ya)))))) # label(fact_396_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	31 (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].
1.41/1.72	32 (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].
1.41/1.72	33 (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].
1.41/1.72	34 (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].
1.41/1.72	35 (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].
1.41/1.72	36 (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,power_power(nat,M_1),N)) = hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),N)))) # label(fact_171_of__nat__power) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	37 (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),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(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_235_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	38 (all X_a all B_1_1 all B_2 hAPP(X_a,X_a,ti(fun(X_a,X_a),B_1_1),B_2) = hAPP(X_a,X_a,B_1_1,B_2)) # label(tsy_c_hAPP_4_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	39 (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].
1.41/1.72	40 (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].
1.41/1.72	41 (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].
1.41/1.72	42 (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].
1.41/1.72	43 (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].
1.41/1.72	44 (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].
1.41/1.72	45 (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].
1.41/1.72	46 (all X_a (comm_semiring_1(X_a) -> (all X one_one(X_a) = hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat))))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	47 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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_281_rel__simps_I22_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	48 (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].
1.41/1.72	49 (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].
1.41/1.72	50 (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(int),number_number_of(int,K_2)),number_number_of(int,L_1))))) # label(fact_16_less__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	51 (all V_1 ((-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)),one_one(nat)) = 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,number_number_of(nat,V_1)),one_one(nat)) = one_one(nat)))) # label(fact_232_nat__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	52 (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_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].
1.41/1.72	53 (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_20_zpower__int) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	54 (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].
1.41/1.72	55 (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].
1.41/1.72	56 (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].
1.41/1.72	57 (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].
1.41/1.72	58 (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].
1.41/1.72	59 (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].
1.41/1.72	60 (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].
1.41/1.72	61 (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].
1.41/1.72	62 (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].
1.41/1.72	63 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_242_less__eq__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.72	64 (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].
1.41/1.72	65 (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].
1.41/1.72	66 (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].
1.41/1.72	67 (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].
1.41/1.72	68 (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].
1.41/1.72	69 (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].
1.41/1.73	70 (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].
1.41/1.73	71 (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].
1.41/1.73	72 (all Xa all Wa (number_number_of(nat,Wa) = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) <-> 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)))))) # label(fact_148_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	73 (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_21_int__power) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	74 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> -(all N_1 K != hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_341_nonneg__int__cases) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	75 (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].
1.41/1.73	76 (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].
1.41/1.73	77 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_311_less__eq__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	78 (all K all L hAPP(int,int,bit1,L) != hAPP(int,int,bit0,K)) # label(fact_69_rel__simps_I49_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	79 (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),A_2),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_2),A_2)),zero_zero(X_a))))))) # label(fact_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	80 (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].
1.41/1.73	81 (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].
1.41/1.73	82 (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),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,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C))))))) # label(fact_224_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	83 (all Ma all Na (Ma != 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)))) # label(fact_120_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	84 (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].
1.41/1.73	85 (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].
1.41/1.73	86 (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) = hAPP(X_a,X_b,ti(fun(X_a,X_b),B_1_1),B_2))) # label(tsy_c_hAPP_0_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	87 (all Ma all Na (Na != Ma & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_349_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	88 (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].
1.41/1.73	89 (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].
1.41/1.73	90 (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].
1.41/1.73	91 (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(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1))))) # label(fact_31_rel__simps_I17_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	92 (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].
1.41/1.73	93 (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,B) = ti(X_a,A_1)))))))) # label(fact_321_power__eq__imp__eq__base) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	94 (all X_a (semiring_1(X_a) -> ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	95 (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].
1.41/1.73	96 (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].
1.41/1.73	97 (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].
1.41/1.73	98 (all X_a (comm_semiring_1(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_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	99 (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].
1.41/1.73	100 (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].
1.41/1.73	101 (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_eq(int),hAPP(int,int,bit1,K_2)),pls)))) # label(fact_307_rel__simps_I29_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	102 (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].
1.41/1.73	103 (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].
1.41/1.73	104 (all Z1 all Z2 all Z3 hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3)) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)) # label(fact_45_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	105 (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].
1.41/1.73	106 (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].
1.41/1.73	107 (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].
1.41/1.73	108 (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].
1.41/1.73	109 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2))))) # label(fact_65_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	110 (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].
1.41/1.73	111 (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].
1.41/1.73	112 (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),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))))))) # label(fact_476_mult__le__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	113 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_156_power__one__right) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	114 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_163_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	115 (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].
1.41/1.73	116 (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].
1.41/1.73	117 (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_eq(X_a),number_number_of(X_a,Va)),number_number_of(X_a,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))))))) # label(fact_275_le__number__of__eq__not__less) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	118 (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].
1.41/1.73	119 (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].
1.41/1.73	120 (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].
1.41/1.73	121 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int))))) # label(fact_56_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	122 (all M_1 all N (N = M_1 | 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_345_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	123 (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].
1.41/1.73	124 (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].
1.41/1.73	125 (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].
1.41/1.73	126 (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].
1.41/1.73	127 (all X_a (semiri456707255roduct(X_a) -> (all B_1 all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> ti(X_a,B_1) = hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2))))) # label(fact_210_add__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	128 (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 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R)) & A_1 = hAPP(nat,real,power_power(real,R),N)))))) # label(fact_230_realpow__pos__nth) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	129 (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,hAPP(int,int,plus_plus(int,V_1),W_1))),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))))) # label(fact_87_add__number__of__left) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	130 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya))))) # label(fact_486_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	131 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)) <-> Ya = Xa | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)))) # label(fact_355_less__eq__real__def) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	132 (all Xa all Na (zero_zero(nat) = Na | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na))))) # label(fact_142_nat__zero__less__power__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	133 (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].
1.41/1.73	134 (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].
1.41/1.73	135 (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].
1.41/1.73	136 (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(int),pls),hAPP(int,int,bit1,K_2))))) # label(fact_306_rel__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	137 (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].
1.41/1.73	138 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int))))) # label(fact_58_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	139 (all Va (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls)) <-> zero_zero(nat) = number_number_of(nat,Va))) # label(fact_305_eq__number__of__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	140 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_151_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	141 (all K K = hAPP(int,int,plus_plus(int,pls),K)) # label(fact_76_add__Pls) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	142 (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),B)),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)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	143 (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].
1.41/1.73	144 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_245_less__eq__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	145 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	146 (all K_2 all Ma all Na (hAPP(nat,nat,plus_plus(nat,K_2),Na) = hAPP(nat,nat,plus_plus(nat,K_2),Ma) <-> Na = Ma)) # label(fact_124_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	147 (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_304_eq__0__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	148 (all K hAPP(int,int,plus_plus(int,K),K) = hAPP(int,int,bit0,K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	149 (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].
1.41/1.73	150 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_402_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	151 (all X_a (semiring_1(X_a) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)))) # label(fact_187_of__nat__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	152 (all X_a (number_ring(X_a) & linordered_idom(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].
1.41/1.73	153 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> ti(X_a,A_2) != zero_zero(X_a))))) # label(fact_95_zero__less__power2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	154 (all X_a (semiring_0(X_a) & power(X_a) -> (all W_1 ((zero_zero(nat) = number_number_of(nat,W_1) -> hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1)) = one_one(X_a)) & (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].
1.41/1.73	155 (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,zero_zero(X_a)),A_1)))) # label(fact_215_add__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	156 (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_417_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	157 (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].
1.41/1.73	158 (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].
1.41/1.73	159 (all X_a (comm_semiring_1(X_a) -> (all X ti(X_a,X) = hAPP(nat,X_a,power_power(X_a,X),one_one(nat))))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	160 (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].
1.41/1.73	161 (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),B_1) = hAPP(X_a,X_a,plus_plus(X_a,A_2),C))))) # label(fact_202_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	162 (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].
1.41/1.73	163 (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].
1.41/1.73	164 (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].
1.41/1.73	165 (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].
1.41/1.73	166 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all Na (zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,A_2),Na) <-> ti(X_a,A_2) = zero_zero(X_a) & Na != zero_zero(nat))))) # label(fact_184_power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	167 (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].
1.41/1.73	168 (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].
1.41/1.73	169 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> 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))))))) # label(fact_44_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	170 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (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))) <-> zero_zero(X_a) = ti(X_a,Xa) & ti(X_a,Ya) = zero_zero(X_a))))) # label(fact_336_sum__power2__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	171 (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),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_223_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	172 (all B_1_1 all X_a (cancel_semigroup_add(X_a) -> plus_plus(X_a,B_1_1) = plus_plus(X_a,ti(X_a,B_1_1)))) # label(tsy_c_Groups_Oplus__class_Oplus_2_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	173 (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].
1.41/1.73	174 (all K_2 all L_1 (hAPP(int,int,bit1,L_1) = hAPP(int,int,bit1,K_2) <-> L_1 = K_2)) # label(fact_42_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	175 (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(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(nat),Xa),Ya))))))) # label(fact_181_power__strict__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	176 (all X_a (ord(X_a) -> ord_less(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	177 (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].
1.41/1.73	178 (all B_1_1 all X_a (cancel_semigroup_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_2_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	179 (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].
1.41/1.73	180 (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].
1.41/1.73	181 (all X_a (order(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_427_order__less__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	182 (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].
1.41/1.73	183 (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].
1.41/1.73	184 (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].
1.41/1.73	185 (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].
1.41/1.73	186 (all M_1 all N (M_1 = hAPP(nat,nat,plus_plus(nat,M_1),N) -> N = zero_zero(nat))) # label(fact_152_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	187 (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].
1.41/1.73	188 (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,bit0,K_2)),pls)))) # label(fact_54_rel__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.73	189 (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].
1.41/1.73	190 (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].
1.41/1.73	191 (all X_a all B_1_1 all 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)) = 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].
1.41/1.74	192 (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].
1.41/1.74	193 (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].
1.41/1.74	194 (all V_2 all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> number_number_of(nat,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)) -> (-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,hAPP(int,int,plus_plus(int,V_1),V_2))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> number_number_of(nat,V_1) = hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2)))))) # label(fact_36_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	195 (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].
1.41/1.74	196 (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].
1.41/1.74	197 (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].
1.41/1.74	198 (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].
1.41/1.74	199 (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].
1.41/1.74	200 (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].
1.41/1.74	201 (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].
1.41/1.74	202 (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)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)))))) # label(fact_425_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	203 (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].
1.41/1.74	204 (all L_1 (pls = hAPP(int,int,bit0,L_1) <-> pls = L_1)) # label(fact_71_rel__simps_I38_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	205 (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].
1.41/1.74	206 (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].
1.41/1.74	207 (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].
1.41/1.74	208 (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,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)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),Na))))))) # label(fact_375_ex__least__nat__less) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	209 (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].
1.41/1.74	210 (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].
1.41/1.74	211 (all K all L hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L))) # label(fact_91_add__Bit0__Bit1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	212 (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].
1.41/1.74	213 (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].
1.41/1.74	214 (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,bit0,L_1))))) # label(fact_246_rel__simps_I31_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	215 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2))))) # label(fact_214_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	216 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls)) = ti(X_a,A_1)))) # label(fact_85_add__numeral__0__right) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	217 (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].
1.41/1.74	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),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].
1.41/1.74	219 (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),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),B_1),A_2))))))) # label(fact_475_mult__le__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	220 (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].
1.41/1.74	221 (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].
1.41/1.74	222 (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].
1.41/1.74	223 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	224 (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].
1.41/1.74	225 (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].
1.41/1.74	226 (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].
1.41/1.74	227 (all Na (zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),Na) <-> Na = zero_zero(nat))) # label(fact_27_int__eq__0__conv) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	228 (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)) -> (hAPP(nat,X_a,power_power(X_a,A_2),Ma) = hAPP(nat,X_a,power_power(X_a,A_2),Na) <-> Ma = Na))))) # label(fact_180_power__inject__exp) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	229 (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].
1.41/1.74	230 (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].
1.41/1.74	231 (all K K = hAPP(int,int,plus_plus(int,K),pls)) # label(fact_75_add__Pls__right) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	232 (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].
1.41/1.74	233 (all Va all 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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,Va)),number_number_of(nat,V))))) # label(fact_371_le__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	234 (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].
1.41/1.74	235 (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].
1.41/1.74	236 (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].
1.41/1.74	237 (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)) -> 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,succ,V_1)))))) # label(fact_296_semiring__number__of__add__1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	238 (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].
1.41/1.74	239 (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].
1.41/1.74	240 (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].
1.41/1.74	241 (all Z_2 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)) <-> Wa != Z_2 & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa)))) # label(fact_254_zless__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	242 (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].
1.41/1.74	243 (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].
1.41/1.74	244 (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].
1.41/1.74	245 (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].
1.41/1.74	246 (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].
1.41/1.74	247 (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].
1.41/1.74	248 (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].
1.41/1.74	249 (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].
1.41/1.74	250 (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].
1.41/1.74	251 (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(P_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa))))) # label(fact_373_conj__le__cong) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	252 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_211_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	253 (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].
1.41/1.74	254 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	255 (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].
1.41/1.74	256 (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].
1.41/1.74	257 (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].
1.41/1.74	258 (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].
1.41/1.74	259 (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].
1.41/1.74	260 (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)),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)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)))))) # label(fact_447_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	261 (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].
1.41/1.74	262 (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].
1.41/1.74	263 (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].
1.41/1.74	264 (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].
1.41/1.74	265 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> 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].
1.41/1.74	266 (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].
1.41/1.74	267 (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].
1.41/1.74	268 (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].
1.41/1.74	269 (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_414_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	270 (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].
1.41/1.74	271 (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].
1.41/1.74	272 (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),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].
1.41/1.74	273 (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].
1.41/1.74	274 (all X_a all B_1_1 all 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) = hAPP(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].
1.41/1.74	275 (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)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> ti(X_a,Ya) = ti(X_a,Xa)))))) # label(fact_437_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	276 (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].
1.41/1.74	277 (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].
1.41/1.74	278 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_440_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	279 (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].
1.41/1.74	280 (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].
1.41/1.74	281 (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].
1.41/1.74	282 (all K_2 (pls = hAPP(int,int,bit0,K_2) <-> K_2 = pls)) # label(fact_70_rel__simps_I44_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	283 (all X_a (number_ring(X_a) -> (all K number_number_of(X_a,hAPP(int,int,succ,K)) = hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,K))))) # label(fact_325_number__of__succ) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	284 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,Y) = ti(X_a,X)))))) # label(fact_391_order__antisym) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	285 (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,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),D) = hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))))) # label(fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	286 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sqrt,X) != zero_zero(real))) # label(fact_482_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	287 (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].
1.41/1.74	288 (all X_a (number_ring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_83_semiring__norm_I112_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	289 (all X_a (linordered_idom(X_a) & number_ring(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].
1.41/1.74	290 (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))) -> zero_zero(X_a) = 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))) -> number_number_of(X_a,V_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))))))) # label(fact_333_of__nat__number__of__lemma) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	291 (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) = hAPP(X_a,X_b,B_1_1,ti(X_a,B_2)))) # label(tsy_c_hAPP_0_arg2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	292 (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].
1.41/1.74	293 (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].
1.41/1.74	294 (all Ma all 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)),Na)) <-> 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].
1.41/1.74	295 (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].
1.41/1.74	296 (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].
1.41/1.74	297 (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].
1.41/1.74	298 (all M_1 all N (N = M_1 -> 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].
1.41/1.74	299 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	300 (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].
1.41/1.74	301 (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].
1.41/1.74	302 (all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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_51_rel__simps_I12_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	303 (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(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].
1.41/1.74	304 (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].
1.41/1.74	305 (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].
1.41/1.74	306 (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].
1.41/1.74	307 (all X_a (number_semiring(X_a) -> number_number_of(X_a,hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	308 (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))))) -> X = zero_zero(int) | one_one(int) = X))) # label(fact_337_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	309 (all Ma all Na (hAPP(nat,nat,power_power(nat,Ma),Na) = zero_zero(nat) <-> Ma = zero_zero(nat) & Na != zero_zero(nat))) # label(fact_226_nat__power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	310 (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].
1.41/1.75	311 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) <-> Na = zero_zero(nat))) # label(fact_313_int__le__0__conv) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	312 (all B_1_1 all B_2 all X_a (power(X_a) -> hAPP(nat,X_a,B_1_1,B_2) = ti(X_a,hAPP(nat,X_a,B_1_1,B_2)))) # label(tsy_c_hAPP_1_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	313 (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_400_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	314 (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].
1.41/1.75	315 (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].
1.41/1.75	316 (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].
1.41/1.75	317 (all P_1 ((all X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_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)))))) # label(fact_291_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	318 (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),hAPP(int,int,bit1,pls)),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))))))) # label(fact_63_less__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	319 (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,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_204_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	320 (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].
1.41/1.75	321 (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),Ya),Xa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_399_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	322 (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].
1.41/1.75	323 (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].
1.41/1.75	324 (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].
1.41/1.75	325 (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].
1.41/1.75	326 (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].
1.41/1.75	327 (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].
1.41/1.75	328 (all K hAPP(int,int,bit1,K) = hAPP(int,int,succ,hAPP(int,int,bit0,K))) # label(fact_315_succ__Bit0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	329 (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].
1.41/1.75	330 (all A_1 all B 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))))) = 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))))) # label(fact_463_zadd__power2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	331 (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].
1.41/1.75	332 (all P_1 ((exists 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)))) <-> (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].
1.41/1.75	333 (all Z_1 hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1) != zero_zero(int)) # label(fact_93_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	334 (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].
1.41/1.75	335 (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].
1.41/1.75	336 (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].
1.41/1.75	337 (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].
1.41/1.75	338 (all B_1_1 all X_a (monoid_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_0_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	339 (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].
1.41/1.75	340 (all X_a (number_semiring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	341 (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].
1.41/1.75	342 (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].
1.41/1.75	343 (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].
1.41/1.75	344 (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].
1.41/1.75	345 (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].
1.41/1.75	346 (all X_a all B_1_1 all B_2 all X_b (ord(X_b) -> ti(X_b,hAPP(X_a,X_b,B_1_1,B_2)) = hAPP(X_a,X_b,B_1_1,B_2))) # label(tsy_c_hAPP_0_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	347 (all X_a (power(X_a) & mult_zero(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) -> (all A_2 all Wa (zero_zero(nat) != number_number_of(nat,Wa) & ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa)))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	348 (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].
1.41/1.75	349 (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].
1.41/1.75	350 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	351 (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].
1.41/1.75	352 (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].
1.41/1.75	353 (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),hAPP(int,int,bit1,pls)),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))))))) # label(fact_262_le__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	354 (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].
1.41/1.75	355 (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,Ya) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Xa))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	356 (all L pls != hAPP(int,int,bit1,L)) # label(fact_67_rel__simps_I39_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	357 (all Wa all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z_2)) <-> (exists N_1 hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = Z_2))) # label(fact_294_zle__iff__zadd) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	358 (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)) -> (hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya) = zero_zero(X_a) <-> ti(X_a,Xa) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Ya))))))) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	359 (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].
1.41/1.75	360 (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),Ya),Xa)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)))))) # label(fact_424_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	361 (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].
1.41/1.75	362 (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].
1.41/1.75	363 (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].
1.41/1.75	364 (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].
1.41/1.75	365 (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].
1.41/1.75	366 (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].
1.41/1.75	367 (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].
1.41/1.75	368 (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(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].
1.41/1.75	369 (all Z_1 hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1) = Z_1) # label(fact_80_zadd__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	370 (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].
1.41/1.75	371 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1))))))) # label(fact_445_real__lbound__gt__zero) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	372 (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].
1.41/1.75	373 (all Xa all Ya (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))))) = zero_zero(real) <-> zero_zero(real) = Ya & zero_zero(real) = Xa)) # label(fact_106_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	374 (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].
1.41/1.75	375 (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].
1.41/1.75	376 (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].
1.41/1.75	377 (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].
1.41/1.75	378 (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(X_a),Xa),Ya)) <-> ti(X_a,Xa) != ti(X_a,Ya))))) # label(fact_422_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	379 (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].
1.41/1.75	380 (all Wa all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)) | 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_60_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	381 (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)),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	382 (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].
1.41/1.75	383 (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].
1.41/1.75	384 (all X 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)))) = hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_10_quartic__square__square) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	385 (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].
1.41/1.75	386 (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].
1.41/1.75	387 (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].
1.41/1.75	388 (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].
1.41/1.75	389 (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].
1.41/1.75	390 (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].
1.41/1.75	391 (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].
1.41/1.75	392 (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].
1.41/1.75	393 (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].
1.41/1.75	394 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) <-> Na != zero_zero(nat))) # label(fact_144_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	395 (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].
1.41/1.75	396 (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].
1.41/1.75	397 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_130_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	398 (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,K),N) = hAPP(nat,nat,plus_plus(nat,M_1),L) -> 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].
1.41/1.75	399 (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].
1.41/1.75	400 (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,C_1),A_1) = hAPP(X_a,X_a,plus_plus(X_a,B),A_1) -> ti(X_a,C_1) = ti(X_a,B))))) # label(fact_197_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	401 (all X_a (ring_char_0(X_a) & number_ring(X_a) -> (all Xa all Ya (number_number_of(X_a,Xa) = number_number_of(X_a,Ya) <-> Xa = Ya)))) # label(fact_40_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	402 (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].
1.41/1.75	403 (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].
1.41/1.75	404 (all M_1 all N all 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)) = 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)) # label(fact_22_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	405 (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].
1.41/1.75	406 (all X_a (semiring_1(X_a) -> one_one(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)))))) # label(fact_3_one__power2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	407 (all X_a (number(X_a) -> (all Wa all Xa (ti(X_a,Xa) = number_number_of(X_a,Wa) <-> ti(X_a,Xa) = number_number_of(X_a,Wa))))) # label(fact_41_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	408 (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].
1.41/1.75	409 (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)) -> Z_1 = W_1))) # label(fact_251_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	410 (all X_a (semiring_1(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)))) = zero_zero(X_a))) # label(fact_4_zero__power2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	411 (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_401_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	412 (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].
1.41/1.75	413 (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].
1.41/1.75	414 (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].
1.41/1.75	415 (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].
1.41/1.75	416 (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].
1.41/1.75	417 (all B_1_1 all X_a (number(X_a) -> ti(X_a,number_number_of(X_a,B_1_1)) = number_number_of(X_a,B_1_1))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	418 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	419 (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].
1.41/1.75	420 (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].
1.41/1.75	421 (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,Ya) = ti(X_a,Xa) | 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].
1.41/1.75	422 (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].
1.41/1.75	423 (all K hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int))) # label(fact_320_succ__def) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	424 (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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),Xa),Ya)) = hAPP(nat,int,semiring_1_of_nat(int),Ya)))) # label(fact_159_int__if__cong) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	425 (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].
1.41/1.75	426 (all Ma all Na (Ma = 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)))) # label(fact_348_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	427 (all B_1_1 all X_a (monoid_add(X_a) -> plus_plus(X_a,B_1_1) = plus_plus(X_a,ti(X_a,B_1_1)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	428 (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].
1.41/1.75	429 (all B_1_1 all X_a (ab_semigroup_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_1_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	430 (all X_a (order(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_429_order__le__less) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	431 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,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)))))))) # label(fact_5_zero__eq__power2) # label(axiom) # label(non_clause).  [assumption].
1.41/1.75	432 (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].
1.41/1.75	433 (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].
1.41/1.76	434 (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].
1.41/1.76	435 (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].
1.41/1.76	436 (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].
1.41/1.76	437 (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].
1.41/1.76	438 (all X_a (power(X_a) -> (all A_1 one_one(X_a) = hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))))) # label(fact_186_power__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	439 (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].
1.41/1.76	440 (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].
1.41/1.76	441 (all M_1 hAPP(nat,nat,plus_plus(nat,M_1),zero_zero(nat)) = M_1) # label(fact_154_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	442 (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].
1.41/1.76	443 (all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))) <-> 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))))) # label(fact_64_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	444 (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),Xa),Ya)) <-> ti(X_a,Ya) = ti(X_a,Xa)))))) # label(fact_432_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	445 (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].
1.41/1.76	446 (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].
1.41/1.76	447 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,Y) = ti(X_a,X))))) # label(fact_438_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	448 (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)) = one_one(nat)) & (-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))))) # label(fact_233_nat__1__add__number__of) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	449 (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].
1.41/1.76	450 (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].
1.41/1.76	451 (all X_a (one(X_a) -> (all Xa (ti(X_a,Xa) = one_one(X_a) <-> ti(X_a,Xa) = one_one(X_a))))) # label(fact_209_one__reorient) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	452 (all Xa all Na (zero_zero(nat) = Na | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na))))) # label(fact_146_zero__less__power__nat__eq) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	453 (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].
1.41/1.76	454 (all X_a (linordered_semidom(X_a) -> (all Ma all 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))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))))) # label(fact_166_of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	455 (all X_a (preorder(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),Xa),Ya)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)))))) # label(fact_428_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	456 (all Xa all Na (one_one(nat) = hAPP(nat,nat,power_power(nat,Xa),Na) <-> Xa = one_one(nat) | zero_zero(nat) = Na)) # label(fact_192_exp__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	457 (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].
1.41/1.76	458 (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].
1.41/1.76	459 (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].
1.41/1.76	460 (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].
1.41/1.76	461 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	462 (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].
1.41/1.76	463 (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].
1.41/1.76	464 (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].
1.41/1.76	465 (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].
1.41/1.76	466 (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].
1.41/1.76	467 (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].
1.41/1.76	468 (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].
1.41/1.76	469 (all X_a (number_ring(X_a) -> number_number_of(X_a,hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_13_numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	470 (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].
1.41/1.76	471 (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].
1.41/1.76	472 (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].
1.41/1.76	473 (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].
1.41/1.76	474 (all X_a (monoid_mult(X_a) -> (all N hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N) = one_one(X_a)))) # label(fact_165_power__one) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	475 (all Ma all K_2 all Na (hAPP(nat,nat,plus_plus(nat,Na),K_2) = hAPP(nat,nat,plus_plus(nat,Ma),K_2) <-> Ma = Na)) # label(fact_125_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	476 (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].
1.41/1.76	477 (all Xa all Ya (Ya = Xa <-> hAPP(nat,int,semiring_1_of_nat(int),Xa) = hAPP(nat,int,semiring_1_of_nat(int),Ya))) # label(fact_158_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	478 (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].
1.41/1.76	479 (all X_a (linordered_semidom(X_a) -> (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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))))))) # label(fact_107_of__nat__0__less__iff) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	480 (all K hAPP(int,int,bit1,K) != pls) # label(fact_66_rel__simps_I46_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	481 (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].
1.41/1.76	482 (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].
1.41/1.76	483 (all X_a (power(X_a) & semiring_0(X_a) -> (all N ((N != zero_zero(nat) -> 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].
1.41/1.76	484 (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].
1.41/1.76	485 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X),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))) # label(fact_173_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	486 (all B_1_1 all X_a (ab_semigroup_add(X_a) -> plus_plus(X_a,B_1_1) = plus_plus(X_a,ti(X_a,B_1_1)))) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg1) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	487 (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].
1.41/1.76	488 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (B = 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),A_1),C_1))))))) # label(fact_395_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	489 (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,C_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),D)) = hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))))) # label(fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	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,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].
1.41/1.76	491 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)))) # label(fact_249_zle__linear) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	492 (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].
1.41/1.76	493 (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].
1.41/1.76	494 (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].
1.41/1.76	495 (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].
1.41/1.76	496 (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].
1.41/1.76	497 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause).  [assumption].
1.41/1.76	498 (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].
1.41/1.76	499 (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].
1.41/1.76	500 (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_eq(int),Wa),Z_2)))) # label(fact_317_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
1.41/1.77	501 (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)) & hAPP(nat,real,power_power(real,X_1),N) = A_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))))))) # label(fact_229_realpow__pos__nth__unique) # label(axiom) # label(non_clause).  [assumption].
1.41/1.77	502 (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)) -> N = M_1))) # label(fact_354_le__antisym) # label(axiom) # label(non_clause).  [assumption].
1.41/1.77	503 (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].
1.41/1.77	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].
1.41/1.77	
1.41/1.77	============================== end of process non-clausal formulas ===
1.41/1.77	
1.41/1.77	============================== PROCESS INITIAL CLAUSES ===============
1.41/1.77	
1.41/1.77	============================== PREDICATE ELIMINATION =================
1.41/1.77	505 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.41/1.77	506 -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(2)].
1.41/1.77	507 -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(10)].
1.41/1.77	508 -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(25)].
1.41/1.77	509 -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(31)].
1.41/1.77	510 -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(40)].
1.41/1.77	511 -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(59)].
1.41/1.77	512 -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(62)].
1.41/1.77	513 -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(88)].
1.41/1.77	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(505,a,506,a)].
1.41/1.77	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(505,a,507,a)].
1.41/1.77	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(505,a,508,a)].
1.41/1.77	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(505,a,509,a)].
1.41/1.77	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(505,a,510,a)].
1.41/1.77	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(505,a,511,a)].
1.41/1.77	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(505,a,512,a)].
1.41/1.77	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(505,a,513,a)].
1.41/1.77	514 -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(93)].
1.41/1.77	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(514,a,505,a)].
1.41/1.77	515 -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(108)].
1.41/1.77	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(515,a,505,a)].
1.41/1.77	516 -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(118)].
1.41/1.77	517 -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(119)].
1.41/1.77	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(517,a,505,a)].
1.41/1.77	518 -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(133)].
1.41/1.77	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(518,a,505,a)].
1.41/1.77	519 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.41/1.77	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(519,a,506,a)].
1.41/1.77	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(519,a,507,a)].
1.41/1.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_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(519,a,508,a)].
1.41/1.77	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(519,a,509,a)].
1.41/1.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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(519,a,511,a)].
1.41/1.78	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(519,a,512,a)].
1.41/1.78	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(519,a,514,a)].
1.41/1.78	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(519,a,515,a)].
1.41/1.78	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(519,a,517,a)].
1.41/1.78	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(519,a,518,a)].
1.41/1.78	520 -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(149)].
1.41/1.78	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(520,a,505,a)].
1.41/1.78	521 -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(149)].
1.41/1.78	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(521,a,505,a)].
1.41/1.78	522 -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(168)].
1.41/1.78	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(168)].
1.41/1.78	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(523,a,505,a)].
1.41/1.78	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(523,a,519,a)].
1.41/1.78	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(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_181_power__strict__increasing__iff) # label(axiom).  [clausify(175)].
1.41/1.78	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(524,a,505,a)].
1.41/1.78	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(524,a,519,a)].
1.41/1.78	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(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_181_power__strict__increasing__iff) # label(axiom).  [clausify(175)].
1.41/1.78	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(525,a,505,a)].
1.41/1.78	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(525,a,519,a)].
1.41/1.78	526 -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(192)].
1.41/1.78	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(526,a,505,a)].
1.41/1.78	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(526,a,519,a)].
1.41/1.78	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),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(195)].
1.41/1.78	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(527,a,505,a)].
1.41/1.78	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(527,a,519,a)].
1.41/1.78	528 -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(210)].
1.41/1.79	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(528,a,505,a)].
1.41/1.79	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(528,a,519,a)].
1.41/1.79	529 -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(213)].
1.41/1.79	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))).  [resolve(529,a,505,a)].
1.41/1.79	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))).  [resolve(529,a,519,a)].
1.41/1.79	530 -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(221)].
1.41/1.79	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(530,a,505,a)].
1.41/1.79	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(530,a,519,a)].
1.41/1.79	531 -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(222)].
1.41/1.79	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(531,a,505,a)].
1.41/1.79	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(531,a,519,a)].
1.41/1.79	532 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom).  [assumption].
1.41/1.79	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(532,a,506,a)].
1.41/1.79	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(532,a,507,a)].
1.41/1.79	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(532,a,508,a)].
1.41/1.79	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(532,a,509,a)].
1.41/1.79	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(532,a,510,a)].
1.41/1.79	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(532,a,511,a)].
1.41/1.79	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(532,a,512,a)].
1.41/1.79	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))).  [resolve(532,a,513,a)].
1.41/1.79	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(532,a,514,a)].
1.41/1.79	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(532,a,515,a)].
1.41/1.79	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(532,a,518,a)].
1.41/1.79	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(532,a,520,a)].
1.41/1.79	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(532,a,521,a)].
1.41/1.79	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(532,a,523,a)].
1.41/1.79	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(532,a,524,a)].
1.41/1.79	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(532,a,525,a)].
1.41/1.79	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(532,a,526,a)].
1.41/1.79	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(532,a,527,a)].
1.41/1.79	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))).  [resolve(532,a,529,a)].
1.41/1.79	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(532,a,530,a)].
1.41/1.79	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(532,a,531,a)].
1.41/1.79	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(226)].
1.41/1.79	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))).  [resolve(533,a,505,a)].
1.41/1.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))).  [resolve(533,a,519,a)].
1.41/1.79	534 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hAPP(nat,A,power_power(A,B),C) != hAPP(nat,A,power_power(A,B),D) | C = D # label(fact_180_power__inject__exp) # label(axiom).  [clausify(228)].
1.41/1.79	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hAPP(nat,real,power_power(real,A),B) != hAPP(nat,real,power_power(real,A),C) | B = C.  [resolve(534,a,505,a)].
1.41/1.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hAPP(nat,int,power_power(int,A),B) != hAPP(nat,int,power_power(int,A),C) | B = C.  [resolve(534,a,519,a)].
1.41/1.79	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hAPP(nat,nat,power_power(nat,A),B) != hAPP(nat,nat,power_power(nat,A),C) | B = C.  [resolve(534,a,532,a)].
1.41/1.79	535 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hAPP(nat,A,power_power(A,B),C) = hAPP(nat,A,power_power(A,B),D) | C != D # label(fact_180_power__inject__exp) # label(axiom).  [clausify(228)].
1.41/1.79	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hAPP(nat,real,power_power(real,A),B) = hAPP(nat,real,power_power(real,A),C) | B != C.  [resolve(535,a,505,a)].
1.41/1.79	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hAPP(nat,int,power_power(int,A),B) = hAPP(nat,int,power_power(int,A),C) | B != C.  [resolve(535,a,519,a)].
1.41/1.79	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hAPP(nat,nat,power_power(nat,A),B) = hAPP(nat,nat,power_power(nat,A),C) | B != C.  [resolve(535,a,532,a)].
1.41/1.79	536 -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(248)].
1.41/1.79	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(536,a,505,a)].
1.41/1.79	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(536,a,519,a)].
1.41/1.79	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(536,a,532,a)].
1.41/1.79	537 -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(250)].
1.41/1.82	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(537,a,505,a)].
1.41/1.82	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(537,a,532,a)].
1.41/1.82	538 -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(256)].
1.41/1.82	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(538,a,505,a)].
1.41/1.82	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(538,a,519,a)].
1.41/1.82	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(538,a,532,a)].
1.41/1.82	539 -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(258)].
1.41/1.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))).  [resolve(539,a,505,a)].
1.41/1.82	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))).  [resolve(539,a,519,a)].
1.41/1.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))).  [resolve(539,a,532,a)].
1.41/1.82	540 -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(366)].
1.41/1.82	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(540,a,505,a)].
1.41/1.82	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(540,a,519,a)].
1.41/1.82	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(540,a,532,a)].
1.41/1.82	541 -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(432)].
1.41/1.82	542 -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(450)].
1.41/1.82	543 -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_166_of__nat__less__iff) # label(axiom).  [clausify(454)].
1.41/1.82	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(543,a,519,a)].
1.41/1.82	544 -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_166_of__nat__less__iff) # label(axiom).  [clausify(454)].
1.41/1.82	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(544,a,519,a)].
1.41/1.82	545 -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(458)].
1.41/1.82	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(545,a,505,a)].
1.41/1.82	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(545,a,519,a)].
1.41/1.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,plus_plus(nat,A),C))).  [resolve(545,a,532,a)].
1.41/1.82	546 -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(471)].
1.41/1.82	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))).  [resolve(546,a,505,a)].
1.41/1.82	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))).  [resolve(546,a,519,a)].
1.41/1.82	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))).  [resolve(546,a,532,a)].
1.41/1.82	547 -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(473)].
1.41/1.82	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,power_power(real,A),B))).  [resolve(547,a,505,a)].
1.41/1.82	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(547,a,519,a)].
1.41/1.82	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B))).  [resolve(547,a,532,a)].
1.41/1.82	548 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_107_of__nat__0__less__iff) # label(axiom).  [clausify(479)].
1.41/1.86	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))).  [resolve(548,a,505,a)].
1.41/1.86	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))).  [resolve(548,a,519,a)].
1.41/1.86	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(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))).  [resolve(548,a,532,a)].
1.41/1.86	549 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_107_of__nat__0__less__iff) # label(axiom).  [clausify(479)].
1.41/1.86	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))).  [resolve(549,a,505,a)].
1.41/1.86	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))).  [resolve(549,a,519,a)].
1.41/1.86	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(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))).  [resolve(549,a,532,a)].
1.41/1.86	550 -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(498)].
1.41/1.86	551 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom).  [assumption].
1.41/1.86	552 -number_ring(A) | number_number_of(A,pls) = zero_zero(A) # label(fact_82_number__of__Pls) # label(axiom).  [clausify(4)].
1.41/1.86	553 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) # label(fact_18_less__number__of) # label(axiom).  [clausify(5)].
1.41/1.86	554 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C))) # label(fact_18_less__number__of) # label(axiom).  [clausify(5)].
1.41/1.86	555 -number_ring(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_8_one__add__one__is__two) # label(axiom).  [clausify(19)].
1.41/1.86	556 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A))) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(23)].
1.41/1.86	557 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A))) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(23)].
1.41/1.86	558 -number_ring(A) | 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_88_add__number__of__eq) # label(axiom).  [clausify(56)].
1.41/1.86	559 -number_ring(A) | number_number_of(A,hAPP(int,int,bit1,B)) = hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))),number_number_of(A,B)) # label(fact_100_number__of__Bit1) # label(axiom).  [clausify(57)].
1.41/1.86	560 -number_ring(A) | hAPP(A,A,plus_plus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D) = hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,number_number_of(A,C)),D)) # label(fact_87_add__number__of__left) # label(axiom).  [clausify(129)].
1.41/1.86	561 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,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(152)].
1.41/1.86	562 -number_ring(A) | number_number_of(A,hAPP(int,int,bit0,B)) = hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,zero_zero(A)),number_number_of(A,B))),number_number_of(A,B)) # label(fact_99_number__of__Bit0) # label(axiom).  [clausify(165)].
1.41/1.86	563 -number_ring(A) | number_number_of(A,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),B)) = hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B)) # label(fact_6_add__special_I2_J) # label(axiom).  [clausify(184)].
1.41/1.86	564 -number_ring(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),number_number_of(A,pls)) # label(fact_85_add__numeral__0__right) # label(axiom).  [clausify(216)].
1.41/1.86	565 -number_ring(A) | number_number_of(A,hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_12_semiring__norm_I110_J) # label(axiom).  [clausify(268)].
1.41/1.86	566 -linordered_idom(A) | -number_ring(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(272)].
1.41/1.86	567 -linordered_idom(A) | -number_ring(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(272)].
1.41/1.86	568 -number_ring(A) | 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_325_number__of__succ) # label(axiom).  [clausify(283)].
1.41/1.86	569 -number_ring(A) | number_number_of(A,pls) = zero_zero(A) # label(fact_83_semiring__norm_I112_J) # label(axiom).  [clausify(288)].
1.41/1.86	570 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A))) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(289)].
1.41/1.86	571 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A))) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(289)].
1.41/1.86	572 -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,B))) | zero_zero(A) = hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B)) # label(fact_333_of__nat__number__of__lemma) # label(axiom).  [clausify(290)].
1.41/1.86	573 -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,B))) | number_number_of(A,B) = hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B)) # label(fact_333_of__nat__number__of__lemma) # label(axiom).  [clausify(290)].
1.41/1.86	574 -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(301)].
1.41/1.86	575 -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(301)].
1.41/1.86	576 -number_ring(A) | ti(A,B) = hAPP(A,A,plus_plus(A,number_number_of(A,pls)),B) # label(fact_84_add__numeral__0) # label(axiom).  [clausify(304)].
1.41/1.86	577 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B))) # label(fact_63_less__special_I2_J) # label(axiom).  [clausify(318)].
1.41/1.86	578 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B))) # label(fact_63_less__special_I2_J) # label(axiom).  [clausify(318)].
1.41/1.86	579 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),number_number_of(A,B))) # label(fact_262_le__special_I2_J) # label(axiom).  [clausify(353)].
1.41/1.86	580 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),number_number_of(A,B))) # label(fact_262_le__special_I2_J) # label(axiom).  [clausify(353)].
1.41/1.86	Derived: number_number_of(int,pls) = zero_zero(int).  [resolve(551,a,552,a)].
1.41/1.86	Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B))).  [resolve(551,a,553,b)].
1.41/1.86	Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B))).  [resolve(551,a,554,b)].
1.41/1.86	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(551,a,555,a)].
1.41/1.86	Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),zero_zero(int))).  [resolve(551,a,556,a)].
1.41/1.86	Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),zero_zero(int))).  [resolve(551,a,557,a)].
1.41/1.86	Derived: number_number_of(int,hAPP(int,int,bit1,A)) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,A))),number_number_of(int,A)).  [resolve(551,a,559,a)].
1.41/1.86	Derived: hAPP(int,int,plus_plus(int,number_number_of(int,hAPP(int,int,plus_plus(int,A),B))),C) = hAPP(int,int,plus_plus(int,number_number_of(int,A)),hAPP(int,int,plus_plus(int,number_number_of(int,B)),C)).  [resolve(551,a,560,a)].
1.41/1.86	Derived: -linordered_idom(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(551,a,561,a)].
1.41/1.86	Derived: number_number_of(int,hAPP(int,int,bit0,A)) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,zero_zero(int)),number_number_of(int,A))),number_number_of(int,A)).  [resolve(551,a,562,a)].
1.41/1.86	Derived: number_number_of(int,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),A)) = hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,A)).  [resolve(551,a,563,a)].
1.41/1.86	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,A),number_number_of(int,pls)).  [resolve(551,a,564,a)].
1.41/1.86	Derived: number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int).  [resolve(551,a,565,a)].
1.41/1.86	Derived: -linordered_idom(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(551,a,566,b)].
1.41/1.86	Derived: -linordered_idom(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(551,a,567,b)].
1.41/1.87	Derived: number_number_of(int,hAPP(int,int,succ,A)) = hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,A)).  [resolve(551,a,568,a)].
1.41/1.87	Derived: -linordered_idom(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(551,a,570,b)].
1.41/1.87	Derived: -linordered_idom(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(551,a,571,b)].
1.41/1.87	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,A))) | zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,A)).  [resolve(551,a,572,a)].
1.41/1.87	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,A))) | number_number_of(int,A) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,A)).  [resolve(551,a,573,a)].
1.41/1.87	Derived: -linordered_idom(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(551,a,574,b)].
1.41/1.87	Derived: -linordered_idom(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(551,a,575,b)].
1.41/1.87	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,number_number_of(int,pls)),A).  [resolve(551,a,576,a)].
1.41/1.87	Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),number_number_of(int,A))).  [resolve(551,a,577,b)].
1.41/1.87	Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),number_number_of(int,A))).  [resolve(551,a,578,b)].
1.41/1.87	Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),number_number_of(int,A))).  [resolve(551,a,579,a)].
1.41/1.87	Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),number_number_of(int,A))).  [resolve(551,a,580,a)].
1.41/1.87	581 -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(386)].
1.41/1.87	Derived: -linordered_idom(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(581,b,551,a)].
1.41/1.87	582 -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(386)].
1.41/1.87	Derived: -linordered_idom(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(582,b,551,a)].
1.41/1.87	583 -ring_char_0(A) | -number_ring(A) | number_number_of(A,B) != number_number_of(A,C) | B = C # label(fact_40_eq__number__of) # label(axiom).  [clausify(401)].
1.41/1.87	Derived: -ring_char_0(int) | number_number_of(int,A) != number_number_of(int,B) | A = B.  [resolve(583,b,551,a)].
1.41/1.87	584 -ring_char_0(A) | -number_ring(A) | number_number_of(A,B) = number_number_of(A,C) | B != C # label(fact_40_eq__number__of) # label(axiom).  [clausify(401)].
1.41/1.87	Derived: -ring_char_0(int) | number_number_of(int,A) = number_number_of(int,B) | A != B.  [resolve(584,b,551,a)].
1.41/1.87	585 -number_ring(A) | 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_89_number__of__add) # label(axiom).  [clausify(420)].
1.41/1.87	586 -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(462)].
1.41/1.87	Derived: -linordered_idom(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(586,a,551,a)].
1.41/1.87	587 -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(462)].
1.41/1.87	Derived: -linordered_idom(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(587,a,551,a)].
1.41/1.87	588 number_ring(real) # label(arity_RealDef_Oreal___Int_Onumber__ring) # label(axiom).  [assumption].
1.41/1.87	Derived: number_number_of(real,pls) = zero_zero(real).  [resolve(588,a,552,a)].
1.41/1.87	Derived: -linordered_idom(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),number_number_of(real,B))).  [resolve(588,a,553,b)].
1.41/1.87	Derived: -linordered_idom(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),number_number_of(real,B))).  [resolve(588,a,554,b)].
1.41/1.87	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(588,a,555,a)].
1.41/1.87	Derived: -linordered_idom(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),zero_zero(real))).  [resolve(588,a,556,a)].
1.41/1.87	Derived: -linordered_idom(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,A)),zero_zero(real))).  [resolve(588,a,557,a)].
1.41/1.87	Derived: 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(588,a,558,a)].
1.41/1.87	Derived: number_number_of(real,hAPP(int,int,bit1,A)) = hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,one_one(real)),number_number_of(real,A))),number_number_of(real,A)).  [resolve(588,a,559,a)].
1.41/1.87	Derived: hAPP(real,real,plus_plus(real,number_number_of(real,hAPP(int,int,plus_plus(int,A),B))),C) = hAPP(real,real,plus_plus(real,number_number_of(real,A)),hAPP(real,real,plus_plus(real,number_number_of(real,B)),C)).  [resolve(588,a,560,a)].
1.41/1.87	Derived: -linordered_idom(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(588,a,561,a)].
1.41/1.87	Derived: number_number_of(real,hAPP(int,int,bit0,A)) = hAPP(real,real,plus_plus(real,hAPP(real,real,plus_plus(real,zero_zero(real)),number_number_of(real,A))),number_number_of(real,A)).  [resolve(588,a,562,a)].
1.41/1.87	Derived: number_number_of(real,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),A)) = hAPP(real,real,plus_plus(real,one_one(real)),number_number_of(real,A)).  [resolve(588,a,563,a)].
1.41/1.87	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,A),number_number_of(real,pls)).  [resolve(588,a,564,a)].
1.41/1.87	Derived: number_number_of(real,hAPP(int,int,bit1,pls)) = one_one(real).  [resolve(588,a,565,a)].
1.41/1.87	Derived: -linordered_idom(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(588,a,566,b)].
1.41/1.87	Derived: -linordered_idom(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(588,a,567,b)].
1.41/1.87	Derived: number_number_of(real,hAPP(int,int,succ,A)) = hAPP(real,real,plus_plus(real,one_one(real)),number_number_of(real,A)).  [resolve(588,a,568,a)].
1.41/1.87	Derived: -linordered_idom(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(588,a,570,b)].
1.41/1.87	Derived: -linordered_idom(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(588,a,571,b)].
1.41/1.87	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,A))) | zero_zero(real) = hAPP(nat,real,semiring_1_of_nat(real),number_number_of(nat,A)).  [resolve(588,a,572,a)].
1.41/1.87	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,A))) | number_number_of(real,A) = hAPP(nat,real,semiring_1_of_nat(real),number_number_of(nat,A)).  [resolve(588,a,573,a)].
1.41/1.87	Derived: -linordered_idom(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(588,a,574,b)].
1.41/1.87	Derived: -linordered_idom(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(588,a,575,b)].
1.41/1.87	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,number_number_of(real,pls)),A).  [resolve(588,a,576,a)].
1.41/1.87	Derived: -linordered_idom(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),number_number_of(real,A))).  [resolve(588,a,577,b)].
1.41/1.87	Derived: -linordered_idom(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),number_number_of(real,A))).  [resolve(588,a,578,b)].
1.41/1.87	Derived: -linordered_idom(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),number_number_of(real,A))).  [resolve(588,a,579,a)].
1.41/1.87	Derived: -linordered_idom(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),number_number_of(real,A))).  [resolve(588,a,580,a)].
1.41/1.87	Derived: -linordered_idom(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(588,a,581,b)].
1.41/1.87	Derived: -linordered_idom(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(588,a,582,b)].
1.41/1.87	Derived: -ring_char_0(real) | number_number_of(real,A) != number_number_of(real,B) | A = B.  [resolve(588,a,583,b)].
1.41/1.87	Derived: -ring_char_0(real) | number_number_of(real,A) = number_number_of(real,B) | A != B.  [resolve(588,a,584,b)].
1.41/1.87	Derived: -linordered_idom(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(588,a,586,a)].
1.41/1.91	Derived: -linordered_idom(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(588,a,587,a)].
1.41/1.91	589 -number_ring(A) | number_number_of(A,hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_13_numeral__1__eq__1) # label(axiom).  [clausify(469)].
1.41/1.91	590 -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(482)].
1.41/1.91	Derived: -linordered_idom(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(590,a,551,a)].
1.41/1.91	Derived: -linordered_idom(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(590,a,588,a)].
1.41/1.91	591 -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(482)].
1.41/1.91	Derived: -linordered_idom(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(591,a,551,a)].
1.41/1.91	Derived: -linordered_idom(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(591,a,588,a)].
1.41/1.91	592 -number_ring(A) | number_number_of(A,hAPP(int,int,plus_plus(int,B),hAPP(int,int,bit1,pls))) = hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A)) # label(fact_7_add__special_I3_J) # label(axiom).  [clausify(499)].
1.41/1.91	Derived: number_number_of(int,hAPP(int,int,plus_plus(int,A),hAPP(int,int,bit1,pls))) = hAPP(int,int,plus_plus(int,number_number_of(int,A)),one_one(int)).  [resolve(592,a,551,a)].
1.41/1.91	Derived: number_number_of(real,hAPP(int,int,plus_plus(int,A),hAPP(int,int,bit1,pls))) = hAPP(real,real,plus_plus(real,number_number_of(real,A)),one_one(real)).  [resolve(592,a,588,a)].
1.41/1.91	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_431_not__leE) # label(axiom).  [clausify(39)].
1.41/1.91	594 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom).  [assumption].
1.41/1.91	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(593,a,594,a)].
1.41/1.91	595 -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(71)].
1.41/1.91	596 -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(80)].
1.41/1.91	597 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom).  [assumption].
1.41/1.91	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(597,a,593,a)].
1.41/1.91	598 -linorder(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),number_number_of(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))) # label(fact_275_le__number__of__eq__not__less) # label(axiom).  [clausify(117)].
1.41/1.91	Derived: -number(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,A)),number_number_of(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,B)),number_number_of(nat,A))).  [resolve(598,a,594,a)].
1.41/1.91	Derived: -number(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,A)),number_number_of(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,B)),number_number_of(int,A))).  [resolve(598,a,597,a)].
1.41/1.91	599 -linorder(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),number_number_of(A,B)),number_number_of(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))) # label(fact_275_le__number__of__eq__not__less) # label(axiom).  [clausify(117)].
1.41/1.91	600 -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(150)].
1.41/1.91	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(600,a,594,a)].
1.41/1.91	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(600,a,597,a)].
1.41/1.91	601 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom).  [assumption].
1.41/1.91	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(601,a,593,a)].
1.41/1.91	Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),number_number_of(real,A)),number_number_of(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),number_number_of(real,B)),number_number_of(real,A))).  [resolve(601,a,598,a)].
1.41/1.91	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(601,a,600,a)].
1.41/1.91	602 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f16(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(196)].
1.41/1.91	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f16(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(602,a,594,a)].
1.41/1.91	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f16(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(602,a,597,a)].
1.41/1.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f16(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(602,a,601,a)].
1.41/1.91	603 -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(199)].
1.41/1.91	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(603,a,594,a)].
1.41/1.91	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(603,a,597,a)].
1.41/1.91	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)).  [resolve(603,a,601,a)].
1.41/1.91	604 -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_425_linorder__not__le) # label(axiom).  [clausify(202)].
1.41/1.91	605 -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_425_linorder__not__le) # label(axiom).  [clausify(202)].
1.41/1.91	606 -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(217)].
1.41/1.93	607 -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_419_linorder__antisym__conv3) # label(axiom).  [clausify(244)].
1.41/1.93	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(nat),B),A)).  [resolve(607,a,594,a)].
1.41/1.93	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(int),B),A)).  [resolve(607,a,597,a)].
1.41/1.93	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(real),B),A)).  [resolve(607,a,601,a)].
1.41/1.93	608 -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_419_linorder__antisym__conv3) # label(axiom).  [clausify(244)].
1.41/1.93	609 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f23(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(261)].
1.41/1.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f23(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(609,a,594,a)].
1.41/1.93	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f23(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(609,a,597,a)].
1.41/1.93	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f23(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(609,a,601,a)].
1.41/1.93	610 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_437_linorder__antisym__conv2) # label(axiom).  [clausify(275)].
1.41/1.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A).  [resolve(610,a,594,a)].
1.41/1.93	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A).  [resolve(610,a,597,a)].
1.41/1.93	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),A),B)) | ti(real,B) = ti(real,A).  [resolve(610,a,601,a)].
1.41/1.93	611 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_437_linorder__antisym__conv2) # label(axiom).  [clausify(275)].
1.41/1.93	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(611,a,594,a)].
1.41/1.93	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A).  [resolve(611,a,597,a)].
1.41/1.93	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),A),B)) | ti(real,B) != ti(real,A).  [resolve(611,a,601,a)].
1.41/1.93	612 -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(313)].
1.41/1.93	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(612,a,601,a)].
1.41/1.93	613 -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_424_linorder__not__less) # label(axiom).  [clausify(360)].
1.41/1.94	614 -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_424_linorder__not__less) # label(axiom).  [clausify(360)].
1.41/1.94	615 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(378)].
1.41/1.94	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B).  [resolve(615,a,594,a)].
1.41/1.94	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B).  [resolve(615,a,597,a)].
1.41/1.94	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) != ti(real,B).  [resolve(615,a,601,a)].
1.41/1.94	616 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(378)].
1.41/1.94	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(616,a,594,a)].
1.41/1.94	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A).  [resolve(616,a,597,a)].
1.41/1.94	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A).  [resolve(616,a,601,a)].
1.41/1.94	617 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_422_linorder__neq__iff) # label(axiom).  [clausify(378)].
1.41/1.94	618 -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_421_not__less__iff__gr__or__eq) # label(axiom).  [clausify(421)].
1.41/1.94	619 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_421_not__less__iff__gr__or__eq) # label(axiom).  [clausify(421)].
1.41/1.94	620 -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(421)].
1.41/1.94	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(620,a,594,a)].
1.41/1.94	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(620,a,597,a)].
1.41/1.94	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(620,a,601,a)].
1.41/1.94	621 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_432_linorder__antisym__conv1) # label(axiom).  [clausify(444)].
1.41/1.94	622 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_432_linorder__antisym__conv1) # label(axiom).  [clausify(444)].
1.41/1.94	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A).  [resolve(622,a,594,a)].
1.41/1.94	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A).  [resolve(622,a,597,a)].
1.41/1.94	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),A),B)) | ti(real,B) != ti(real,A).  [resolve(622,a,601,a)].
1.41/1.94	623 -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(445)].
1.41/1.94	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(623,a,594,a)].
1.41/1.98	624 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f40(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(449)].
1.41/1.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f40(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)).  [resolve(624,a,594,a)].
1.41/1.98	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f40(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)).  [resolve(624,a,597,a)].
1.41/1.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f40(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)).  [resolve(624,a,601,a)].
1.41/1.98	625 -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(470)].
1.41/1.98	626 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f41(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(478)].
1.41/1.98	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f41(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)).  [resolve(626,a,594,a)].
1.41/1.98	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f41(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)).  [resolve(626,a,597,a)].
1.41/1.98	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f41(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(626,a,601,a)].
1.41/1.98	627 -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(13)].
1.41/1.98	628 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
1.41/1.98	Derived: hAPP(real,real,plus_plus(real,A),B) != hAPP(real,real,plus_plus(real,A),C) | ti(real,B) = ti(real,C).  [resolve(627,a,628,a)].
1.41/1.98	629 -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(21)].
1.41/1.98	Derived: ti(real,A) != ti(real,B) | hAPP(real,real,plus_plus(real,A),C) = hAPP(real,real,plus_plus(real,B),C).  [resolve(629,a,628,a)].
1.41/1.98	630 -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(21)].
1.41/1.98	Derived: ti(real,A) = ti(real,B) | hAPP(real,real,plus_plus(real,A),C) != hAPP(real,real,plus_plus(real,B),C).  [resolve(630,a,628,a)].
1.41/1.98	631 -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(161)].
1.41/1.98	Derived: ti(real,A) != ti(real,B) | hAPP(real,real,plus_plus(real,C),A) = hAPP(real,real,plus_plus(real,C),B).  [resolve(631,a,628,a)].
1.41/1.98	632 -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(161)].
1.41/1.98	633 -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(172)].
1.41/1.98	Derived: plus_plus(real,ti(real,A)) = plus_plus(real,A).  [resolve(633,a,628,a)].
1.41/1.98	634 -cancel_semigroup_add(A) | plus_plus(A,B) = ti(fun(A,A),plus_plus(A,B)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom).  [clausify(178)].
1.41/1.98	Derived: plus_plus(real,A) = ti(fun(real,real),plus_plus(real,A)).  [resolve(634,a,628,a)].
1.41/1.98	635 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
1.41/1.98	Derived: hAPP(nat,nat,plus_plus(nat,A),B) != hAPP(nat,nat,plus_plus(nat,A),C) | ti(nat,B) = ti(nat,C).  [resolve(635,a,627,a)].
1.41/2.07	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,plus_plus(nat,A),C) = hAPP(nat,nat,plus_plus(nat,B),C).  [resolve(635,a,629,a)].
1.41/2.07	Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,nat,plus_plus(nat,A),C) != hAPP(nat,nat,plus_plus(nat,B),C).  [resolve(635,a,630,a)].
1.41/2.07	Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,plus_plus(nat,C),A) = hAPP(nat,nat,plus_plus(nat,C),B).  [resolve(635,a,631,a)].
1.41/2.07	Derived: plus_plus(nat,ti(nat,A)) = plus_plus(nat,A).  [resolve(635,a,633,a)].
1.41/2.07	Derived: plus_plus(nat,A) = ti(fun(nat,nat),plus_plus(nat,A)).  [resolve(635,a,634,a)].
1.41/2.07	636 -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(400)].
1.41/2.07	637 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
1.41/2.07	Derived: hAPP(int,int,plus_plus(int,A),B) != hAPP(int,int,plus_plus(int,A),C) | ti(int,B) = ti(int,C).  [resolve(637,a,627,a)].
1.41/2.07	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,plus_plus(int,A),C) = hAPP(int,int,plus_plus(int,B),C).  [resolve(637,a,629,a)].
1.41/2.07	Derived: ti(int,A) = ti(int,B) | hAPP(int,int,plus_plus(int,A),C) != hAPP(int,int,plus_plus(int,B),C).  [resolve(637,a,630,a)].
1.41/2.07	Derived: ti(int,A) != ti(int,B) | hAPP(int,int,plus_plus(int,C),A) = hAPP(int,int,plus_plus(int,C),B).  [resolve(637,a,631,a)].
1.41/2.07	Derived: plus_plus(int,ti(int,A)) = plus_plus(int,A).  [resolve(637,a,633,a)].
1.41/2.07	Derived: plus_plus(int,A) = ti(fun(int,int),plus_plus(int,A)).  [resolve(637,a,634,a)].
1.41/2.07	638 -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(113)].
1.41/2.07	639 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom).  [assumption].
1.41/2.07	Derived: ti(nat,A) = hAPP(nat,nat,power_power(nat,A),one_one(nat)).  [resolve(638,a,639,a)].
1.41/2.07	640 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom).  [assumption].
1.41/2.07	Derived: ti(real,A) = hAPP(nat,real,power_power(real,A),one_one(nat)).  [resolve(640,a,638,a)].
1.41/2.07	641 -monoid_mult(A) | one_one(A) = hAPP(nat,A,power_power(A,one_one(A)),B) # label(fact_165_power__one) # label(axiom).  [clausify(474)].
1.41/2.07	Derived: one_one(nat) = hAPP(nat,nat,power_power(nat,one_one(nat)),A).  [resolve(641,a,639,a)].
1.41/2.07	Derived: one_one(real) = hAPP(nat,real,power_power(real,one_one(real)),A).  [resolve(641,a,640,a)].
1.41/2.07	642 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom).  [assumption].
1.41/2.07	Derived: ti(int,A) = hAPP(nat,int,power_power(int,A),one_one(nat)).  [resolve(642,a,638,a)].
1.41/2.07	Derived: one_one(int) = hAPP(nat,int,power_power(int,one_one(int)),A).  [resolve(642,a,641,a)].
1.41/2.07	643 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.41/2.07	644 -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(27)].
1.41/2.08	645 -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(69)].
1.41/2.08	646 -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(89)].
1.41/2.08	647 -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(125)].
1.41/2.08	648 -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(209)].
1.41/2.08	649 -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(257)].
1.41/2.08	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(643,a,644,a)].
1.41/2.08	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(643,a,645,a)].
1.41/2.08	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(643,a,646,a)].
1.41/2.08	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),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(643,a,647,a)].
1.41/2.08	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(643,a,648,a)].
1.41/2.08	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(643,a,649,a)].
1.41/2.09	650 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.41/2.09	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(650,a,644,a)].
1.41/2.09	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(650,a,645,a)].
1.41/2.09	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(650,a,646,a)].
1.41/2.09	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(650,a,647,a)].
1.41/2.09	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(650,a,648,a)].
1.41/2.09	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(650,a,649,a)].
1.41/2.09	651 -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(416)].
1.41/2.09	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(651,a,643,a)].
1.41/2.09	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(651,a,650,a)].
1.41/2.09	652 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
1.41/2.09	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(652,a,644,a)].
1.41/2.09	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(652,a,645,a)].
1.41/2.09	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(652,a,646,a)].
1.41/2.09	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(652,a,647,a)].
1.41/2.09	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(652,a,649,a)].
1.41/2.09	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(652,a,651,a)].
1.41/2.09	653 -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(442)].
1.41/2.09	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(653,a,643,a)].
1.41/2.09	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(653,a,650,a)].
1.41/2.09	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(653,a,652,a)].
1.41/2.09	654 -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(464)].
1.41/2.09	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(654,a,643,a)].
1.41/2.09	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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(654,a,650,a)].
1.41/2.09	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(654,a,652,a)].
1.41/2.09	655 -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(465)].
1.41/2.09	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(655,a,643,a)].
1.41/2.09	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(655,a,650,a)].
1.41/2.09	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(655,a,652,a)].
1.41/2.09	656 -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(487)].
1.41/2.09	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(656,a,643,a)].
1.41/2.13	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(656,a,650,a)].
1.41/2.13	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(656,a,652,a)].
1.41/2.13	657 -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(503)].
1.41/2.13	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(657,a,643,a)].
1.41/2.13	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(657,a,650,a)].
1.41/2.13	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(657,a,652,a)].
1.41/2.13	658 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) | zero_zero(A) = ti(A,B) # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(166)].
1.41/2.13	659 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom).  [assumption].
1.41/2.13	660 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom).  [assumption].
1.41/2.13	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -power(nat) | zero_zero(nat) != hAPP(nat,nat,power_power(nat,A),B) | zero_zero(nat) = ti(nat,A).  [resolve(658,c,659,a)].
1.41/2.13	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -power(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B) | zero_zero(int) = ti(int,A).  [resolve(658,c,660,a)].
1.41/2.13	661 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(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(166)].
1.41/2.13	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -power(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B) | zero_zero(nat) != B.  [resolve(661,c,660,a)].
1.41/2.13	662 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) = hAPP(nat,A,power_power(A,B),C) | zero_zero(A) != ti(A,B) | zero_zero(nat) = C # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(166)].
1.41/2.13	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -power(nat) | zero_zero(nat) = hAPP(nat,nat,power_power(nat,A),B) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) = B.  [resolve(662,c,659,a)].
1.41/2.13	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -power(int) | zero_zero(int) = hAPP(nat,int,power_power(int,A),B) | zero_zero(int) != ti(int,A) | zero_zero(nat) = B.  [resolve(662,c,660,a)].
1.41/2.13	663 mult_zero(real) # label(arity_RealDef_Oreal___Rings_Omult__zero) # label(axiom).  [assumption].
1.89/2.19	Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -power(real) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B) | zero_zero(real) = ti(real,A).  [resolve(663,a,658,c)].
1.89/2.19	Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -power(real) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B) | zero_zero(nat) != B.  [resolve(663,a,661,c)].
1.89/2.19	Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -power(real) | zero_zero(real) = hAPP(nat,real,power_power(real,A),B) | zero_zero(real) != ti(real,A) | zero_zero(nat) = B.  [resolve(663,a,662,c)].
1.89/2.19	664 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | number_number_of(nat,B) = zero_zero(nat) | zero_zero(A) != ti(A,C) | zero_zero(A) = hAPP(nat,A,power_power(A,C),number_number_of(nat,B)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(347)].
1.89/2.19	Derived: -power(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) = hAPP(nat,nat,power_power(nat,B),number_number_of(nat,A)).  [resolve(664,b,659,a)].
1.89/2.19	Derived: -power(int) | -zero_neq_one(int) | -no_zero_divisors(int) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(int) != ti(int,B) | zero_zero(int) = hAPP(nat,int,power_power(int,B),number_number_of(nat,A)).  [resolve(664,b,660,a)].
1.89/2.19	Derived: -power(real) | -zero_neq_one(real) | -no_zero_divisors(real) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(real) != ti(real,B) | zero_zero(real) = hAPP(nat,real,power_power(real,B),number_number_of(nat,A)).  [resolve(664,b,663,a)].
1.89/2.19	665 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | number_number_of(nat,B) != zero_zero(nat) | zero_zero(A) != hAPP(nat,A,power_power(A,C),number_number_of(nat,B)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(347)].
1.89/2.19	Derived: -power(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | number_number_of(nat,A) != zero_zero(nat) | zero_zero(nat) != hAPP(nat,nat,power_power(nat,B),number_number_of(nat,A)).  [resolve(665,b,659,a)].
1.89/2.19	Derived: -power(int) | -zero_neq_one(int) | -no_zero_divisors(int) | number_number_of(nat,A) != zero_zero(nat) | zero_zero(int) != hAPP(nat,int,power_power(int,B),number_number_of(nat,A)).  [resolve(665,b,660,a)].
1.89/2.19	Derived: -power(real) | -zero_neq_one(real) | -no_zero_divisors(real) | number_number_of(nat,A) != zero_zero(nat) | zero_zero(real) != hAPP(nat,real,power_power(real,B),number_number_of(nat,A)).  [resolve(665,b,663,a)].
1.89/2.19	666 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(nat,A,power_power(A,B),number_number_of(nat,C)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(347)].
1.89/2.19	667 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.89/2.19	668 -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(29)].
1.89/2.19	669 -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(64)].
1.89/2.19	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(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(143)].
1.89/2.19	671 -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(157)].
1.89/2.19	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),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(220)].
1.89/2.19	673 -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(246)].
1.89/2.19	674 -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(277)].
1.89/2.19	675 -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(316)].
1.89/2.19	676 -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(337)].
1.89/2.19	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(667,a,668,a)].
1.89/2.19	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),B))).  [resolve(667,a,669,a)].
1.89/2.19	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(667,a,671,a)].
1.89/2.19	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(667,a,672,a)].
1.89/2.19	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(667,a,673,a)].
1.89/2.19	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(667,a,674,a)].
1.89/2.19	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(667,a,675,a)].
1.89/2.19	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(667,a,676,a)].
1.89/2.20	677 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) | zero_zero(A) = ti(A,B) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(358)].
1.89/2.20	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),B) | zero_zero(int) = ti(int,A).  [resolve(677,a,667,a)].
1.89/2.20	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)) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) | zero_zero(A) = ti(A,C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(358)].
1.89/2.20	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),B) | zero_zero(int) = ti(int,B).  [resolve(678,a,667,a)].
1.89/2.20	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),zero_zero(A)),C)) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),C) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(358)].
1.89/2.20	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | zero_zero(int) = hAPP(int,int,plus_plus(int,A),B) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B).  [resolve(679,a,667,a)].
1.89/2.20	680 -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(387)].
1.89/2.20	681 -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(395)].
1.89/2.20	682 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.89/2.20	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(682,a,668,a)].
1.89/2.20	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,plus_plus(real,A),B))).  [resolve(682,a,669,a)].
1.89/2.20	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(682,a,671,a)].
1.89/2.20	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(682,a,672,a)].
1.89/2.20	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(682,a,673,a)].
1.89/2.20	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(682,a,674,a)].
1.89/2.20	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(682,a,675,a)].
1.89/2.20	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,676,a)].
1.89/2.20	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) != hAPP(real,real,plus_plus(real,A),B) | zero_zero(real) = ti(real,A).  [resolve(682,a,677,a)].
1.89/2.20	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) != hAPP(real,real,plus_plus(real,A),B) | zero_zero(real) = ti(real,B).  [resolve(682,a,678,a)].
1.89/2.20	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | zero_zero(real) = hAPP(real,real,plus_plus(real,A),B) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B).  [resolve(682,a,679,a)].
1.89/2.20	683 -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(460)].
1.89/2.20	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(683,a,667,a)].
1.89/2.20	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(683,a,682,a)].
1.89/2.20	684 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
1.89/2.20	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,plus_plus(nat,A),C))).  [resolve(684,a,668,a)].
1.89/2.20	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,A),B))).  [resolve(684,a,669,a)].
1.89/2.20	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(684,a,671,a)].
1.89/2.20	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(684,a,672,a)].
1.97/2.24	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,C),A))).  [resolve(684,a,674,a)].
1.97/2.24	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(684,a,675,a)].
1.97/2.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) != hAPP(nat,nat,plus_plus(nat,A),B) | zero_zero(nat) = ti(nat,A).  [resolve(684,a,677,a)].
1.97/2.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) != hAPP(nat,nat,plus_plus(nat,A),B) | zero_zero(nat) = ti(nat,B).  [resolve(684,a,678,a)].
1.97/2.24	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | zero_zero(nat) = hAPP(nat,nat,plus_plus(nat,A),B) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B).  [resolve(684,a,679,a)].
1.97/2.24	685 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
1.97/2.24	686 -linord581940658strict(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,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(32)].
1.97/2.24	687 -linord581940658strict(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,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(32)].
1.97/2.24	688 -linord581940658strict(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,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(32)].
1.97/2.24	689 -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(44)].
1.97/2.24	690 -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),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),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_476_mult__le__cancel__left__pos) # label(axiom).  [clausify(112)].
1.97/2.24	691 -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),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),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_476_mult__le__cancel__left__pos) # label(axiom).  [clausify(112)].
1.97/2.24	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(685,a,686,a)].
1.97/2.25	Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(685,a,687,a)].
1.97/2.25	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(685,a,688,a)].
1.97/2.25	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(685,a,689,a)].
1.97/2.25	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_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))).  [resolve(685,a,690,a)].
1.97/2.25	692 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_475_mult__le__cancel__left__neg) # label(axiom).  [clausify(219)].
1.97/2.25	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)).  [resolve(692,a,685,a)].
1.97/2.25	693 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_475_mult__le__cancel__left__neg) # label(axiom).  [clausify(219)].
1.97/2.25	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)).  [resolve(693,a,685,a)].
1.97/2.25	694 -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(324)].
1.97/2.25	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(694,a,685,a)].
1.97/2.25	695 -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(341)].
1.97/2.25	696 -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(341)].
1.97/2.25	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(696,a,685,a)].
1.97/2.25	697 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
1.97/2.25	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(697,a,686,a)].
1.97/2.25	Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(697,a,687,a)].
1.97/2.25	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(697,a,688,a)].
1.97/2.25	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(697,a,689,a)].
1.97/2.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))).  [resolve(697,a,690,a)].
1.97/2.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)).  [resolve(697,a,692,a)].
1.97/2.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)).  [resolve(697,a,693,a)].
1.97/2.25	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(697,a,694,a)].
1.97/2.25	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(697,a,696,a)].
2.05/2.35	698 -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(393)].
2.05/2.35	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(698,a,685,a)].
2.05/2.35	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(698,a,697,a)].
2.05/2.35	699 -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(135)].
2.05/2.35	700 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.05/2.35	701 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.05/2.35	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B.  [resolve(699,a,700,a)].
2.05/2.35	702 -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(135)].
2.05/2.35	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B.  [resolve(702,a,700,a)].
2.05/2.35	703 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom).  [assumption].
2.05/2.35	Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B.  [resolve(703,a,699,a)].
2.05/2.35	Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B.  [resolve(703,a,702,a)].
2.05/2.35	704 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom).  [assumption].
2.05/2.35	705 -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(36)].
2.05/2.35	706 -semiring_1(A) | semiring_1_of_nat(A) = ti(fun(nat,A),semiring_1_of_nat(A)) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom).  [clausify(94)].
2.05/2.35	Derived: semiring_1_of_nat(int) = ti(fun(nat,int),semiring_1_of_nat(int)).  [resolve(706,a,704,a)].
2.05/2.35	707 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,plus_plus(nat,B),C)) = hAPP(A,A,plus_plus(A,hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) # label(fact_169_of__nat__add) # label(axiom).  [clausify(116)].
2.05/2.35	708 -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(151)].
2.05/2.35	Derived: zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)).  [resolve(708,a,704,a)].
2.05/2.35	709 -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(185)].
2.05/2.35	Derived: one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)).  [resolve(709,a,704,a)].
2.05/2.35	710 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom).  [assumption].
2.05/2.35	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(710,a,705,a)].
2.05/2.35	Derived: semiring_1_of_nat(nat) = ti(fun(nat,nat),semiring_1_of_nat(nat)).  [resolve(710,a,706,a)].
2.05/2.35	Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,plus_plus(nat,A),B)) = hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)).  [resolve(710,a,707,a)].
2.15/2.40	Derived: zero_zero(nat) = hAPP(nat,nat,semiring_1_of_nat(nat),zero_zero(nat)).  [resolve(710,a,708,a)].
2.15/2.40	Derived: one_one(nat) = hAPP(nat,nat,semiring_1_of_nat(nat),one_one(nat)).  [resolve(710,a,709,a)].
2.15/2.40	711 semiring_1(real) # label(arity_RealDef_Oreal___Rings_Osemiring__1) # label(axiom).  [assumption].
2.15/2.40	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(711,a,705,a)].
2.15/2.40	Derived: semiring_1_of_nat(real) = ti(fun(nat,real),semiring_1_of_nat(real)).  [resolve(711,a,706,a)].
2.15/2.40	Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,plus_plus(nat,A),B)) = hAPP(real,real,plus_plus(real,hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)).  [resolve(711,a,707,a)].
2.15/2.40	Derived: zero_zero(real) = hAPP(nat,real,semiring_1_of_nat(real),zero_zero(nat)).  [resolve(711,a,708,a)].
2.15/2.40	Derived: one_one(real) = hAPP(nat,real,semiring_1_of_nat(real),one_one(nat)).  [resolve(711,a,709,a)].
2.15/2.40	712 -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(406)].
2.15/2.40	713 -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(410)].
2.15/2.40	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(713,a,704,a)].
2.15/2.40	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(713,a,710,a)].
2.15/2.40	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(713,a,711,a)].
2.15/2.40	714 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.15/2.40	715 -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_235_add__le__cancel__left) # label(axiom).  [clausify(37)].
2.15/2.40	716 -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_235_add__le__cancel__left) # label(axiom).  [clausify(37)].
2.15/2.40	717 -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,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_224_add__less__cancel__right) # label(axiom).  [clausify(82)].
2.15/2.40	718 -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,B),D)),hAPP(A,A,plus_plus(A,C),D))) # label(fact_224_add__less__cancel__right) # label(axiom).  [clausify(82)].
2.15/2.40	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),B)),hAPP(int,int,plus_plus(int,A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(714,a,715,a)].
2.15/2.40	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),B)),hAPP(int,int,plus_plus(int,A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)).  [resolve(714,a,716,a)].
2.15/2.40	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,A),C)),hAPP(int,int,plus_plus(int,B),C))).  [resolve(714,a,718,a)].
2.15/2.40	719 -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_223_add__less__cancel__left) # label(axiom).  [clausify(171)].
2.15/2.41	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,A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(719,a,714,a)].
2.15/2.41	720 -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_223_add__less__cancel__left) # label(axiom).  [clausify(171)].
2.15/2.41	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,A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)).  [resolve(720,a,714,a)].
2.15/2.41	721 ordere236663937imp_le(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.15/2.41	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,A),B)),hAPP(real,real,plus_plus(real,A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(721,a,715,a)].
2.15/2.41	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(721,a,717,a)].
2.15/2.41	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(721,a,718,a)].
2.15/2.41	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,A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)).  [resolve(721,a,719,a)].
2.15/2.41	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,A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)).  [resolve(721,a,720,a)].
2.15/2.41	722 -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(259)].
2.15/2.41	723 -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(295)].
2.15/2.41	724 -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(348)].
2.15/2.41	725 -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(372)].
2.15/2.41	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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_eq(int),A),C)).  [resolve(725,a,714,a)].
2.15/2.41	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(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_eq(real),A),C)).  [resolve(725,a,721,a)].
2.15/2.41	726 -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(435)].
2.15/2.41	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(726,a,714,a)].
2.17/2.51	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,A),C)),hAPP(real,real,plus_plus(real,B),C))).  [resolve(726,a,721,a)].
2.17/2.51	727 -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(435)].
2.17/2.51	728 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
2.17/2.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(728,a,715,a)].
2.17/2.51	Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)).  [resolve(728,a,716,a)].
2.17/2.51	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),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))).  [resolve(728,a,718,a)].
2.17/2.51	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,A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(728,a,719,a)].
2.17/2.51	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,A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).  [resolve(728,a,720,a)].
2.17/2.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(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_eq(nat),A),C)).  [resolve(728,a,725,a)].
2.17/2.51	Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))).  [resolve(728,a,726,a)].
2.17/2.51	729 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
2.17/2.51	730 -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(41)].
2.17/2.51	731 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
2.17/2.51	732 linord893533164strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
2.17/2.51	733 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
2.17/2.51	734 -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(45)].
2.17/2.51	735 -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(102)].
2.17/2.51	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(735,a,733,a)].
2.27/2.56	736 -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(105)].
2.27/2.56	737 -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(235)].
2.27/2.56	738 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
2.27/2.56	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(738,a,735,a)].
2.27/2.56	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(738,a,737,a)].
2.27/2.56	739 -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(270)].
2.27/2.56	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(739,a,733,a)].
2.27/2.56	740 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
2.27/2.56	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(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(740,a,735,a)].
2.27/2.56	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(740,a,737,a)].
2.27/2.56	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(740,a,739,a)].
2.27/2.56	741 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.27/2.56	742 -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(46)].
2.27/2.56	743 -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(54)].
2.27/2.56	744 -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(98)].
2.27/2.56	745 -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(142)].
2.27/2.57	746 -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(159)].
2.27/2.57	Derived: one_one(nat) = hAPP(nat,nat,power_power(nat,A),zero_zero(nat)).  [resolve(741,a,742,a)].
2.27/2.57	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(741,a,743,a)].
2.27/2.57	Derived: ti(nat,A) = hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),A).  [resolve(741,a,744,a)].
2.27/2.57	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(741,a,745,a)].
2.27/2.57	747 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.27/2.57	Derived: one_one(int) = hAPP(nat,int,power_power(int,A),zero_zero(nat)).  [resolve(747,a,742,a)].
2.27/2.57	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(747,a,743,a)].
2.27/2.57	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,zero_zero(int)),A).  [resolve(747,a,744,a)].
2.27/2.57	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(747,a,745,a)].
2.27/2.57	748 -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(285)].
2.27/2.57	749 -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(365)].
2.27/2.57	Derived: hAPP(nat,nat,plus_plus(nat,A),B) = hAPP(nat,nat,plus_plus(nat,B),A).  [resolve(749,a,741,a)].
2.27/2.57	Derived: hAPP(int,int,plus_plus(int,A),B) = hAPP(int,int,plus_plus(int,B),A).  [resolve(749,a,747,a)].
2.27/2.57	750 -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(418)].
2.27/2.57	Derived: ti(nat,A) = hAPP(nat,nat,plus_plus(nat,A),zero_zero(nat)).  [resolve(750,a,741,a)].
2.27/2.57	Derived: ti(int,A) = hAPP(int,int,plus_plus(int,A),zero_zero(int)).  [resolve(750,a,747,a)].
2.27/2.57	751 -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(489)].
2.27/2.57	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(751,a,741,a)].
2.27/2.57	Derived: hAPP(int,int,plus_plus(int,A),hAPP(int,int,plus_plus(int,B),C)) = hAPP(int,int,plus_plus(int,B),hAPP(int,int,plus_plus(int,A),C)).  [resolve(751,a,747,a)].
2.27/2.57	752 -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(490)].
2.27/2.57	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(752,a,741,a)].
2.27/2.57	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(752,a,747,a)].
2.27/2.57	753 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
2.27/2.57	Derived: one_one(real) = hAPP(nat,real,power_power(real,A),zero_zero(nat)).  [resolve(753,a,742,a)].
2.27/2.57	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(753,a,743,a)].
2.35/2.62	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,zero_zero(real)),A).  [resolve(753,a,744,a)].
2.35/2.62	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(753,a,745,a)].
2.35/2.62	Derived: hAPP(real,real,plus_plus(real,A),B) = hAPP(real,real,plus_plus(real,B),A).  [resolve(753,a,749,a)].
2.35/2.62	Derived: ti(real,A) = hAPP(real,real,plus_plus(real,A),zero_zero(real)).  [resolve(753,a,750,a)].
2.35/2.62	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(753,a,751,a)].
2.35/2.62	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(753,a,752,a)].
2.35/2.62	754 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
2.35/2.62	755 -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(48)].
2.35/2.62	756 -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(203)].
2.35/2.62	757 -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(229)].
2.35/2.62	Derived: number_number_of(int,hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),A).  [resolve(757,a,754,a)].
2.35/2.62	758 -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(237)].
2.35/2.62	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(758,a,754,a)].
2.35/2.62	759 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom).  [assumption].
2.35/2.62	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(759,a,755,a)].
2.35/2.62	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(759,a,756,a)].
2.35/2.62	Derived: number_number_of(nat,hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,nat,semiring_1_of_nat(nat),A).  [resolve(759,a,757,a)].
2.35/2.62	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(759,a,758,a)].
2.35/2.62	760 -number_semiring(A) | number_number_of(A,hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_101_semiring__numeral__1__eq__1) # label(axiom).  [clausify(307)].
2.35/2.62	761 -number_semiring(A) | number_number_of(A,pls) = zero_zero(A) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom).  [clausify(340)].
2.35/2.62	Derived: number_number_of(nat,pls) = zero_zero(nat).  [resolve(761,a,759,a)].
2.35/2.62	762 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom).  [assumption].
2.35/2.62	Derived: number_number_of(real,hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,real,semiring_1_of_nat(real),A).  [resolve(762,a,757,a)].
2.35/2.62	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(762,a,758,a)].
2.48/2.72	763 -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(362)].
2.48/2.72	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(763,a,759,a)].
2.48/2.72	764 -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(193)].
2.48/2.72	765 linordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.48/2.72	766 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.48/2.72	767 -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(205)].
2.48/2.72	Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)).  [resolve(767,a,765,a)].
2.48/2.72	Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)).  [resolve(767,a,766,a)].
2.48/2.72	768 -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(263)].
2.48/2.72	769 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom).  [assumption].
2.48/2.72	Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)).  [resolve(769,a,767,a)].
2.48/2.72	770 -linord219039673up_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),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A))) # label(fact_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(79)].
2.48/2.72	771 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
2.48/2.72	772 -linord219039673up_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),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A))) # label(fact_195_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(79)].
2.48/2.72	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),A)),zero_zero(int))).  [resolve(772,a,771,a)].
2.48/2.72	773 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
2.48/2.72	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,plus_plus(real,A),A)),zero_zero(real))).  [resolve(773,a,772,a)].
2.48/2.72	774 -linord219039673up_add(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),B) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(109)].
2.48/2.72	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,plus_plus(int,A),A).  [resolve(774,a,771,a)].
2.48/2.72	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,plus_plus(real,A),A).  [resolve(774,a,773,a)].
2.48/2.72	775 -linord219039673up_add(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),B) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(109)].
2.50/2.77	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,plus_plus(int,A),A).  [resolve(775,a,771,a)].
2.50/2.77	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,plus_plus(real,A),A).  [resolve(775,a,773,a)].
2.50/2.77	776 -linord219039673up_add(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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(145)].
2.50/2.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))).  [resolve(776,a,771,a)].
2.50/2.77	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))).  [resolve(776,a,773,a)].
2.50/2.77	777 -linord219039673up_add(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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_265_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(145)].
2.50/2.77	778 -linord219039673up_add(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,plus_plus(A,B),B) # label(fact_214_double__zero__sym) # label(axiom).  [clausify(215)].
2.50/2.77	779 -linord219039673up_add(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),B) # label(fact_214_double__zero__sym) # label(axiom).  [clausify(215)].
2.50/2.77	780 -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(335)].
2.50/2.77	781 -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(335)].
2.50/2.77	Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),A))).  [resolve(781,a,771,a)].
2.50/2.77	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(781,a,773,a)].
2.50/2.77	782 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(381)].
2.50/2.77	Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)).  [resolve(782,a,771,a)].
2.50/2.77	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,plus_plus(real,A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)).  [resolve(782,a,773,a)].
2.50/2.77	783 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_264_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(381)].
2.50/2.77	784 -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(85)].
2.50/2.77	785 cancel146912293up_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
2.60/2.88	786 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
2.60/2.88	787 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
2.60/2.88	788 -semiring_0(A) | -power(A) | number_number_of(nat,B) != zero_zero(nat) | 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(154)].
2.60/2.88	789 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom).  [assumption].
2.60/2.88	790 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom).  [assumption].
2.60/2.88	Derived: -power(nat) | number_number_of(nat,A) != zero_zero(nat) | one_one(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),number_number_of(nat,A)).  [resolve(788,a,789,a)].
2.60/2.88	Derived: -power(int) | number_number_of(nat,A) != zero_zero(nat) | one_one(int) = hAPP(nat,int,power_power(int,zero_zero(int)),number_number_of(nat,A)).  [resolve(788,a,790,a)].
2.60/2.88	791 -semiring_0(A) | -power(A) | number_number_of(nat,B) = zero_zero(nat) | 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(154)].
2.60/2.88	Derived: -power(nat) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),number_number_of(nat,A)).  [resolve(791,a,789,a)].
2.60/2.88	Derived: -power(int) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(int) = hAPP(nat,int,power_power(int,zero_zero(int)),number_number_of(nat,A)).  [resolve(791,a,790,a)].
2.60/2.88	792 semiring_0(real) # label(arity_RealDef_Oreal___Rings_Osemiring__0) # label(axiom).  [assumption].
2.60/2.88	Derived: -power(real) | number_number_of(nat,A) != zero_zero(nat) | one_one(real) = hAPP(nat,real,power_power(real,zero_zero(real)),number_number_of(nat,A)).  [resolve(792,a,788,a)].
2.60/2.88	Derived: -power(real) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(real) = hAPP(nat,real,power_power(real,zero_zero(real)),number_number_of(nat,A)).  [resolve(792,a,791,a)].
2.60/2.88	793 -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(483)].
2.60/2.88	Derived: -power(nat) | zero_zero(nat) = A | zero_zero(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),A).  [resolve(793,b,789,a)].
2.60/2.88	Derived: -power(int) | zero_zero(nat) = A | zero_zero(int) = hAPP(nat,int,power_power(int,zero_zero(int)),A).  [resolve(793,b,790,a)].
2.60/2.88	Derived: -power(real) | zero_zero(nat) = A | zero_zero(real) = hAPP(nat,real,power_power(real,zero_zero(real)),A).  [resolve(793,b,792,a)].
2.60/2.88	794 -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(483)].
2.60/2.88	Derived: -power(nat) | zero_zero(nat) != A | one_one(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),A).  [resolve(794,b,789,a)].
2.60/2.88	Derived: -power(int) | zero_zero(nat) != A | one_one(int) = hAPP(nat,int,power_power(int,zero_zero(int)),A).  [resolve(794,b,790,a)].
2.60/2.88	Derived: -power(real) | zero_zero(nat) != A | one_one(real) = hAPP(nat,real,power_power(real,zero_zero(real)),A).  [resolve(794,b,792,a)].
2.60/2.88	795 -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(201)].
2.60/2.88	796 linordered_ring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring) # label(axiom).  [assumption].
2.60/2.88	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(795,a,796,a)].
2.60/2.88	797 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom).  [assumption].
2.60/2.88	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(797,a,795,a)].
2.80/3.11	798 -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(319)].
2.80/3.11	799 ab_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.80/3.11	800 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.80/3.11	801 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom).  [assumption].
2.80/3.11	802 -ab_semigroup_add(A) | plus_plus(A,B) = ti(fun(A,A),plus_plus(A,B)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(429)].
2.80/3.11	803 -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(486)].
2.80/3.11	804 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom).  [clausify(177)].
2.80/3.11	805 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom).  [assumption].
2.80/3.11	Derived: zero_zero(nat) = ti(nat,zero_zero(nat)).  [resolve(804,a,805,a)].
2.80/3.11	806 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom).  [assumption].
2.80/3.11	Derived: zero_zero(int) = ti(int,zero_zero(int)).  [resolve(806,a,804,a)].
2.80/3.11	807 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom).  [assumption].
2.80/3.11	Derived: zero_zero(real) = ti(real,zero_zero(real)).  [resolve(807,a,804,a)].
2.80/3.11	808 -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(155)].
2.80/3.11	809 comm_monoid_add(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
2.80/3.11	810 -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(252)].
2.80/3.11	811 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
2.80/3.11	812 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
2.80/3.11	813 -one(A) | ti(A,one_one(A)) = one_one(A) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(497)].
2.80/3.11	814 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom).  [assumption].
2.80/3.11	815 one(real) # label(arity_RealDef_Oreal___Groups_Oone) # label(axiom).  [assumption].
2.80/3.11	816 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom).  [assumption].
2.80/3.11	Derived: ti(nat,one_one(nat)) = one_one(nat).  [resolve(813,a,814,a)].
2.80/3.11	Derived: ti(real,one_one(real)) = one_one(real).  [resolve(813,a,815,a)].
2.80/3.11	Derived: ti(int,one_one(int)) = one_one(int).  [resolve(813,a,816,a)].
2.80/3.11	817 -semiri456707255roduct(A) | zero_zero(A) != ti(A,B) | ti(A,C) = hAPP(A,A,plus_plus(A,C),B) # label(fact_210_add__0__iff) # label(axiom).  [clausify(127)].
2.80/3.11	818 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom).  [assumption].
2.80/3.11	819 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
2.80/3.11	Derived: zero_zero(real) != ti(real,A) | ti(real,B) = hAPP(real,real,plus_plus(real,B),A).  [resolve(817,a,818,a)].
2.80/3.11	Derived: zero_zero(nat) != ti(nat,A) | ti(nat,B) = hAPP(nat,nat,plus_plus(nat,B),A).  [resolve(817,a,819,a)].
2.80/3.11	820 -semiri456707255roduct(A) | zero_zero(A) = ti(A,B) | ti(A,C) != hAPP(A,A,plus_plus(A,C),B) # label(fact_210_add__0__iff) # label(axiom).  [clausify(127)].
2.80/3.11	Derived: zero_zero(real) = ti(real,A) | ti(real,B) != hAPP(real,real,plus_plus(real,B),A).  [resolve(820,a,818,a)].
2.80/3.11	Derived: zero_zero(nat) = ti(nat,A) | ti(nat,B) != hAPP(nat,nat,plus_plus(nat,B),A).  [resolve(820,a,819,a)].
2.80/3.11	821 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom).  [assumption].
3.02/3.26	Derived: zero_zero(int) != ti(int,A) | ti(int,B) = hAPP(int,int,plus_plus(int,B),A).  [resolve(821,a,817,a)].
3.02/3.26	Derived: zero_zero(int) = ti(int,A) | ti(int,B) != hAPP(int,int,plus_plus(int,B),A).  [resolve(821,a,820,a)].
3.02/3.26	822 -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(167)].
3.02/3.26	823 ordere779506340up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
3.02/3.26	824 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
3.02/3.26	825 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
3.02/3.26	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(822,a,823,a)].
3.02/3.26	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(822,a,825,a)].
3.02/3.26	826 -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(247)].
3.02/3.26	827 -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(436)].
3.02/3.26	828 -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(315)].
3.02/3.26	829 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom).  [assumption].
3.02/3.26	830 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom).  [assumption].
3.02/3.26	831 -monoid_add(A) | plus_plus(A,B) = ti(fun(A,A),plus_plus(A,B)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(338)].
3.02/3.26	832 monoid_add(real) # label(arity_RealDef_Oreal___Groups_Omonoid__add) # label(axiom).  [assumption].
3.02/3.26	833 -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(415)].
3.02/3.26	834 -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(427)].
3.02/3.26	835 -ring_11004092258visors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) # label(fact_164_field__power__not__zero) # label(axiom).  [clausify(265)].
3.02/3.26	836 ring_11004092258visors(real) # label(arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
3.02/3.26	Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(nat,real,power_power(real,A),B).  [resolve(835,a,836,a)].
3.02/3.26	837 -ring_11004092258visors(A) | zero_zero(A) != ti(A,B) | 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_5_zero__eq__power2) # label(axiom).  [clausify(431)].
3.02/3.26	Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(837,a,836,a)].
3.02/3.26	838 -ring_11004092258visors(A) | zero_zero(A) = ti(A,B) | 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_5_zero__eq__power2) # label(axiom).  [clausify(431)].
3.02/3.26	839 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
4.01/4.29	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B).  [resolve(839,a,835,a)].
4.01/4.29	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(nat,int,power_power(int,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))).  [resolve(839,a,837,a)].
4.01/4.29	840 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom).  [assumption].
4.01/4.29	841 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f25(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(276)].
4.01/4.29	842 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f25(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(276)].
4.01/4.29	Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f25(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(840,a,841,a)].
4.01/4.29	Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f25(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)).  [resolve(840,a,842,a)].
4.01/4.29	843 -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),f35(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(370)].
4.01/4.29	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),f35(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(843,a,840,a)].
4.01/4.29	844 -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),f35(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(370)].
4.01/4.29	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),f35(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(844,a,840,a)].
4.01/4.29	845 -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),f35(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(370)].
4.01/4.29	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),f35(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)).  [resolve(845,a,840,a)].
4.01/4.29	
4.01/4.29	============================== end predicate elimination =============
4.01/4.29	
4.01/4.29	Auto_denials:  (non-Horn, no changes).
4.01/4.29	
4.01/4.29	Term ordering decisions:
4.01/4.29	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. ti=1. power_power=1. f2=1. f13=1. f16=1. f20=1. f23=1. f24=1. f34=1. f36=1. f37=1. f40=1. f41=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. f8=1. f14=1. f19=1. f28=1. f29=1. f30=1. f31=1. f39=1. f1=1. f5=1. f9=1. f10=1. f25=1. f32=1. f33=1. hAPP=1. f15=1. f35=1. f38=1. f3=1. f4=1. f6=1. f7=1. f11=1. f12=1. f17=1. f18=1. f21=1. f22=1. f26=1. f27=1. f42=1. f43=1. f44=1. f45=1.
4.01/4.29	
4.01/4.29	============================== end of process initial clauses ========
4.01/4.29	
4.01/4.29	============================== CLAUSES FOR SEARCH ====================
4.01/4.29	
4.01/4.29	============================== end of clauses for search =============
4.01/4.29	
4.01/4.29	============================== SEARCH ================================
4.01/4.29	
4.01/4.29	% Starting search at 1.88 seconds.
4.01/4.29	
4.01/4.29	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 68 (0.00 of 2.63 sec).
4.88/5.16	
4.88/5.16	Low Water (keep): wt=110.000, iters=3625
4.88/5.16	
4.88/5.16	Low Water (keep): wt=108.000, iters=3844
4.88/5.16	
4.88/5.16	Low Water (keep): wt=100.000, iters=3786
4.88/5.16	
4.88/5.16	Low Water (keep): wt=84.000, iters=3490
4.88/5.16	
4.88/5.16	Low Water (keep): wt=79.000, iters=3554
4.88/5.16	
4.88/5.16	Low Water (keep): wt=70.000, iters=3339
4.88/5.16	
4.88/5.16	Low Water (keep): wt=68.000, iters=3498
4.88/5.16	
4.88/5.16	Low Water (keep): wt=67.000, iters=3432
4.88/5.16	
4.88/5.16	Low Water (keep): wt=66.000, iters=3437
4.88/5.16	
4.88/5.16	Low Water (keep): wt=64.000, iters=3444
4.88/5.16	
4.88/5.16	Low Water (keep): wt=63.000, iters=3360
4.88/5.16	
4.88/5.16	Low Water (keep): wt=62.000, iters=3376
4.88/5.16	
4.88/5.16	Low Water (keep): wt=61.000, iters=3421
4.88/5.16	
4.88/5.16	Low Water (keep): wt=60.000, iters=3405
4.88/5.16	
4.88/5.16	Low Water (keep): wt=59.000, iters=3356
4.88/5.16	
4.88/5.16	Low Water (keep): wt=57.000, iters=3353
4.88/5.16	
4.88/5.16	Low Water (keep): wt=56.000, iters=3337
4.88/5.16	
4.88/5.16	Low Water (keep): wt=55.000, iters=3425
4.88/5.16	
4.88/5.16	Low Water (keep): wt=54.000, iters=3399
4.88/5.16	
4.88/5.16	Low Water (keep): wt=53.000, iters=3334
4.88/5.16	
4.88/5.16	Low Water (keep): wt=51.000, iters=3399
4.88/5.16	
4.88/5.16	Low Water (keep): wt=50.000, iters=3360
4.88/5.16	
4.88/5.16	============================== PROOF =================================
4.88/5.16	% SZS status Theorem
4.88/5.16	% SZS output start Refutation
4.88/5.16	
4.88/5.16	% Proof 1 at 3.48 (+ 0.04) seconds.
4.88/5.16	% Length of proof is 44.
4.88/5.16	% Level of proof is 7.
4.88/5.16	% Maximum clause weight is 42.000.
4.88/5.16	% Given clauses 1060.
4.88/5.16	
4.88/5.16	15 (all K number_number_of(int,K) = K) # label(fact_119_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
4.88/5.16	166 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all Na (zero_zero(X_a) = hAPP(nat,X_a,power_power(X_a,A_2),Na) <-> ti(X_a,A_2) = zero_zero(X_a) & Na != zero_zero(nat))))) # label(fact_184_power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
4.88/5.16	216 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls)) = ti(X_a,A_1)))) # label(fact_85_add__numeral__0__right) # label(axiom) # label(non_clause).  [assumption].
4.88/5.16	266 (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].
4.88/5.16	268 (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].
4.88/5.16	283 (all X_a (number_ring(X_a) -> (all K number_number_of(X_a,hAPP(int,int,succ,K)) = hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,K))))) # label(fact_325_number__of__succ) # label(axiom) # label(non_clause).  [assumption].
4.88/5.16	358 (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)) -> (hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya) = zero_zero(X_a) <-> ti(X_a,Xa) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Ya))))))) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
4.88/5.16	392 (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].
4.88/5.16	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].
4.88/5.16	551 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom).  [assumption].
4.88/5.16	564 -number_ring(A) | ti(A,B) = hAPP(A,A,plus_plus(A,B),number_number_of(A,pls)) # label(fact_85_add__numeral__0__right) # label(axiom).  [clausify(216)].
4.88/5.16	565 -number_ring(A) | number_number_of(A,hAPP(int,int,bit1,pls)) = one_one(A) # label(fact_12_semiring__norm_I110_J) # label(axiom).  [clausify(268)].
4.88/5.16	568 -number_ring(A) | 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_325_number__of__succ) # label(axiom).  [clausify(283)].
4.88/5.16	658 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) != hAPP(nat,A,power_power(A,B),C) | zero_zero(A) = ti(A,B) # label(fact_184_power__eq__0__iff) # label(axiom).  [clausify(166)].
4.88/5.16	660 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom).  [assumption].
4.88/5.16	667 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
4.88/5.16	677 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | zero_zero(A) != hAPP(A,A,plus_plus(A,B),C) | zero_zero(A) = ti(A,B) # label(fact_267_add__nonneg__eq__0__iff) # label(axiom).  [clausify(358)].
4.88/5.16	863 number_number_of(int,A) = A # label(fact_119_number__of__is__id) # label(axiom).  [clausify(15)].
4.88/5.16	910 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
4.88/5.16	945 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].
4.88/5.16	1103 one_one(int) != zero_zero(int) # label(fact_74_int__0__neq__1) # label(axiom).  [assumption].
4.88/5.16	1124 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_292_zero__zle__int) # label(axiom).  [clausify(266)].
4.88/5.16	1275 hAPP(int,int,plus_plus(int,A),zero_zero(int)) = A # label(fact_79_zadd__0__right) # label(axiom).  [clausify(392)].
4.88/5.16	1317 zero_zero(int) = number_number_of(int,pls) # label(fact_19_zero__is__num__zero) # label(axiom).  [assumption].
4.88/5.16	1318 pls = zero_zero(int).  [copy(1317),rewrite([863(5)]),flip(a)].
4.88/5.16	1349 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom).  [assumption].
4.88/5.16	1358 no_zero_divisors(int) # label(arity_Int_Oint___Rings_Ono__zero__divisors) # label(axiom).  [assumption].
4.88/5.16	1370 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)].
4.88/5.16	1371 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,zero_zero(int))))) = zero_zero(int).  [copy(1370),rewrite([1318(27)]),flip(a)].
4.88/5.16	1490 ti(int,A) = hAPP(int,int,plus_plus(int,A),number_number_of(int,pls)).  [resolve(551,a,564,a)].
4.88/5.16	1491 ti(int,A) = A.  [copy(1490),rewrite([1318(8),863(10),1275(9)])].
4.88/5.16	1492 number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int).  [resolve(551,a,565,a)].
4.88/5.16	1493 hAPP(int,int,bit1,zero_zero(int)) = one_one(int).  [copy(1492),rewrite([1318(5),863(8)])].
4.88/5.16	1496 number_number_of(int,hAPP(int,int,succ,A)) = hAPP(int,int,plus_plus(int,one_one(int)),number_number_of(int,A)).  [resolve(551,a,568,a)].
4.88/5.16	1497 hAPP(int,int,plus_plus(int,one_one(int)),A) = hAPP(int,int,succ,A).  [copy(1496),rewrite([863(6),863(12)]),flip(a)].
4.88/5.16	1724 -zero_neq_one(int) | -no_zero_divisors(int) | -power(int) | zero_zero(int) != hAPP(nat,int,power_power(int,A),B) | zero_zero(int) = ti(int,A).  [resolve(658,c,660,a)].
4.88/5.16	1725 hAPP(nat,int,power_power(int,A),B) != zero_zero(int) | zero_zero(int) = A.  [copy(1724),rewrite([1491(18)]),flip(d),unit_del(a,1349),unit_del(b,1358),unit_del(c,910)].
4.88/5.16	1758 -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) != hAPP(int,int,plus_plus(int,A),B) | zero_zero(int) = ti(int,A).  [resolve(677,a,667,a)].
4.88/5.16	1759 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,plus_plus(int,A),B) != zero_zero(int) | zero_zero(int) = A.  [copy(1758),rewrite([1491(38)]),flip(c)].
4.88/5.16	2085 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(1371),rewrite([1497(16),1493(24)])].
4.88/5.16	4747 -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(1759,a,945,a),rewrite([1497(20)]),flip(c),unit_del(c,1103)].
4.88/5.16	6561 hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = zero_zero(int).  [resolve(2085,a,1725,a),flip(a)].
4.88/5.16	7873 hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),A)) != zero_zero(int).  [resolve(4747,a,1124,a)].
4.88/5.16	7874 $F.  [resolve(7873,a,6561,a)].
4.88/5.16	
4.88/5.16	% SZS output end Refutation
4.88/5.16	============================== end of proof ==========================
4.88/5.16	
4.88/5.16	============================== STATISTICS ============================
4.88/5.16	
4.88/5.16	Given=1060. Generated=20625. Kept=6702. proofs=1.
4.88/5.16	Usable=1034. Sos=5237. Demods=392. Limbo=6, Disabled=1772. Hints=0.
4.88/5.16	Megabytes=28.14.
4.88/5.16	User_CPU=3.48, System_CPU=0.04, Wall_clock=3.
4.88/5.16	
4.88/5.16	============================== end of statistics =====================
4.88/5.16	
4.88/5.16	============================== end of search =========================
4.88/5.16	
4.88/5.16	THEOREM PROVED
4.88/5.16	% SZS status Theorem
4.88/5.16	
4.88/5.16	Exiting with 1 proof.
4.88/5.16	
4.88/5.16	Process 25054 exit (max_proofs) Thu Jul  2 06:42:33 2020
4.88/5.16	Prover9 interrupted
4.88/5.16	EOF