0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.35 % Computer : n013.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 14:08:16 EDT 2019 0.14/0.35 % CPUTime : 7.46/7.52 ============================== Prover9 =============================== 7.46/7.52 Prover9 (32) version 2009-11A, November 2009. 7.46/7.52 Process 19748 was started by sandbox2 on n013.cluster.edu, 7.46/7.52 Thu Aug 29 14:08:22 2019 7.46/7.52 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_19591_n013.cluster.edu". 7.46/7.52 ============================== end of head =========================== 7.46/7.52 7.46/7.52 ============================== INPUT ================================= 7.46/7.52 7.46/7.52 % Reading from file /tmp/Prover9_19591_n013.cluster.edu 7.46/7.52 7.46/7.52 set(prolog_style_variables). 7.46/7.52 set(auto2). 7.46/7.52 % set(auto2) -> set(auto). 7.46/7.52 % set(auto) -> set(auto_inference). 7.46/7.52 % set(auto) -> set(auto_setup). 7.46/7.52 % set(auto_setup) -> set(predicate_elim). 7.46/7.52 % set(auto_setup) -> assign(eq_defs, unfold). 7.46/7.52 % set(auto) -> set(auto_limits). 7.46/7.52 % set(auto_limits) -> assign(max_weight, "100.000"). 7.46/7.52 % set(auto_limits) -> assign(sos_limit, 20000). 7.46/7.52 % set(auto) -> set(auto_denials). 7.46/7.52 % set(auto) -> set(auto_process). 7.46/7.52 % set(auto2) -> assign(new_constants, 1). 7.46/7.52 % set(auto2) -> assign(fold_denial_max, 3). 7.46/7.52 % set(auto2) -> assign(max_weight, "200.000"). 7.46/7.52 % set(auto2) -> assign(max_hours, 1). 7.46/7.52 % assign(max_hours, 1) -> assign(max_seconds, 3600). 7.46/7.52 % set(auto2) -> assign(max_seconds, 0). 7.46/7.52 % set(auto2) -> assign(max_minutes, 5). 7.46/7.52 % assign(max_minutes, 5) -> assign(max_seconds, 300). 7.46/7.52 % set(auto2) -> set(sort_initial_sos). 7.46/7.52 % set(auto2) -> assign(sos_limit, -1). 7.46/7.52 % set(auto2) -> assign(lrs_ticks, 3000). 7.46/7.52 % set(auto2) -> assign(max_megs, 400). 7.46/7.52 % set(auto2) -> assign(stats, some). 7.46/7.52 % set(auto2) -> clear(echo_input). 7.46/7.52 % set(auto2) -> set(quiet). 7.46/7.52 % set(auto2) -> clear(print_initial_clauses). 7.46/7.52 % set(auto2) -> clear(print_given). 7.46/7.52 assign(lrs_ticks,-1). 7.46/7.52 assign(sos_limit,10000). 7.46/7.52 assign(order,kbo). 7.46/7.52 set(lex_order_vars). 7.46/7.52 clear(print_given). 7.46/7.52 7.46/7.52 % formulas(sos). % not echoed (5740 formulas) 7.46/7.52 7.46/7.52 ============================== end of input ========================== 7.46/7.52 7.46/7.52 % From the command line: assign(max_seconds, 180). 7.46/7.52 7.46/7.52 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 7.46/7.52 7.46/7.52 % Formulas that are not ordinary clauses: 7.46/7.52 1 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_1208_zero__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 2 (all D all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat))) # label(fact_3272_coprime__rmult__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 3 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))))) # label(fact_716_divides__mul__r) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 4 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sqrt,X) != zero_zero(real))) # label(fact_1626_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 5 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(int,nat,nat_1,Z))))) # label(fact_1379_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 6 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2813_complex__of__real__i) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 7 (all X all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))))) # label(fact_3369_ceiling__le__real) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 8 (all Ma all N_1 hAPP(fun(product_prod(nat,nat),bool),product_prod(nat,nat),the(product_prod(nat,nat)),hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1)) # label(fact_4144_divmod__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 9 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))) # label(fact_1052_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 10 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))))))) # label(fact_1059_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 11 (all W hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W))) # label(fact_3830_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 12 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),hAPP(real,real,F,X_1))))))) # label(fact_4927_isCont__inv__fun) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 13 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),N))) # label(fact_3273_gcd__diff2__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 14 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U_1)) # label(fact_4222_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 15 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 16 (all I (zero_zero(nat) = hAPP(int,nat,nat_1,I) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))))) # label(fact_1124_nat__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 17 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_c) & topological_space(X_b) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) & ti(X_a,X_2) != ti(X_a,A_2) -> hAPP(X_a,X_b,F,X_2) != ti(X_b,B_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4608_LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 18 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))) # label(fact_1472_odd__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 19 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_702_divides__add__revr) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 20 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_2369_two__realpow__gt) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 21 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 22 (all X_b all X_a (comm_monoid_mult(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,one_one(X_a)),one_one(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),S)))))))))) # label(fact_4779_setprod_Orelated) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 23 (all N_1 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3891_DERIV__pow) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 24 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_372_mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 25 (all N all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N))) & (M = zero_zero(nat) -> N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_1415_add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 26 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_1 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,X_3,N_3))))),K_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)))))))) # label(fact_3490_Bseq__iff3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 27 (all X_a (real_normed_vector(X_a) -> (all F all G all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially))))))) # label(fact_4448_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 28 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),N))))) # label(fact_718_divides__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 29 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & zero_zero(X_a) != ti(X_a,X_1))))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 30 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) = zero_zero(X_a))))) # label(fact_794_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 31 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_2875_floor__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 32 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1))))))))) # label(fact_4623_Cauchy__product__sums) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 33 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,D_1) = ti(X_a,B_1))))))) # label(fact_4195_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 34 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4951_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 35 (all X_a all X_b all X_c all X_2 all Xa hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),X_2,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Xa)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Xa)) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),X_2),Xa)) # label(fact_4014_split__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 36 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)) # label(fact_661_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 37 (all R_4 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X)))) # label(fact_4744_complex__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 38 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_2889_floor__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 39 (all Q_3 ((all A_4 all B_4 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) = Q_3 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (ti(int,A_4) != zero_zero(int) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4))))) -> zero_zero(rat) = Q_3)) # label(fact_4411_Rat__cases__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 40 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_461_one__less__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 41 (all X_a (linordered_semidom(X_a) -> (all M hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)))))) # label(fact_1278_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 42 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,abs_abs(int),Y))) # label(fact_4374_gcd__abs2__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 43 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),D_2),E_3)))))))) # label(fact_3822_DERIV__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 44 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1))))))) # label(fact_4527_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 45 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1586_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 46 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(X_a,bool),X_a),the(X_a)) = the(X_a))) # label(tsy_c_HOL_OThe_3_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 47 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))))) # label(fact_2602_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 48 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)))) # label(fact_295_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 49 (all P_2 all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_2)))) # label(fact_4334_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 50 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_438_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 51 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,suc,N)),N)) # label(fact_3262_coprime__Suc__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 52 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3111_div__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 53 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_3115_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 54 (all X_a frac(X_a) = ti(fun(int,fun(int,X_a)),frac(X_a))) # label(tsy_c_Nitpick_Ofrac_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 55 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = ti(X_a,A_1)))) # label(fact_111_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 56 (all X_a all X_b all X_c (topological_space(X_a) & topological_space(X_b) & topological_space(X_c) -> (all F all A_2 all G all L (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),L)) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4881_isCont__LIM__compose) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 57 (all X_a (comm_semiring_1(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 58 (all Ma all V_1 (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(int,int,number_number_of(int),V_1) <-> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V_1)) = Ma & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V_1))))) # label(fact_1408_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 59 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1261_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 60 (all X_a (ord(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)))) # label(fact_4837_min__ord__min) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 61 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_2059_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 62 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1)) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b)))) # label(fact_4145_The__split) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 63 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),hAPP(nat,nat,suc,N_1))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),N_1))))))))) # label(fact_3887_DERIV__power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 64 (all N_1 all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & (all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))) # label(fact_4280_Maclaurin2__objl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 65 (all X_a (semiring_1(X_a) -> (all M all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_1286_of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 66 (all N exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)) & hBOOL(hAPP(nat,bool,prime,P_6)))) # label(fact_3105_euclid) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 67 (all X_a (semiring_0(X_a) & dvd(X_a) -> (all P_1 all L ((exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),zero_zero(X_a)))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),L),X_2)))))))) # label(fact_602_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 68 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),F),A_3)))) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 69 (all N_1 (zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),N_1) <-> zero_zero(nat) = N_1)) # label(fact_1290_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 70 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat)) = ti(X_a,X)))) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 71 (all B all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3224_gcd__left__commute__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 72 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all N hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N)))) # label(fact_2518_power__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 73 (all Z_1 exists A_4 exists R_2 Z_1 = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(complex,complex,expi,A_4))) # label(fact_2914_complex__expi__Ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 74 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> ti(int,M) = ti(int,N)))))) # label(fact_205_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 75 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1679_divide__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 76 (all N_1 all Ma (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),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma)),Ma)) <-> N_1 = one_one(nat)))) # label(fact_506_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 77 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))))) # label(fact_85_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 78 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))))))) # label(fact_2435_zero__le__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 79 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1735_le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 80 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 81 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_766_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 82 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),sequentially)))))) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 83 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N)) # label(fact_1411_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 84 (all X_a (comm_ring_1(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1)))))))) # label(fact_478_dvd__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 85 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> N = M))) # label(fact_632_dvd__antisym) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 86 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_2452_fact__diff__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 87 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_3),B_2)),finite_psubset(X_a))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)))) # label(fact_3179_in__finite__psubset) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 88 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3882_card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 89 (all X_1 all K (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K)),one_one(int)) = ti(int,X_1) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_903_zOddI) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 90 (all X_b all X_c all X_a (comm_monoid_add(X_a) -> (all F all B_2 all A_3 hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_3)),B_2) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B_2)),A_3)))) # label(fact_4214_setsum__commute) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 91 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),combi(X_a)),A_2),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4560_LIM__ident) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 92 (all X_a (ring_1(X_a) -> (all N hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_2123_power__minus1__odd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 93 (all X_a (semiring_div(X_a) -> ti(fun(X_a,fun(X_a,X_a)),div_mod(X_a)) = div_mod(X_a))) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.52 94 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),C_1))),zero_zero(real)),sequentially)))) # label(fact_4490_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 95 (all Ma all N_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1) = zero_zero(int) <-> zero_zero(int) = ti(int,Ma) & ti(int,N_1) = zero_zero(int))) # label(fact_4361_gcd__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 96 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> P_5 = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),P_5)))) # label(fact_3079_prime__odd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 97 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)),Xa_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1))))) # label(fact_4716_scaleR__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 98 (all X_a all X_b (real_n1866405975lgebra(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (zero_zero(X_b) != ti(X_b,A_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),A_2)),A_3))))))) # label(fact_4481_tendsto__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 99 (all X_a (metric_space(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y))))))) # label(fact_3512_dist__pos__lt) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 100 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1369_odd__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 101 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(int,X_a,number_number_of(X_a),K_4)))) # label(fact_3581_number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 102 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3)))))) # label(fact_3803_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 103 (all X_a all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),A_3))) # label(fact_1995_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 104 (all X_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2450_even__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 105 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),zero_zero(int)))) # label(fact_2175_negative__zless__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 106 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1))))))) # label(fact_4990_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 107 (all X_a all X_b (real_normed_vector(X_b) -> (all R_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),A_2)),A_3)))))) # label(fact_4728_scaleR__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 108 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,M),zero_zero(int)),M))) # label(fact_352_zcong__id) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 109 (all X_a all X_b all X_c all X_d all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)))) # label(fact_3154_prod__induct4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 110 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B))) # label(fact_1082_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 111 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1) = zero_zero(real) <-> ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_3517_dist__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 112 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))))) # label(fact_2436_power__less__zero__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 113 (all N hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N)) # label(fact_2940_complex__cnj__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 114 (all X_b (number(X_b) & monoid_mult(X_b) -> (all V all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3872_power__number__of__even__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 115 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int)))))) # label(fact_983_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 116 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_4968_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 117 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4008_divide_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 118 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Y_2))))) -> L = zero_zero(real))))) # label(fact_2659_DERIV__local__min) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 119 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_3207_Bnor__mem__zle) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 120 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_2109_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 121 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),zero_zero(int)),X) = hAPP(int,int,abs_abs(int),X)) # label(fact_4387_gcd__0__left__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 122 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hAPP(X_a,nat,F,X_2) = hAPP(nat,nat,suc,zero_zero(nat)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,Xa) != ti(X_a,X_2) -> zero_zero(nat) = hAPP(X_a,nat,F,Xa)))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)))) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)))) # label(fact_4256_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 123 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_4944_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 124 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3595_ceiling__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 125 (all X_b all X_a (real_vector(X_a) -> (all A_2 all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2)),G)),A_3) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4730_scaleR__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 126 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,suc,zero_zero(nat))),A_1))) # label(fact_2861_coprime__Suc0_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 127 (all K_4 hAPP(int,real,number_number_of(real),K_4) = hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3762_number__of__real__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 128 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> ti(int,X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int)))) # label(fact_1201_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 129 (all P_5 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1160_Euler_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 130 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (ti(int,K) = zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,N_1))))) # label(fact_1061_split__zmod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 131 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3892_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 132 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) -> A_1 = zero_zero(nat))) # label(fact_892_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 133 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_946_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 134 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_688_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 135 (all X_a (semiring_1(X_a) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_12_one__power2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 136 (all Ma all N_1 ((zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),Ma)) & (-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | N_1 = zero_zero(nat)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1) = hAPP(product_prod(nat,nat),product_prod(nat,nat),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(product_prod(nat,nat),product_prod(nat,nat)),product_prod_case(nat,nat,product_prod(nat,nat)),hAPP(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat))),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat)))),combb(nat,fun(nat,product_prod(nat,nat)),nat),product_Pair(nat,nat)),suc)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1)),N_1))))) # label(fact_4052_divmod__nat__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 137 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arcsin),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))))) # label(fact_2656_DERIV__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 138 (all Ma all K all N_1 (zero_zero(nat) = K | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_724_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 139 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_833_int__less__induct) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 140 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),zero_zero(int))))))) # label(fact_3603_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 141 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))))) # label(fact_155_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 142 (all A_1 all B all C all D all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),C) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C),A_1) = one_one(int) -> (exists K_1 exists L_3 exists M_2 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N) = hAPP(int,int,abs_abs(int),A_1) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),N) = hAPP(int,int,abs_abs(int),B) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),N) = hAPP(int,int,abs_abs(int),C))))))))) # label(fact_3483_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 143 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> N = zero_zero(nat) | hAPP(nat,nat,suc,zero_zero(nat)) = N)) # label(fact_1451_less__2__cases) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 144 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))))))) # label(fact_4201_setsum__add__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 145 (all X_b (ring(X_b) & number(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_492_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 146 (all Ma all N_1 (zero_zero(nat) = Ma | (exists J_1 (Ma = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))))) # label(fact_1320_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 147 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),zEven))))) # label(fact_1271_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 148 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),hAPP(complex,complex,uminus_uminus(complex),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) # label(fact_2153_complex__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 149 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2494_of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 150 (all X_a (real_normed_algebra(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),sequentially))))))) # label(fact_4477_LIMSEQ__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 151 (all X_a (order(X_a) -> (all N_1 all Ma all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma))))))) # label(fact_1497_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 152 (all X_a (semiring_div(X_a) -> (all A_1 all B all C ((zero_zero(X_a) = ti(X_a,C) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) & (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))))))) # label(fact_998_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 153 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = ti(int,K_4)) # label(fact_130_add__Pls__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 154 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) -> one_one(nat) = A_1)) # label(fact_897_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 155 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),C_1)),zero_zero(real)),sequentially)))) # label(fact_4491_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 156 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co1399186613setsum(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4658_LIMSEQ__setsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 157 (all X_1 all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_1)) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,A_2))))))) # label(fact_4928_DERIV__isconst2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 158 (all X_a all X_b (no_zero_divisors(X_b) & comm_semiring_1(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = zero_zero(X_b) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & zero_zero(X_b) = hAPP(X_a,X_b,F,X_2)))))))) # label(fact_3949_setprod__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 159 (all X hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,X)) = X) # label(fact_3535_int__of__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 160 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> (all P_6 -(hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),B_1)))))) # label(fact_3062_coprime__prime__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 161 (all X_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int))) # label(fact_1062_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 162 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4544_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 163 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),Ma))))) # label(fact_681_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 164 (all X_a (mult_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)))) # label(fact_323_mult__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 165 (all X_a all X_b (real_n2089651433ebra_1(X_a) & metric_space(X_b) -> (all K all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,L_2) = ti(X_b,K))))) # label(fact_4557_LIM__const__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 166 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))))))) # label(fact_4524_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 167 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X_1))))),X_1)))))) # label(fact_2005_best__odd__division__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 168 (all X_b all X_c all X_a (topological_space(X_b) & topological_space(X_c) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),G),hAPP(X_a,X_b,F,A_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_c),fun(X_a,bool),isCont(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),A_2))))))) # label(fact_4900_isCont__o2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 169 (all X_a all A_2 all F all V_1 all N_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),N_1)),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))))) # label(fact_4152_nat__rec__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 170 (all V_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)))) # label(fact_4797_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 171 (all N_1 all X_1 (zero_zero(real) != X_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,exp(real),X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4)))))))) # label(fact_4269_Maclaurin__exp__lt) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 172 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) | Ma = hAPP(nat,nat,suc,N_1))) # label(fact_1245_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 173 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1536_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 174 (all X all I_1 hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),I_1)),pi)))) # label(fact_3399_tan__periodic__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 175 (all Ma all K all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,Ma)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)))))) # label(fact_857_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 176 (all X_b (minus(X_b) -> minus_minus(X_b) = ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 177 (all Real1_1 all Real2_1 hAPP(complex,nat,size_size(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2754_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 178 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_1590_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 179 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_3065_prime__nd__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 180 (all X_a (real_normed_vector(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1791_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 181 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)))) # label(fact_4389_Fract__coprime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 182 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_915_mod__div__equality) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 183 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1761_SRStar__finite) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 184 (all N all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N))))) # label(fact_1519_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 185 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1520_SRStar__card) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 186 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)) -> (hAPP(nat,nat,suc,I_1) != K_4 -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> hAPP(nat,nat,suc,J_1) != K_4))))) # label(fact_1542_lessE) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 187 (all X_a (dist_norm(X_a) -> norm_norm(X_a) = ti(fun(X_a,real),norm_norm(X_a)))) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 188 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),X)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2265_arccos__cos2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 189 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))))))) # label(fact_2046_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 190 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),X))))) # label(fact_2114_minus1__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 191 (all V hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_3337_real__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 192 (all X hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_270_quartic__square__square) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 193 (all X all N hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),N)),pi)))) # label(fact_2257_tan__periodic__n) # label(axiom) # label(non_clause). [assumption]. 7.46/7.53 194 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4295_setsum__mono__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 195 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arccos),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))))) # label(fact_2631_DERIV__arccos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 196 (all X all Y hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = X) # label(fact_2993_Re) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 197 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1351_mod__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 198 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),H)),A_3))))) # label(fact_4219_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 199 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_2825_dense__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 200 (all X_a all A_3 all F all N_1 (hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) = ti(fun(X_a,bool),A_3) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3868_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 201 (all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) = one_one(real)) # label(fact_4240_sumr__cos__zero__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 202 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_4 (ti(X_a,R_4) != zero_zero(X_a) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,D) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_4),D)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_4),C))))))) # label(fact_252_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 203 (all Z all P_1 ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),N_2)))) -> ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) -> hBOOL(hAPP(int,bool,P_1,Z))))) # label(fact_3527_int__of__nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 204 (all W all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z_1)))) # label(fact_83_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 205 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_3849_Im_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 206 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1)))) # label(fact_4884_isCont__real__root) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 207 (all X_a (linordered_idom(X_a) -> (all X_1 all A_2 all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),R_1)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),R_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),A_2))),R_1)))))) # label(fact_1883_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 208 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,cos,X_1)))) # label(fact_4097_cos__converges) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 209 (all X all Z_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D))),Z_1)))) # label(fact_1986_decr__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 210 (all N (N != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) # label(fact_1460_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 211 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))) # label(fact_4749_summable__norm__exp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 212 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),X_3)),Y_3)))))) # label(fact_4841_vanishes__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 213 (all X_a (real_normed_field(X_a) -> (all Y_3 all F all X_1 all X_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),X_3)) -> (ti(X_a,Y_3) = ti(X_a,X_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Y_3))))))) # label(fact_2634_DERIV__cong) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 214 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A_3),B_2)))))) # label(fact_3669_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 215 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),pls)))))) # label(fact_47_le__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 216 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4583_LIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 217 (all X_1 all Y_1 (hAPP(complex,complex,cnj,X_1) = hAPP(complex,complex,cnj,Y_1) <-> Y_1 = X_1)) # label(fact_2937_complex__cnj__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 218 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z))))) # label(fact_1126_nat__mono__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 219 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hAPP(int,real,number_number_of(real),min_1) = hAPP(real,real,sgn_sgn(real),X))) # label(fact_2226_real__sgn__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 220 (all M all N (one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)) -> hAPP(int,int,abs_abs(int),M) = one_one(int))) # label(fact_1927_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 221 (all L all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),L))) -> ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,N_2)),E)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)))))) # label(fact_4878_increasing__LIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 222 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,suc,N))) = X)) # label(fact_2703_real__root__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 223 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hAPP(X_a,X_a,F,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 224 (all V hAPP(complex,real,re,hAPP(int,complex,number_number_of(complex),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_3005_complex__Re__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 225 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)) # label(fact_1961_set__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 226 (all M all N all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_1)) -> Qr_1 = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3099_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 227 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (ti(X_a,E_3) = ti(X_a,D_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3))))))) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 228 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_772_one__reorient) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 229 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))),B)))))) # label(fact_1731_gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 230 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3793_one__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 231 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1544_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 232 (all Ma hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ma),one_one(int))),Ma) = hAPP(int,fun(int,bool),norRRset,Ma)) # label(fact_3560_norRRset__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 233 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))))) # label(fact_715_divides__mul__l) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 234 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),zero_zero(real)),sequentially)) -> (exists L_3 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially)) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L_3),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),L_3)))))))))) # label(fact_4514_Bolzano__nest__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 235 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> N = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_2877_floor__eq3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 236 (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4018_summable__rabs__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 237 (all X_a (real_normed_algebra(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_4678_mult_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 238 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2)),sequentially)))) # label(fact_4511_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 239 (all X_a (group_add(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = hAPP(X_a,X_a,uminus_uminus(X_a),X_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a))))) # label(fact_2064_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 240 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1836_arctan__monotone) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 241 (all X_a hilbert_Eps(X_a) = ti(fun(fun(X_a,bool),X_a),hilbert_Eps(X_a))) # label(tsy_c_Hilbert__Choice_OEps_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 242 (all Q_3 all R_4 all B all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)))))) # label(fact_1134_mod__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 243 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 244 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_3304_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 245 (all V all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))) # label(fact_67_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 246 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_369_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 247 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_4689_scaleR_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 248 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))))) # label(fact_448_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 249 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),M)) # label(fact_963_zpower__zmod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 250 (all X hAPP(int,real,number_number_of(real),X) = hAPP(int,real,ring_1_of_int(real),X)) # label(fact_3582_number__of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 251 (all N all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),N))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N)))) # label(fact_1517_power__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 252 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),J_2)))))) # label(fact_1402_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 253 (all B_1 all C_1 all A_2 all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),D_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B_1),C_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),D_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),C_1) <-> D_1 = C_1 & B_1 = A_2)))) # label(fact_3270_coprime__crossproduct__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 254 (all X_a all X_b all X_c all X_d all X_e all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_4),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)))) # label(fact_3152_prod__induct5) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 255 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_325_one__neq__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 256 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)))) # label(fact_942_mod__add__self2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 257 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_1797_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 258 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),im),hAPP(complex,real,im,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4569_Im_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 259 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3183_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 260 (all N all M hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N))) # label(fact_923_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 261 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S))) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2)))))))) # label(fact_3939_setprod__pos__nat__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 262 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3039_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 263 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),Z_1) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2101_mult__minus1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 264 (all X_a (semiring_div(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),W)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),W)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1))))))) # label(fact_1000_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 265 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)))) # label(fact_795_diff__self) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 266 (all X_a (number_ring(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_364_power__m1__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 267 (all A_3 all K (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))))) -> hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))) = A_3)) # label(fact_4232_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 268 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))))),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),X_1),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3967_DERIV__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 269 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) -> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4325_finite__nat__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 270 (all X_a all X_b all C_1 all P_4 ((all A_4 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) = ti(product_prod(X_a,X_b),P_4) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,A_4),B_4)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)))) # label(fact_4061_splitI2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 271 (all X hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))) = hAPP(int,int,abs_abs(int),X)) # label(fact_1932_int__nat__abs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 272 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))))))))) # label(fact_1708_less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 273 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3187_fact__less__mono__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 274 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),ii)) # label(fact_2767_Complex__mult__i) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 275 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4801_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 276 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),X) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)))))) # label(fact_3295_ceiling__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 277 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int))))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X)))))) # label(fact_3616_floor__exists) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 278 (all X_a all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2188_subsetI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 279 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_659_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 280 (all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit1,L_4))) # label(fact_512_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 281 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_4812_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 282 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D)))) # label(fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 283 (all N_1 zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_4237_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 284 (all D_1 all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),A_2)))) # label(fact_2851_coprime__mul__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 285 (all X hAPP(int,int,succ,hAPP(int,int,pred,X)) = ti(int,X)) # label(fact_2899_succ__pred) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 286 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_4045_cnj_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 287 (all X all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),K_4))) # label(fact_2684_real__root__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 288 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1))))) # label(fact_3588_of__int__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 289 (all A_1 all B (A_1 != B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_625_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 290 (all X hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X)) # label(fact_2291_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 291 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))))))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 292 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 293 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> ti(int,B_1) = ti(int,A_2) | ti(int,B_1) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_2))))) # label(fact_841_wset__mem__imp__or) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 294 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3031_cis__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 295 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))) # label(fact_4964_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 296 (all A_1 all N all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))) # label(fact_3217_gcd__exp__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 297 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4941_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 298 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_433_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 299 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Q_3)) -> P_5 = Q_3)))) # label(fact_3048_primes__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 300 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4444_LIMSEQ__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 301 (all X_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),X_1),sequentially)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),X_1))) & (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,M_2)),hAPP(nat,real,A_2,N_2))))) | (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),hAPP(nat,real,A_2,M_2))))) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,A_2,N_2))))))) # label(fact_4434_monoseq__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 302 (all Z_1 hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = zero_zero(real)) # label(fact_2984_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 303 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2824_pinf_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 304 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5))))))))) # label(fact_850_MultInv__zcong__prop3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 305 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))))) # label(fact_1116_SRStar__SR__prop) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 306 (all X_a (group_add(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),zero_zero(X_a)))) # label(fact_2025_minus__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 307 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd))))) # label(fact_1365_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 308 (all X_1 all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),A_3)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))))) # label(fact_3900_RsetR__zmult__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 309 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))))) # label(fact_1307_power__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 310 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))))) # label(fact_175_odd__less__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 311 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1)))) # label(fact_4534_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 312 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 ((all S_2 ((all N_2 hAPP(nat,real,S_2,N_2) != A_2) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) -> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))))))) # label(fact_4661_LIMSEQ__SEQ__conv2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 313 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1276_odd__iff__not__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 314 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)))) # label(fact_3649_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 315 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),C_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),D_2),C_1))))))) # label(fact_3836_DERIV__cdivide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 316 (all X_a (field_inverse_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2525_field__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 317 (all X_a (metric_space(X_a) -> (all K all L (ti(X_a,L) = ti(X_a,K) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),L),sequentially)))))) # label(fact_4465_LIMSEQ__const__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 318 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y_1))) # label(fact_1464_even__prod__div__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 319 (all M all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)))) # label(fact_3455_zgcd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 320 (all N all X (X = hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)) -> hAPP(real,nat,natfloor,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(real,nat,natfloor,X)),N))) # label(fact_2334_natfloor__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 321 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (P_5 != Q_3 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),Q_3)))))) # label(fact_3049_distinct__prime__coprime) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 322 (all N_1 all N_4 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)))) # label(fact_3675_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 323 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_a),product_fst(X_a,X_b)) = product_fst(X_a,X_b)) # label(tsy_c_Product__Type_Ofst_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 324 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> (exists K_1 ti(int,B_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),K_1))))) # label(fact_421_zcong__iff__lin) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 325 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_2842_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 326 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2162_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 327 (all X_b all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all G all A_3 hAPP(real,X_a,of_real(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,real),fun(X_b,X_a),hAPP(fun(real,X_a),fun(fun(X_b,real),fun(X_b,X_a)),combb(real,X_a,X_b),of_real(X_a)),G)),A_3)))) # label(fact_4189_of__real_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 328 (all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1608_zero__induct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 329 (all X_a (comm_semiring_1(X_a) -> (all A_2 all D_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1))))))) # label(fact_4324_arith__series__general) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 330 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4579_LIM__add__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 331 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))))))) # label(fact_4518_LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 332 (all Ma all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ma),hAPP(int,int,number_number_of(int),N_1))))) # label(fact_3389_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 333 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) != zero_zero(int))) # label(fact_2159_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 334 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma)),N_1)))) # label(fact_4120_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 335 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) = X)))) # label(fact_3406_powr__log__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 336 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N)) # label(fact_4807_min__0L) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 337 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2013_norm__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 338 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_3247_gcd__add2__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 339 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4274_series__pos__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 340 (all X_a all X_b all X_c combs(X_a,X_b,X_c) = ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 341 (all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4354_gcd__add1__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 342 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B)))) # label(fact_978_mod__mult__self2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 343 (all X_a (semiring_1(X_a) -> (all M all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))))) # label(fact_1287_of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 344 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),N)) = one_one(X_a)))) # label(fact_1896_abs__power__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 345 (all X_a (real_normed_field(X_a) -> (all N all Z_1 all K_5 all H_2 (zero_zero(X_a) != ti(X_a,H_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),Z_1)),K_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2))),K_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2)),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),N))),H_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),N)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),K_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(X_a,real,norm_norm(X_a),H_2)))))))))) # label(fact_1773_lemma__termdiff3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 346 (all X hAPP(complex,real,im,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2992_complex__Im__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 347 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,inverse_inverse(real),X))) # label(fact_2623_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 348 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X_1)))))) # label(fact_3310_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 349 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 350 (all Ma all K all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_605_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 351 (all X_a all R_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_3)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))))) # label(fact_4339_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 352 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,B) != zero_zero(int) -> ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1192_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 353 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2384_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 354 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1625_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 355 (all X_a (number_ring(X_a) -> (all V hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls)))))) # label(fact_16_add__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 356 (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(nat,fun(real,complex)),fun(fun(nat,real),fun(nat,complex)),combs(nat,real,complex),hAPP(fun(nat,real),fun(nat,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(nat,real),fun(nat,fun(real,complex))),combb(real,fun(real,complex),nat),complex_1),X_3)),Y_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),sequentially))))) # label(fact_4513_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 357 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (exists N_2 hAPP(nat,int,semiring_1_of_nat(int),N_2) = ti(int,K_4)))) # label(fact_1490_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 358 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 359 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3))))) # label(fact_1952_equalityE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 360 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N))) # label(fact_665_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 361 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),A_1))))) # label(fact_979_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 362 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all G all X_1 all Ma (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Ma)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),exp(X_a)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,G,X_1))),Ma))))))) # label(fact_3864_DERIV__fun__exp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 363 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (exists B_4 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3)))))) # label(fact_2727_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 364 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2340_cos__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 365 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),zero_zero(int)))) # label(fact_2166_negative__zle__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 366 (all A_1 all C all B all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1643_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 367 (all X_a (semiring_div(X_a) -> (all A_2 all B_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_1),A_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)))))) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 368 (all X_a (real_normed_vector(X_a) -> (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),zero_zero(real)))))) # label(fact_1780_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 369 (all X_b all X_c all X_a all X_d all X_e all F all G all P_4 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_4)) = hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_4)) # label(fact_4005_split__twice) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 370 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3914_DERIV__cos__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 371 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))))) # label(fact_128_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 372 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_1305_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 373 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))))) # label(fact_53_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 374 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_3294_ceiling__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 375 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),R_4))) # label(fact_3344_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 376 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2095_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 377 (all X_a (field_char_0(X_a) -> ti(fun(X_a,bool),field_char_0_Rats(X_a)) = field_char_0_Rats(X_a))) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 378 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 379 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B_5)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))))) # label(fact_934_mod__mult__cong) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 380 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3788_one__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 381 (all X_a (linordered_idom(X_a) -> (all X all Y all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2440_power__mono__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 382 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4567_cnj_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 383 (all X_a all G all A_3 hAPP(complex,real,im,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),A_3)) # label(fact_4248_Im_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 384 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),K)))) # label(fact_4936_finite__atMost) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 385 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C)) # label(fact_954_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 386 (all X_a (real_n2089651433ebra_1(X_a) -> (all N hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,real,semiring_1_of_nat(real),N)))) # label(fact_1775_norm__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 387 (all X_a (field_inverse_zero(X_a) -> (all A_2 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2) <-> (ti(X_a,C_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_2)) & (zero_zero(X_a) != ti(X_a,C_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1)))))) # label(fact_1685_eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 388 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3493_Cauchy__Bseq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 389 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N)))))))) # label(fact_404_power__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 390 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_883_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 391 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_813_add__increasing2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 392 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists X_2 ((all Y_2 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_2),N) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) -> Y_2 = X_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_2),N) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2))))))) # label(fact_733_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 393 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_3365_floor__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 394 (all X_a (metric_space(X_a) -> (all X2_1 all Y all X1_1 all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X1_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X2_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3502_dist__triangle__half__r) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 395 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a)))))) # label(fact_282_dvd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 396 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_a) & topological_space(X_b) -> (all F all A_2 all G all L (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),hAPP(X_a,X_b,G,L)),hAPP(X_a,filter(X_a),at(X_a),L))) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4558_LIM__compose) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 397 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_939_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 398 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_1976_ln__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 399 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2446_even__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 400 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,A_1) != zero_zero(int) -> ti(int,R_4) = zero_zero(int)))) # label(fact_1188_self__remainder) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 401 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))))) # label(fact_1121_div__less__dividend) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 402 (all X hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) # label(fact_3342_real__of__int__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 403 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_261_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 404 (all X_3 ((all R_2 exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),X_3)),zero_zero(real)),sequentially)))) # label(fact_4660_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 405 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_3528_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 406 (all X_a all X_b all P_1 all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,P_1))),Q_1)),X_2)) <-> hBOOL(P_1) & hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)))) # label(fact_4044_split__part) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 407 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3195_fact__ge__one__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 408 (all X_a all X_b all R_3 all S (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_3)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S))))) # label(fact_4335_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 409 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_4803_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 410 (all X_a all X_1 all A_3 (hBOOL(hAPP(X_a,bool,A_3,X_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 411 (all M all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_2912_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 412 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2))))))) # label(fact_1711_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 413 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)),N))) # label(fact_1120_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 414 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)))) # label(fact_3681_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 415 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_2177_power3__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 416 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_3307_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 417 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_3306_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 418 (all N_1 all X_1 ((-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = zero_zero(real)) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = hAPP(real,real,uminus_uminus(real),hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),hAPP(real,real,uminus_uminus(real),X_1))))))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),X_1))) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)))) # label(fact_4136_root__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 419 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),A_2))))))) # label(fact_4896_isCont__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 420 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2712_real__root__increasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 421 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M)) # label(fact_693_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 422 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3381_powr__minus__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 423 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_4046_Re_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 424 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_459_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 425 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1540_field__le__epsilon) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 426 (all Y_1 hAPP(real,real,arctan,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),tan)),Y_1))))) # label(fact_4132_arctan__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 427 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_501_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 428 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y)),hAPP(real,real,tan,X))))))) # label(fact_2272_tan__monotone) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 429 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_1577_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 430 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)))) # label(fact_3282_ceiling__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 431 (all X_b all X_a all Q_1 all P_1 ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)))) # label(fact_4342_predicate2I) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 432 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),R_4))) # label(fact_2814_i__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 433 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_4)) # label(fact_3165_rcis__zero__arg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 434 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1796_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 435 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1)))))) # label(fact_713_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 436 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2)))) # label(fact_423_zcong__zero__equiv__div) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 437 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_2891_le__mult__floor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 438 (all X_b all X_a all A_1 all B hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),A_1),B)) = ti(X_a,B)) # label(fact_3138_snd__conv) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 439 (all Z_1 (-hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)) = ti(int,Z_1))) # label(fact_1509_not__neg__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 440 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),int_gcd,X),Y) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y))))) # label(fact_3671_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 441 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1))),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1165_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 442 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int)) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a)))))) # label(fact_2887_floor__add__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 443 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_774_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 444 (all P_5 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B)) & hBOOL(hAPP(nat,bool,prime,P_5))))) # label(fact_3060_coprime__prime) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 445 (all Z_1 all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_648_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 446 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4619_DERIV__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 447 (all X_a all X_b (real_n2089651433ebra_1(X_b) & metric_space(X_a) -> (all A_2 all K all L_2 (ti(X_a,K) != ti(X_a,L_2) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),L_2),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4559_LIM__const__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 448 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (ti(int,X_2) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4638_aset_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 449 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1))))) # label(fact_2581_left__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 450 (all M hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),one_one(int)) = one_one(int)) # label(fact_4360_gcd__1__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 451 (all X_a (real_normed_algebra(X_a) & power(X_a) -> (all Ma all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(nat,fun(nat,X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),combc(nat,nat,X_a),hAPP(fun(nat,X_a),fun(nat,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(nat,X_a),fun(nat,fun(nat,X_a))),combb(X_a,fun(nat,X_a),nat),power_power(X_a)),X_3)),Ma)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma)),sequentially)))))) # label(fact_4467_LIMSEQ__pow) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 452 (all Y_1 hAPP(real,real,arcsin,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),sin)),Y_1))))) # label(fact_4133_arcsin__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 453 (all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))))) # label(fact_1478_mod__induct__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 454 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1))) # label(fact_3857_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 455 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_814_add__increasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 456 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2584_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 457 (all X_b all X_a (ab_group_add(X_a) -> (all F all A_3 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),uminus_uminus(X_a)),F)),A_3)))) # label(fact_4213_setsum__negf) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 458 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),one_one(int))) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1476_inv__is__inv__aux) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 459 (all X_a all X_b (zero(X_a) & metric_space(X_a) & real_n2089651433ebra_1(X_b) -> (all A_2 all K (zero_zero(X_a) != ti(X_a,K) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),zero_zero(X_a)),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4562_LIM__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 460 (all P_5 all X hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)) # label(fact_1154_MultInv__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 461 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_1041_div__add__self1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 462 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),hAPP(X_a,real,norm_norm(X_a),A_2)),sequentially)))))) # label(fact_4466_LIMSEQ__norm) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 463 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_796_diff__0__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 464 (all X_a (field(X_a) -> (all N all M all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))))))) # label(fact_1751_power__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 465 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),hAPP(nat,nat,suc,L)) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1))) # label(fact_3683_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 466 (all I all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_1522_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 467 (all Z_1 -(all M_2 all N_2 ti(int,Z_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_1521_int__diff__cases) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 468 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool)),bijR(X_a,X_b)) = bijR(X_a,X_b)) # label(tsy_c_BijectionRel_ObijR_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 469 (all X_b all X_a all A_2 all B_1 all A_8 all B_7 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_8),B_7) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) <-> ti(X_b,B_7) = ti(X_b,B_1) & ti(X_a,A_2) = ti(X_a,A_8))) # label(fact_3136_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 470 (all A_2 all Ma hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)))) # label(fact_3208_Bnor__fin) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 471 (all X_a (group_add(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = ti(X_a,B))))) # label(fact_2069_minus__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 472 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W_1)))) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 473 (all A_2 all C_1 all D_1 all B_1 (ti(int,B_1) != zero_zero(int) -> (ti(int,D_1) != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1) <-> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))))) # label(fact_3753_eq__rat_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 474 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),zero_zero(int)) = zero_zero(X_a))) # label(fact_3580_of__int__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 475 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2713_real__root__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 476 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4591_LIM__norm) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 477 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3185_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 478 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int))) <-> ti(int,Z) = zero_zero(int))) # label(fact_1939_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 479 (all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),M)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1147_add__self__div__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 480 (all X_1 all Y_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_1),Y_1))) -> (zero_zero(nat) != Y_1 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),Y_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1)) & (zero_zero(nat) = Y_1 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1) = X_1))) # label(fact_3670_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 481 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool))),prod(X_a,X_b)) = prod(X_a,X_b)) # label(tsy_c_Nitpick_Oprod_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 482 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_1566_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 483 (all X_a (metric_space(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_1))))))))) # label(fact_4521_metric__LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 484 (all X_a (semiring(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 485 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,exp(real),hAPP(real,real,ln,X)) = X)) # label(fact_2601_exp__ln) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 486 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))))) # label(fact_687_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 487 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4503_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 488 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2341_nat__less__real__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 489 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))))) # label(fact_1014_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 490 (all X_a (field(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2558_field__divide__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 491 (all X_b all X_a (real_normed_vector(X_b) & real_algebra_1(X_b) & topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4595_LIM__of__real) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 492 (all X_a all X_b all X_c all X_1 all P_1 ((all A_4 all B_4 all C_4 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)))) # label(fact_3148_prod__induct3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 493 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,W_1)),zero_zero(int))))) # label(fact_161_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 494 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = zero_zero(real)) # label(fact_2297_sin__npi) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 495 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),pls)))) # label(fact_158_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 496 (all I (zero_zero(int) != ti(int,I) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),dvd_dvd(int)),I)))))) # label(fact_3841_finite__divisors__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 497 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_408_less__add__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 498 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)))))) # label(fact_2269_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 499 (all X_a (semiring_1(X_a) -> iszero(X_a) = ti(fun(X_a,bool),iszero(X_a)))) # label(tsy_c_Int_Oiszero_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 500 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_2621_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 501 (all X_a (number_ring(X_a) -> (all V all W all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C)))) # label(fact_507_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 502 (all X_a (real_normed_vector(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X_1)),zero_zero(real))) <-> zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_1786_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 503 (all X_a (ring_char_0(X_a) -> (all Z (hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a) <-> ti(int,Z) = zero_zero(int))))) # label(fact_3579_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 504 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3120_mod__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 505 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1558_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 506 (all X_a (monoid_mult(X_a) -> (all Z_1 all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W)))))) # label(fact_3871_power__number__of__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 507 (all Z_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,Z_1)) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_2941_complex__mod__cnj) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 508 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3109_div__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 509 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2626_exp__bound) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 510 (all X_a (boolean_algebra(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2953_double__compl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 511 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))))) # label(fact_1798_SetS__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 512 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 513 (all X_a (power(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 514 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),P_5)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),one_one(int)),P_5)))))) # label(fact_535_zcong__square) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 515 (all A_1 all B ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> (ti(int,A_1) = zero_zero(int) | zero_zero(int) = ti(int,B) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) & (-(ti(int,B) = zero_zero(int) | ti(int,A_1) = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B)))) # label(fact_3925_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 516 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3) = one_one(X_b))))) # label(fact_3952_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 517 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),exp(X_a)),X_1))))) # label(fact_4891_isCont__exp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 518 (all R_4 all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),R_4)),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3174_rcis__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 519 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(X_a,X_b,B_1,A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S)))))) # label(fact_4215_setsum__delta) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 520 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hAPP(real,real,F,Y_2) = hAPP(real,real,F,X_1))) -> L = zero_zero(real))))) # label(fact_2661_DERIV__local__const) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 521 (all B all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),M) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),M) = one_one(int))))) # label(fact_3468_zgcd__zcong__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 522 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),plus_plus(rat)),X_3)),Y_3)))))) # label(fact_4842_vanishes__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 523 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)) = hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1604_MultInvPair__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 524 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & hAPP(nat,int,semiring_1_of_nat(int),N_2) = ti(int,K_4))))) # label(fact_1480_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 525 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))) # label(fact_2052_minus__diff__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 526 (all M (hBOOL(hAPP(int,bool,zprime,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int))) = one_one(int))) # label(fact_469_Legendre__1mod4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 527 (all B_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2))))) # label(fact_1023_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 528 (all X_1 ((exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)) <-> X_1 = hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1)))) # label(fact_3341_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 529 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = zero_zero(nat) <-> Ma = zero_zero(nat) | zero_zero(nat) = N_1)) # label(fact_551_mult__is__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 530 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))) <-> zero_zero(X_a) != ti(X_a,X_1) | zero_zero(X_a) != ti(X_a,Y_1))))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 531 (all X_a (field(X_a) -> (all A_1 all N all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)),N))))) # label(fact_1697_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 532 (all X_2 hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),X_2)) # label(fact_4119_exp__fdiffs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 533 (all A_9 all B_8 all Y all R_6 (ti(int,A_9) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Y)),R_6) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),R_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_6),zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_6),B_8))) -> (zero_zero(int) != ti(int,B_8) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_9),B_8) = ti(int,Y))))) # label(fact_1054_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 534 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),M))) # label(fact_1091_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 535 (all X_a (division_ring(X_a) -> (all B_1 all A_2 all C_1 (zero_zero(X_a) != ti(X_a,C_1) -> (ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1)))))) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 536 (all N all A_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)) = hAPP(complex,real,im,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N))) # label(fact_3024_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 537 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1810_divide_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 538 (all X_a (comple44059174attice(X_a) -> (all Z all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),Z)))))) # label(fact_2734_complete__lattice__class_OSup__least) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 539 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2837_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 540 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2794_of__real_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 541 (all M all N hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_4808_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 542 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),K_4))) # label(fact_3456_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 543 (all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)))) # label(fact_3414_floor__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 544 (all A_9 all B_8 all Q_6 all Y (ti(int,A_9) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Q_6)),Y) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_8)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),Y))) -> (zero_zero(int) != ti(int,B_8) -> ti(int,Y) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_9),B_8))))) # label(fact_1056_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 545 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),K_4)) # label(fact_1093_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 546 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3876_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 547 (all X hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1968_abs__power3__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 548 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4746_scaleR__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 549 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1)))))))) # label(fact_449_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 550 (all X all Y all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),R_4)),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4))) # label(fact_2810_Complex__add__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 551 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_3529_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 552 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)))))) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 553 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2)))))) # label(fact_101_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 554 (all P_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,P_1,J)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,P_1,I_2))))) -> hBOOL(hAPP(nat,bool,P_1,I)))))) # label(fact_1483_inc__induct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 555 (all Y_1 all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1163_SRStar__mult__prop1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 556 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 557 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 558 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) = zero_frac(X_a)) # label(fact_3680_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 559 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2566_exp__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 560 (all X_a (linordered_idom(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))) # label(fact_10_power2__less__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 561 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5))))) # label(fact_887_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 562 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),C_1)),X_2) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2))))) # label(fact_4113_diffs__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 563 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) = hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))))) # label(fact_3875_card__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 564 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_683_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 565 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_4828_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 566 (all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_2)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_4260_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 567 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N) = hAPP(nat,nat,suc,N)) # label(fact_1344_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 568 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4)))))) # label(fact_598_mult__less__mono1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 569 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z)))) # label(fact_80_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 570 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),B)),M)))) # label(fact_359_zcong__scalar2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 571 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2829_pinf_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 572 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_388_mult__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 573 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_1207_lessI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 574 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_1243_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 575 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(real,real,sin,X_1)))) # label(fact_4076_sin__paired) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 576 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2847_floor__le__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 577 (all N all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))))))) # label(fact_3460_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 578 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) <-> K = zero_zero(nat) | Ma = N_1)) # label(fact_744_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 579 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,inverse_inverse(real),X_1))))) # label(fact_2641_DERIV__ln) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 580 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_4))))) # label(fact_527_le__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 581 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma))))) # label(fact_1035_zcong__zmod__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 582 (all X_1 all K (ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1450_zEvenI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 583 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4000_mult__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 584 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),Y_1),X_1)) = X_1)) # label(fact_4525_Sup__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 585 (all A_1 all B hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))) # label(fact_3777_quotient__of__Fract) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 586 (all X_a all X_b all Z all F all A_3 ((exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & ti(X_a,Z) = hAPP(X_b,X_a,F,X_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))))) # label(fact_3637_image__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 587 (all A_1 A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),A_1)) # label(fact_3218_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 588 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4646_LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 589 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)))))))) # label(fact_1375_power__gt1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 590 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))))) # label(fact_804_inv__g__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 591 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2007_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 592 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)))))) # label(fact_1381_one__less__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 593 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)))))) # label(fact_3437_zgcd__greatest) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 594 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2846_coprime__sos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 595 (all I_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = ti(int,I_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,uminus_uminus(int),I_1) = hAPP(int,int,abs_abs(int),I_1)))) # label(fact_2168_zabs__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 596 (all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J))) # label(fact_4539_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 597 (all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_1)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1))))))))) # label(fact_4645_LIM__D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 598 (all Ma all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))) # label(fact_3206_Bnor__mem__zle__swap) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 599 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_2942_cnj_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 600 (all X_b all X_a (comm_monoid_add(X_a) -> (all A_3 zero_zero(X_a) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_3)))) # label(fact_4217_setsum__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 601 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J_2),K_4))))) # label(fact_136_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 602 (all A_2 all A_3 all Ma ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma))) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2) = zero_zero(int)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma)))) = hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)))) # label(fact_4153_RRset2norRR__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 603 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> ti(int,A_1) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_807_inv__distinct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 604 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N)) = zero_zero(real))) # label(fact_2410_lemma__STAR__cos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 605 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(nat,X_a,F,N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,N_1)))))) # label(fact_4321_setsum__lessThan__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 606 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_437_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 607 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1018_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 608 (all X_a all X_b ti(fun(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat))),product_prod_size(X_a,X_b)) = product_prod_size(X_a,X_b)) # label(tsy_c_Product__Type_Oprod_Oprod__size_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 609 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N))),pi)) = zero_zero(real)) # label(fact_2333_sin__2npi) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 610 (all X_a all X_b all X_1 all Y_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4340_predicate2D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 611 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_618_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 612 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = zero_zero(X_a)))) # label(fact_2065_right__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 613 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_4103_Ln_Oaux2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 614 (all A_2 all N_1 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),hAPP(nat,nat,suc,N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2874_coprime__exp2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 615 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))) # label(fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 616 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2))))))) # label(fact_4081_mult__right_Osums) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 617 (all X_a (linordered_semidom(X_a) -> (all M -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a)))))) # label(fact_1280_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 618 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M)) # label(fact_3550_div__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 619 (all F all G all N_1 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),F)),G)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_4235_sum__split__even__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 620 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))))) # label(fact_1239_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 621 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_3362_le__floor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 622 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_1533_semiring__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 623 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),A_2))))) # label(fact_3361_floor__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 624 (all X all Y ((zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))) & (Y = zero_zero(nat) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)))) # label(fact_3665_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 625 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_1))),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_4))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)))) # label(fact_2178_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 626 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_21_zle__refl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 627 (all X_b all X_a (real_normed_vector(X_b) & real_algebra_1(X_b) & topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4613_of__real_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 628 (all X_a (linordered_field(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2559_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 629 (all Ma all N_1 hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),hAPP(nat,nat,suc,N_1))) # label(fact_4123_diff__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 630 (all M all N hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_1312_zadd__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 631 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3042_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 632 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)))) # label(fact_1270_EvenOdd_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 633 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_825_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 634 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_4756_scaleR__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 635 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_2885_floor__less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 636 (all X_a (archim1727834104eiling(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3281_ceiling__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 637 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))) # label(fact_1666_power__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 638 (all X_a (zero(X_a) -> zero_zero(X_a) = ti(X_a,zero_zero(X_a)))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 639 (all X_a (ab_group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1) = zero_zero(X_a)))) # label(fact_2068_ab__left__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 640 (all X_1 all N_1 exists T_4 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,sin,X_1)) # label(fact_4267_Maclaurin__sin__expansion) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 641 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))) # label(fact_1359_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 642 (all X_a (real_n2089651433ebra_1(X_a) & number_ring(X_a) -> (all W hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),W))))) # label(fact_1892_norm__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 643 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_2427_even__difference__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 644 (all X all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),B)) -> hAPP(int,int,abs_abs(int),X) = one_one(int))))) # label(fact_4402_coprime__common__divisor__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 645 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_1))))))) # label(fact_2607_inverse__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 646 (all M all N hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)) # label(fact_3125_div__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 647 (all X_a all X_b (uminus(X_b) -> (all A_3 all X_2 hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_3,X_2)) = hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_3),X_2)))) # label(fact_2965_fun__Compl__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 648 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) # label(fact_1428_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 649 (all X_a (ring_1(X_a) -> (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_1371_of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 650 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3))))) # label(fact_3038_infinite__super) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 651 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)))) # label(fact_255_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 652 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4077_of__real_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 653 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_944_mod__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 654 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4)))) # label(fact_2728_z3mod__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 655 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = zero_zero(X_b)))))) # label(fact_4216_setsum__delta_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 656 (all X_a (ring_1(X_a) -> (all F all N_1 all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),R_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4172_sumr__diff__mult__const2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 657 (all M all N all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)))))) # label(fact_3472_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 658 (all X_1 (one_one(real) = X_1 <-> one_one(real) = hAPP(real,real,sqrt,X_1))) # label(fact_1619_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 659 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_2 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) <-> ti(X_a,C_1) = ti(X_a,B_1))))) # label(fact_769_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 660 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4442_LIMSEQ__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 661 (all X_a (idom(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) | zero_zero(X_a) = ti(X_a,C_1))))) # label(fact_410_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 662 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,arctan,X)) = hAPP(real,real,arctan,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2055_arctan__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 663 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> (zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) -> hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,tan,X))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2250_tan__double) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 664 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_4845_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 665 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,expi,A_1)),hAPP(complex,complex,expi,B)) = hAPP(complex,complex,expi,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A_1),B))) # label(fact_2820_expi__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 666 (all Z_1 exists R_2 exists A_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_4)),hAPP(real,real,sin,A_4))) = Z_1) # label(fact_2823_complex__split__polar) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 667 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),A_2))))) # label(fact_4908_mult__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 668 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & Y = hAPP(real,real,sin,Y_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) -> X_2 = Y_2)) & hAPP(real,real,sin,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2))))))) # label(fact_2405_sin__total) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 669 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X_1))))) # label(fact_2645_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 670 (all A_1 one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,one_one(real)),A_1)) # label(fact_3323_powr__one__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 671 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_4718_scaleR__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 672 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),N_1))))))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 673 (all M all N all K_4 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_3462_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 674 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))))))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 675 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),X))))) # label(fact_3057_prime__divexp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 676 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all Sa all F (zero_zero(X_a) = hAPP(nat,X_a,F,zero_zero(nat)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa))))))) # label(fact_4094_sums__Suc__imp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 677 (all K_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,one_one(int)),hAPP(int,int,number_number_of(int),K_4))) # label(fact_3733_Fract__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 678 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))))) # label(fact_1736_divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 679 (all A_2 all B_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) <-> -(exists P_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_2)) & hBOOL(hAPP(int,bool,zprime,P_6)))))) # label(fact_3467_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 680 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all G all K_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),K_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),hAPP(X_a,X_b,G,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),K_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),K_3))))))) # label(fact_4343_setsum__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 681 (all P (ti(bool,P) = fTrue | fFalse = ti(bool,P))) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 682 (all X X = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1771_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 683 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2097_power__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 684 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_1345_Suc__diff__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 685 (all X_a (no_zero_divisors(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_5_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 686 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)),X)))) # label(fact_4938_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.57 687 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_187_cube__square) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 688 (all X_a (semiring_char_0(X_a) -> (all Ma all N_1 (hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma) <-> N_1 = Ma)))) # label(fact_1214_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 689 (all X_1 all N_1 all Y_1 (X_1 = Y_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1)))) # label(fact_1254_exp__mono__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 690 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),X_1))))) # label(fact_1777_norm__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 691 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,Z))))) # label(fact_1132_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 692 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2))))) # label(fact_1953_subset__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 693 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))) # label(fact_2680_real__root__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 694 (all Z_5 (hBOOL(hAPP(int,bool,nat_neg,Z_5)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_5),zero_zero(int))))) # label(fact_1502_neg__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 695 (all X zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,arctan,X))) # label(fact_2210_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 696 (all X_a (real_normed_vector(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_4755_scaleR_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 697 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),A_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),B_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))))) # label(fact_3471_zcong__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 698 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_2882_floor__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 699 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 700 (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)))),one_one(int))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W)))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))))) # label(fact_899_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 701 (all X_a (real_vector(X_a) -> (all X zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),X)))) # label(fact_4709_scaleR__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 702 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 703 (all A_1 all B hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,abs_abs(int),A_1)),hAPP(int,int,abs_abs(int),B))) # label(fact_3757_abs__rat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 704 (all X_a (real_normed_field(X_a) -> (all X_1 (ti(X_a,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),inverse_inverse(X_a)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_3888_DERIV__inverse) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 705 (all A_1 -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)))) # label(fact_888_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 706 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_3280_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 707 (all V all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),one_one(int))),hAPP(int,int,number_number_of(int),W))))) # label(fact_1065_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 708 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_2668_DERIV__even__real__root) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 709 (all M all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),M)) -> ti(int,X) = ti(int,Y)))))))) # label(fact_419_zcong__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 710 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),A_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) # label(fact_4363_gcd__commute__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 711 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_4688_scaleR__minus__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 712 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S) = one_one(X_b)))))) # label(fact_3955_setprod__delta_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 713 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1954_set__mp) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 714 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_710_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 715 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> ti(int,A_1) = ti(int,B))))))) # label(fact_453_zcong__zless__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 716 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2774_PowI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 717 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,abs_abs(real),X)))) # label(fact_2689_real__root__abs) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 718 (all Ma all D_1 ((exists Q_4 ti(int,Ma) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Q_4)) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ma),D_1))) # label(fact_991_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 719 (all X_1 all Y_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))))) # label(fact_3766_real__less__eq__code) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 720 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_2575_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 721 (all Ma (one_one(nat) = Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat))))) # label(fact_477_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 722 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X) = Y)))) # label(fact_2710_real__root__pos__unique) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 723 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_614_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 724 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4019_summable__rabs) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 725 (all X_a (semiring_div(X_a) -> (all N all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))) # label(fact_1006_div__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 726 (all Z_1 all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z_1)),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2142_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 727 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))))))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 728 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4441_LIMSEQ__diff__const) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 729 (all Z_1 all Z_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1144_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 730 (all X_b all X_a all H all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),F_1))))) # label(fact_3633_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 731 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> Ma != N_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_563_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 732 (all C all A_1 all B (A_1 = B -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_636_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 733 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> zero_zero(X_a) = hAPP(nat,X_a,F,M_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))))))) # label(fact_4291_series__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 734 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1615_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 735 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)))) # label(fact_3652_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 736 (all X_a (ring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_6),B_5)),C)))))) # label(fact_943_mod__diff__cong) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 737 (all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),W))) # label(fact_657_real__le__refl) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 738 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),min_1) = hAPP(int,int,pred,K_4)) # label(fact_2907_add__Min__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 739 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_4352_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 740 (all X1_2 all X2_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X1_2),X2_2),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X2_2) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X1_2)))) # label(fact_1051_StandardRes__prop2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 741 (all X_a all X_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4336_predicate1D) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 742 (all M_5 all D_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_5),D_4) = zero_zero(nat) -> (exists Q_4 M_5 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_4),Q_4)))) # label(fact_1184_mod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 743 (all B_5 all A_6 all A_1 all B (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_6),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) = ti(int,A_1) -> (ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_6),B_5))))) # label(fact_4351_gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 744 (all K all F (zero_zero(nat) = hAPP(nat,nat,F,zero_zero(nat)) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),K)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))) # label(fact_4589_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 745 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 746 (all X_a all X_b all X all Y all A_1 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Y)) = ti(X_a,A_1) -> ti(X_a,A_1) = ti(X_a,X))) # label(fact_3141_fst__eqD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 747 (all Ma all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ma),hAPP(int,int,number_number_of(int),N_1))))) # label(fact_3387_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 748 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_1547_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 749 (all N_1 all X_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))))) # label(fact_4285_Maclaurin__all__le__objl) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 750 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3))))))) # label(fact_3983_suminf__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 751 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_558_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 752 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))))) # label(fact_2349_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 753 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)))) # label(fact_1048_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 754 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_930_mod__mult__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 755 (all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2367_sin__cos__npi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 756 (all X_a all X all Y (ti(X_a,X) = ti(X_a,Y) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 757 (all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3705_Sup__upper__EX) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 758 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (ti(int,K) = hAPP(nat,int,F,I_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)))))))) # label(fact_2008_int__val__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 759 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,cos,X)) # label(fact_2239_cos__periodic) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 760 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1))) # label(fact_4259_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 761 (all X_a (ring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2012_mod__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 762 (all K hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_atMost(nat),K)) # label(fact_4953_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 763 (all X_1 all N_1 (zero_zero(int) != ti(int,X_1) | N_1 = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X_1)),N_1))))) # label(fact_1967_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 764 (all N hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N)) # label(fact_3335_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 765 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))))) # label(fact_3345_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 766 (all Y_1 hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),cos)),Y_1)))) = hAPP(real,real,arccos,Y_1)) # label(fact_4137_arccos__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 767 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) # label(fact_986_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 768 (all N_1 all X_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & zero_zero(real) != X_1 & (all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4))))))) # label(fact_4277_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 769 (all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))))) # label(fact_1189_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 770 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4))) # label(fact_664_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 771 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X1))))))) # label(fact_4090_summable__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 772 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),zero_zero(nat)) = one_one(X_a)))) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 773 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_max(X_a))) # label(fact_4991_dual__min) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 774 (all M all N (M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_528_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 775 (all X_a (semiring_1(X_a) -> (all Inc all N_1 all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),N_1),hAPP(X_a,X_a,Inc,I)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),hAPP(nat,nat,suc,N_1)),I)))) # label(fact_4161_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 776 (all K_4 zero_zero(rat) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K_4))) # label(fact_3709_Frct__code__post_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 777 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_1844_power__abs) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 778 (all X_a (monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)))) # label(fact_778_add__0__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 779 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),one_one(real))))) # label(fact_1630_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 780 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2616_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 781 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),zero_zero(X_a))))))) # label(fact_1861_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 782 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> ti(X_a,B) = ti(X_a,A_1))))))) # label(fact_2531_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 783 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> X = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_2460_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 784 (all X_a ti(X_a,one_frac(X_a)) = one_frac(X_a)) # label(tsy_c_Nitpick_Oone__frac_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.57 785 (all X_a (linordered_semidom(X_a) -> (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1397_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 786 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))))))) # label(fact_1675_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 787 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,A_1) != zero_zero(int) -> ti(int,Q_3) = one_one(int)))) # label(fact_1190_self__quotient) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 788 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2697_real__root__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 789 (all R_1 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_1))))))) # label(fact_4864_vanishesD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 790 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))))) # label(fact_2556_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 791 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))))) # label(fact_596_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 792 (all P_5 all A_1 hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5)) # label(fact_1159_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 793 (all Z all W_1 (ti(int,W_1) != ti(int,Z) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W_1)))) # label(fact_37_zless__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 794 (all X_a all D_2 all B_2 all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),D_2)))))) # label(fact_1996_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 795 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_2586_mult__exp__exp) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 796 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4748_summable__exp__generic) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 797 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,number_number_of(int),min_1)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),one_one(int)),P_5))))) # label(fact_317_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 798 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4668_scaleR__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 799 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N)))) # label(fact_1388_diff__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 800 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) <-> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2))) # label(fact_1959_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 801 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_6),B_5)),C)))))) # label(fact_935_mod__add__cong) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 802 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (ti(int,Ta) != ti(int,X_2) -> ti(int,Ta) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))) # label(fact_4640_bset_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 803 (all Y_1 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (X_1 = Y_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))))) # label(fact_627_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 804 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (A_1 != B -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_629_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 805 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N))) # label(fact_2892_floor__eq4) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 806 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hAPP(real,real,arctan,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3966_arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 807 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_740_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 808 (all J all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J),zero_zero(int)),P_4)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4),J)))))))) # label(fact_1538_MultInvPair__card__two) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 809 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_1))))) # label(fact_1328_less__add__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 810 (all K_4 hAPP(int,int,bit0,K_4) = hAPP(int,int,pred,hAPP(int,int,bit1,K_4))) # label(fact_2900_pred__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 811 (all X_a all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_4)) -> -hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)))))) # label(fact_1832_UnionE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 812 (all X_a all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1955_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 813 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 814 (all Z1 all Z2 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W))) # label(fact_706_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 815 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))) # label(fact_365_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 816 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_786_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 817 (all X_c all X_a all X_b all C_1 all P_4 all Z (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),Z)) -> -(all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),P_4) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,X_2),Y_2),Z)))))) # label(fact_4058_splitE_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 818 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)))))) # label(fact_3988_mult__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 819 (all X_1 all Y_1 (Y_1 = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_620_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 820 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M) # label(fact_667_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 821 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_35_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 822 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))) # label(fact_3232_dvd__gcd__D1__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 823 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2688_real__root__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 824 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 825 (all X_b all X_a all X all Y all A_1 (hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X),Y)) = ti(X_a,A_1) -> ti(X_a,A_1) = ti(X_a,Y))) # label(fact_3139_snd__eqD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 826 (all M all K_4 all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3268_gcd__mult__cancel__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 827 (all X_a (real_normed_algebra(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 828 (all N all M hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),code_d418564891umeral,N),M) = hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),product_Pair(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),N),M)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),N),M))) # label(fact_3081_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 829 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),X),Y)) # label(fact_3519_dist__real__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 830 (all X hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,cos,X)) # label(fact_2198_cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 831 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N))) # label(fact_1441_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 832 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),No)) & (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4517_LIMSEQ__iff__nz) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 833 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3696_Rats__diff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 834 (all V_3 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_231_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 835 (all N all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),N)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),D)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),D))))) # label(fact_2354_real__of__nat__div) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 836 (all N_1 all Ma (ti(int,N_1) = ti(int,Ma) <-> hAPP(int,quickcheck_code_int,quickcheck_of_int,N_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,Ma))) # label(fact_3534_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 837 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),X)))) # label(fact_3318_ceiling__eq2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 838 (all X_1 all N_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1))) <-> N_1 != zero_zero(nat) & hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1363_even__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 839 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),standardRes,Ma)),X_3)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Ma))))))) # label(fact_3897_SR__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 840 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1920_subsetD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 841 (all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X))) = hAPP(int,int,fact_fact(int),X)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> zero_zero(int) = hAPP(int,int,fact_fact(int),X)))) # label(fact_3178_fact__int__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 842 (all X_a (comm_ring_1(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_2424_Parity_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 843 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_3014_complex__add__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 844 (all N all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)) = one_one(int))) # label(fact_3450_zgcd__1__power__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 845 (all A_1 all B ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_918_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 846 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_765_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 847 (all K_4 hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),K_4)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,K_4))) # label(fact_2138_minus__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 848 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4635_aset_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 849 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),ln),X_1)))) # label(fact_4883_isCont__ln) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 850 (all K_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),pls)) # label(fact_479_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 851 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1820_finite__Diff2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 852 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))))))) # label(fact_2390_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 853 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_310_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 854 (all X all Y all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) # label(fact_31_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 855 (all F all N_1 all R_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),R_1))) # label(fact_4176_sumr__diff__mult__const) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 856 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),N_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_3889_DERIV__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 857 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4564_divide_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 858 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))))))) # label(fact_380_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 859 (all X_a (linorder(X_a) -> (all Ma all I all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),N_1)) -> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),N_1),Ma) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),Ma)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),N_1)))))) # label(fact_4205_ivl__diff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 860 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (J = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I) = K))) # label(fact_692_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 861 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2565_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 862 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)))))) # label(fact_4368_gcd__greatest__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 863 (all X_b all X_a (comm_monoid_add(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,zero_zero(X_a)),zero_zero(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),S)))))))))) # label(fact_4795_setsum_Orelated) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 864 (all X_a power_1(X_a) = ti(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)))),power_1(X_a))) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 865 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq))))) # label(fact_3488_pair__leqI2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 866 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 867 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_884_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 868 (all X_1 all N_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 != zero_zero(real) -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4)))))))))) # label(fact_4276_Maclaurin__all__lt) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 869 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),K)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),K)),Ma)))))) # label(fact_3470_zcong__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 870 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)))))) # label(fact_3236_gcd__greatest__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 871 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2678_real__root__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 872 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_2023_equal__neg__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 873 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2700_real__root__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 874 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),cos),X_1))) # label(fact_4887_isCont__cos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 875 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),zero_zero(X_a)) = hAPP(X_a,real,norm_norm(X_a),X)))) # label(fact_3524_norm__conv__dist) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 876 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,int,fact_fact(int),N_1) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),N_1)))) # label(fact_4614_fact__altdef__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 877 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_3423_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 878 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_259_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 879 (all X all N hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) # label(fact_1357_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 880 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)))))) # label(fact_4798_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 881 (all X_a (number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),pls))))) <-> hAPP(int,X_a,number_number_of(X_a),X_1) = zero_zero(X_a))))) # label(fact_2625_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 882 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K_4)),L_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))),L_4)) # label(fact_113_mult__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 883 (all X_a (real_normed_field(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_1656_divide_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 884 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)),M))))) # label(fact_361_zcong__zadd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 885 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_399_pos__add__strict) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 886 (all N_1 all X_1 exists T_4 (hAPP(real,real,cos,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4242_Maclaurin__cos__expansion) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 887 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_39_eq__number__of__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 888 (all X_a (ord(X_a) -> ord_atLeastLessThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 889 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4365_gcd__assoc__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 890 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1819_finite) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 891 (all X_a (real_normed_vector(X_a) -> (all X_3 all K (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3826_Bseq__offset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 892 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1)))))) # label(fact_3352_powr__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 893 (all X_1 all Ma (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Ma) = hAPP(nat,nat,suc,zero_zero(nat)) <-> X_1 = hAPP(nat,nat,suc,zero_zero(nat)) | zero_zero(nat) = Ma)) # label(fact_1353_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 894 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N))) -> (zero_zero(int) != ti(int,K_4) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N))))) # label(fact_206_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 895 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_2))))) # label(fact_4870_Powp__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 896 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4551_mult__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 897 (all A_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),one_one(int)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),zero_zero(int))) # label(fact_3736_eq__rat_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 898 (all X_a (order(X_a) -> ti(fun(fun(nat,X_a),bool),monoseq(X_a)) = monoseq(X_a))) # label(tsy_c_SEQ_Omonoseq_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 899 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_1279_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 900 (all Z_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z_1)),Z_1)) # label(fact_2154_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 901 (all X_a all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_3) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) # label(fact_4255_card__eq__setsum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 902 (all X_a all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(real,fun(X_a,real),combk(real,X_a),one_one(real))),A_3) = hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) # label(fact_4229_real__of__card) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 903 (all X_a (real_normed_field(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1))))))) # label(fact_4086_sums__divide) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 904 (all X_a (division_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),one_one(X_a))))) # label(fact_1663_divide__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 905 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4753_scaleR__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 906 (all N (N != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) # label(fact_1475_Suc__mult__two__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 907 (all N hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,N)),one_one(code_code_numeral)) = N) # label(fact_2955_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 908 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,im,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1)) = hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z_1))) # label(fact_2985_Im__sgn) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 909 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),B_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),N_1)))))) # label(fact_869_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 910 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4))))))))) # label(fact_4281_Maclaurin__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 911 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1977_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 912 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y))))) # label(fact_1096_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 913 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_881_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 914 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)))))) # label(fact_1879_abs__mult__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 915 (all X_a all Q_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4869_someI2__ex) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 916 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,X)) = hAPP(real,real,tan,X)) # label(fact_2329_tan__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 917 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1))) # label(fact_3227_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 918 (all X_a all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2))))) # label(fact_3654_finite__surjI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 919 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3459_zgcd__non__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 920 (all D_2 all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (zero_zero(real) != X_1 -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> D_2 = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))) -> ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = D_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),D_2)))))))) # label(fact_2669_DERIV__real__root__generic) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 921 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat))))) # label(fact_1903_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 922 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))) # label(fact_153_number__of__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 923 (all N_1 all Ma (ti(int,Ma) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1)),Ma)) <-> one_one(int) = hAPP(int,int,abs_abs(int),N_1)))) # label(fact_1969_zdvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 924 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1436_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 925 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,inverse_inverse(real),X))))) # label(fact_2715_real__root__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 926 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)) = hAPP(real,X_a,of_real(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)))))) # label(fact_4020_of__real_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.57/7.58 927 (all X_a finite_psubset(X_a) = hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),collect(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),product_prod_case(fun(X_a,bool),fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),ord_less(fun(X_a,bool))))),finite_finite_1(X_a))))) # label(fact_4050_finite__psubset__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 928 (all L_4 pls != hAPP(int,int,bit1,L_4)) # label(fact_117_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 929 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F2,Nat),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),Nat))) # label(fact_4154_nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 930 (all X_a (number_ring(X_a) -> (all X ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(int,X_a,number_number_of(X_a),min_1)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = one_one(X_a)))))) # label(fact_2458_neg__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 931 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_917_div__mod__equality) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 932 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 ti(int,Z_1) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3564_ceiling__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 933 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(fun(int,bool),bool),nat,finite_card(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))))))) # label(fact_1603_SetS__card) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 934 (all X_a all X_c all X_b all Z all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1)))))) # label(fact_4038_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 935 (all M all N all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1118_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 936 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)))))) # label(fact_3056_prime__divexp__n) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 937 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = ti(int,N)))) # label(fact_3398_floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 938 (all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int))),N) = one_one(int)) # label(fact_4357_coprime__minus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 939 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)))) # label(fact_2330_real__natfloor__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 940 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b)))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),P_1)) # label(fact_4781_split__paired__Eps) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 941 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_403_not__one__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 942 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),M) = ti(int,M))) # label(fact_3444_zgcd__self) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 943 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),one_one(real))))) # label(fact_3402_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 944 (all B all A_1 (zero_zero(int) != ti(int,B) | ti(int,A_1) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = one_one(int))) # label(fact_4390_div__gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 945 (all X_a all A_3 all X_3 all C_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_1651_UnionI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 946 (all X_a all X_b all P_5 all Q_3 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Q_3) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5) -> (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_5) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Q_3) -> ti(product_prod(X_a,X_b),P_5) = ti(product_prod(X_a,X_b),Q_3)))) # label(fact_3142_prod__eqI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 947 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hAPP(real,real,F,X_2) = hAPP(real,real,F,A_2))))))) # label(fact_4930_DERIV__isconst1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 948 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_395_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 949 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1032_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 950 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,X_a),sgn_sgn(X_a)) = sgn_sgn(X_a))) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 951 (all X_a all R_1 ((all X_2 hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,refl(X_a),R_1)))) # label(fact_3554_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 952 (all X_a (power(X_a) & semiring_0(X_a) -> (all N zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(nat,nat,suc,N))))) # label(fact_1300_power__0__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 953 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)))))) # label(fact_1383_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 954 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),pi),X))) # label(fact_2325_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 955 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4650_aset_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 956 (all X_a (real_algebra_1(X_a) -> zero_zero(X_a) = hAPP(real,X_a,of_real(X_a),zero_zero(real)))) # label(fact_2783_of__real__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 957 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2004_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 958 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1029_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 959 (all N all P_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,fact,N)))))) # label(fact_3532_divides__fact) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 960 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1342_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 961 (all K all F all N_1 all Ma ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,Ma)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) & ti(int,K) = hAPP(nat,int,F,I_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1))))))))) # label(fact_2128_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 962 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)))) # label(fact_3100_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 963 (all Y all X (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,sqrt,X) = Y))) # label(fact_1639_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 964 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,nat,nat_1,N_1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3810_card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 965 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 966 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_334_dvd__mult2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 967 (all X_a (zero(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_764_zero__reorient) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 968 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_536_not__less0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 969 (all X_a all X_b (real_normed_algebra(X_b) & comm_ring_1(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co302546470etprod(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4657_LIMSEQ__setprod) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 970 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N)) # label(fact_1355_int__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 971 (all A_2 (one_one(nat) != A_2 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_2)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))))) # label(fact_895_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 972 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3506_dist__triangle) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 973 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_990_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 974 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1758_real__less__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 975 (all X_a (uminus(X_a) -> uminus_uminus(X_a) = ti(fun(X_a,X_a),uminus_uminus(X_a)))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 976 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_547_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 977 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2338_cos__diff2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 978 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,fun(nat,X_a)),fun(fun(nat,nat),fun(nat,X_a)),combs(nat,nat,X_a),F)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(fun(product_prod(nat,nat),bool),X_a,hAPP(fun(product_prod(nat,nat),X_a),fun(fun(product_prod(nat,nat),bool),X_a),big_co1399186613setsum(product_prod(nat,nat),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(product_prod(nat,nat),X_a),product_prod_case(nat,nat,X_a),F)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),N_1))))))) # label(fact_4622_setsum__triangle__reindex) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 979 (all X_a ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),accp(X_a)) = accp(X_a)) # label(tsy_c_Wellfounded_Oaccp_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 980 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))) # label(fact_1795_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 981 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) = N_1) # label(fact_3866_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 982 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(fun(X_a,bool),bool),nat,finite_card(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)))) # label(fact_2773_card__Pow) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 983 (all M all N all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1))) # label(fact_1313_zadd__int__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 984 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)))))) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 985 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W)) # label(fact_99_zadd__commute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 986 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))))) # label(fact_2459_even__num__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 987 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) # label(fact_1317_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 988 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,P_5)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),one_one(nat)))))) # label(fact_1149_Euler_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 989 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = zero_zero(nat)))) # label(fact_1417_div__if) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 990 (all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat))) # label(fact_1510_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 991 (all Code_numeral_2 hAPP(code_code_numeral,nat,size_size(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,size_size(code_code_numeral),Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2969_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 992 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3223_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 993 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N))) # label(fact_3278_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 994 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)))) # label(fact_3404_powr__realpow) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 995 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,X),Y)) # label(fact_3658_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 996 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)))) # label(fact_159_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 997 (all X_a all X_b all Sa all Ta (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Sa) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Ta) & hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Ta) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Sa) <-> ti(product_prod(X_a,X_b),Ta) = ti(product_prod(X_a,X_b),Sa))) # label(fact_3143_prod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 998 (all X_c all X_a all X_b all R_3 all A_2 all B_1 all C_1 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_3),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),C_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_3,A_2),B_1),C_1)))) # label(fact_4042_splitD_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 999 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> ti(X_a,B) = ti(X_a,A_1)))))))) # label(fact_460_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1000 (all X_a (number_ring(X_a) -> (all Y_1 (hAPP(int,X_a,number_number_of(X_a),Y_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2624_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1001 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),Q_3),hAPP(rat,rat,uminus_uminus(rat),R_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),Q_3),R_4)) # label(fact_3722_diff__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1002 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4647_aset_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1003 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),one_one(real))),R_4))) # label(fact_3403_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1004 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J))) # label(fact_4540_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1005 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_180_less__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1006 (all Z_1 Z_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1)) # label(fact_703_real__mult__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1007 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1008 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zEven))))) # label(fact_1398_power__preserves__even) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1009 (all X_a (real_normed_algebra(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1805_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1010 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4918_isCont__root__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1011 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1461_even__div__2__prop1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1012 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_510_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1013 (all U_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_1)) -> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(int,nat,nat_1,U_1))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1))) # label(fact_4323_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1014 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2753_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1015 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,uminus_uminus(int),Y))) # label(fact_4377_gcd__neg2__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1016 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)))))) # label(fact_2086_dvd__div__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1017 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1018 (all X_a all A_2 all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(nat,X_a,F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_4125_nat__case__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1019 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M)))) # label(fact_2499_fact__mod) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1020 (all D_1 all A_2 all B_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)) = one_one(int) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),A_2) & one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),B_1))) # label(fact_4386_coprime__mul__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1021 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all L all F all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4600_LIM__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1022 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1109_mod__geq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1023 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4563_divide_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1024 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3))))) # label(fact_1311_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1025 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),B_2)))))))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1026 (all X_a (dvd(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)) -> -(all K_1 ti(X_a,A_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_1)))))) # label(fact_2772_dvdE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1027 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int)))))) # label(fact_1019_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1028 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)))))) # label(fact_1004_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1029 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3037_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1030 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3)) # label(fact_28_zmult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1031 (all X_a (division_ring(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)))))) # label(fact_2078_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1032 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2448_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1033 (all A_1 all B all Qr_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)),Qr_1)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,Qr_1))))) # label(fact_3073_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1034 (all P (ti(bool,P) = fFalse | fTrue = ti(bool,P))) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1035 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)))))) # label(fact_2085_dvd__neg__div) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1036 (all V_3 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(nat,nat,suc,zero_zero(nat))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_1498_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1037 (all A_2 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),d22set,A_2)))) # label(fact_1671_d22set__fin) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1038 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all W_1 all A_2 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)))))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1039 (all B all A_1 (zero_zero(int) != ti(int,A_1) | zero_zero(int) != ti(int,B) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))) = one_one(int))) # label(fact_3458_div__zgcd__relprime) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1040 (all X_b all X_a (order(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2827_xt5) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1041 (all N all A_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)) = hAPP(complex,real,re,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N))) # label(fact_3025_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1042 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> Ma != N_1)) # label(fact_515_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1043 (all X_a (metric_space(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E_2))))))))))) # label(fact_3523_metric__CauchyD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1044 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1589_not__leE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1045 (all X_a (linordered_field(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1046 (all X_b all X_c all X_a (topological_space(X_a) & real_normed_vector(X_c) & real_normed_vector(X_b) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_a,X_c,G,X_2)),Ma))),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4654_LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1047 (all X_a (real_normed_vector(X_a) -> (all A_1 all X hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A_1)),hAPP(X_a,real,norm_norm(X_a),X))))) # label(fact_4665_norm__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1048 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),Y_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) <-> ti(X_a,Y_1) = ti(X_a,X_1) | A_2 = zero_zero(real))))) # label(fact_4700_scaleR__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1049 (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_1570_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1050 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C)))) # label(fact_932_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1051 (all X -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)))) # label(fact_619_dvd_Oless__irrefl) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1052 (all X_a (order(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4792_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1053 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all B_1 all C_1 all W_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_1754_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1054 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))))) # label(fact_3838_Ints__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1055 (all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B))))) # label(fact_3053_prime__divprod) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1056 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M))))) # label(fact_418_zcong__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1057 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1)))))))))))) # label(fact_2663_DERIV__neg__dec__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1058 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a)))))) # label(fact_3980_summable__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1059 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4610_LIM__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1060 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),R_4))),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),S_3))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3))) # label(fact_3780_Ratreal__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1061 (all X_a (real_normed_vector(X_a) -> (all Ra all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4696_scaleR__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1062 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2036_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1063 (all Ma hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))) # label(fact_3613_phi__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1064 (all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real)))) # label(fact_3853_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1065 (all Z_1 all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z_1)) -> W = Z_1))) # label(fact_651_real__le__antisym) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1066 (all X_1 (zero_zero(real) != hAPP(real,real,cos,X_1) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),sin)),cos)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3915_lemma__DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1067 (all X_a all X_b (real_normed_vector(X_b) & real_algebra_1(X_b) -> (all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),A_2)),A_3)))))) # label(fact_4458_of__real_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.57/7.59 1068 (all P_1 ((all X_2 exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))))) & (all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> (all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))))) # label(fact_3210_lemma__BOLZANO2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1069 (all Ma all N_1 all Qr (Ma = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr)),N_1)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)) & (zero_zero(nat) != N_1 -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),zero_zero(nat)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))))) & (N_1 = zero_zero(nat) -> zero_zero(nat) = hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr)) <-> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1),Qr)))) # label(fact_3127_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1070 (all X_a (linordered_idom(X_a) -> (all A_2 (hAPP(X_a,X_a,sgn_sgn(X_a),A_2) = one_one(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2222_sgn__1__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1071 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all F all G all A_2 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4766_LIM__equal) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1072 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(X_a,nat,F,I_2)),X_1))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)),X_1) = one_one(nat))) # label(fact_4128_setprod__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1073 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),one_one(real))))) # label(fact_2594_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1074 (all X all M hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2351_sin__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1075 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)))) # label(fact_3078_prime__ge__2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1076 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_1576_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1077 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_4 all B_4 all C_4 all D_3 all E hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_4),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E)))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y))) # label(fact_3153_prod__cases5) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1078 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)))) # label(fact_3089_divmod__nat__step) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1079 (all X_a (monoid_mult(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),X))))) # label(fact_717_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1080 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))))))) # label(fact_3298_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1081 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))))))) # label(fact_4799_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1082 (all X_a (ring_1(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2115_power2__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1083 (all X_a all F1 all Real1 all Real2 hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2) = hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_case(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2))) # label(fact_2759_complex_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1084 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2031_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1085 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all C_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,B_1,A_2)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)),one_one(nat))))) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),S))))))) # label(fact_3936_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1086 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) & Ma = hAPP(int,nat,nat_1,Z) <-> ti(int,Z) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_1377_int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1087 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,I)))))))) # label(fact_4300_setsum__nonneg__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1088 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1089 (all R_4 all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_3166_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1090 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4981_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1091 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1))) # label(fact_2974_Im__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1092 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_1)),A_3))))))) # label(fact_4439_tendsto__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1093 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1)))))) # label(fact_1504_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1094 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_1130_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1095 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_2) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1)))) # label(fact_1180_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1096 (all M hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_2287_cos__pi__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1097 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_593_zdiff__power3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1098 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)))))) # label(fact_2609_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1099 (all X_a (comm_semiring_1(X_a) -> (all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),semiring_1_of_nat(X_a)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),one_one(X_a)))))) # label(fact_4617_gauss__sum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1100 (all X_a all X_b all F all A_2 all B_1 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)))) # label(fact_4043_splitD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1101 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)))) # label(fact_2513_exp__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1102 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2536_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1103 (all X_a all F all A_3 hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3))) # label(fact_4245_int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1104 (all X_a (field_inverse_zero(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> hAPP(X_a,X_a,inverse_inverse(X_a),X_1) = one_one(X_a))))) # label(fact_2517_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1105 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_3496_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1106 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4825_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1107 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_504_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1108 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)))) # label(fact_577_add__leD2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1109 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2001_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1110 (all R_4 all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_4683_complex__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1111 (all X_b all X_a (real_normed_algebra(X_a) -> (all X_1 all G all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),G)),A_3)))) # label(fact_4191_mult__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1112 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3626_ex__le__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1113 (all X all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) -> (B != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,B)),hAPP(real,real,ln,A_1))),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X))))))) # label(fact_2651_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1114 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2002_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1115 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_1571_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1116 (all K all N_2 all F_3 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K)))) # label(fact_4183_sumr__offset4) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1117 (all X_a all X_b (real_normed_algebra(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1)),A_3))))))) # label(fact_4474_mult_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1118 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> Y = X)) # label(fact_1213_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1119 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_1843_abs__ge__self) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1120 (all A_2 all B_1 (one_one(real) = A_2 & zero_zero(real) = B_1 <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) = one_one(complex))) # label(fact_2744_Complex__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1121 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(nat,X_a),fun(X_a,bool)),sums(X_a)) = sums(X_a))) # label(tsy_c_Series_Osums_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1122 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all K all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),K))),L_2),hAPP(X_a,filter(X_a),at(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),K)))))))) # label(fact_4585_LIM__offset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1123 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1298_zless__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1124 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_3285_ceiling__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1125 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,int,number_number_of(int),min_1)),P_5)))) # label(fact_756_Wilson__Russ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1126 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1229_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1127 (all X_a all M_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,finite_finite_1(list(X_a)),M_1)) -> (exists N_2 all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_2)),N_2)))))) # label(fact_3558_finite__maxlen) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1128 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1812_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1129 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_470_le0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1130 (all X_a all X_b nat_tr1645093318rphism(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),nat_tr1645093318rphism(X_a,X_b))) # label(tsy_c_Nat__Transfer_Otransfer__morphism_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1131 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),K_4)))))) # label(fact_3196_fact__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1132 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)),X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)))))) # label(fact_4741_scaleR__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1133 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2466_nat__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1134 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4) = hAPP(int,fun(int,bool),d22set,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_858_d22set__eq__wset) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1135 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),min_1)))) # label(fact_294_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1136 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_4))))) # label(fact_1531_number__of__succ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1137 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_4971_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1138 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2079_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1139 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_324_zero__neq__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1140 (all K_4 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),K_4),M))) # label(fact_314_zcong__refl) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1141 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(X_a,int,archim2085082626_floor(X_a),R_4) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R_4)))))) # label(fact_3357_ceiling__floor) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1142 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1)))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1073_SRStar__mult__prop2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1143 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(real,nat,natfloor,X)),Y) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(nat,real,real_1(nat),Y)))))) # label(fact_2382_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1144 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),X),Y))) # label(fact_3770_real__divide__code) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1145 (all R_4 all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3))) # label(fact_4403_quotient__of__coprime) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1146 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),zero_zero(int))) <-> zero_zero(nat) = N_1)) # label(fact_1372_int__le__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1147 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)) = ord_max(X_a))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1148 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X)))) # label(fact_1887_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1149 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_447_power__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1150 (all K_4 hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4)) = K_4) # label(fact_3536_of__int__int__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1151 (all N all X (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X)) = X -> hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(real,int,archim2085082626_floor(real),X)),N))) # label(fact_3370_floor__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1152 (all B all D all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat)))) # label(fact_3269_coprime__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1153 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_2890_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1154 (all N hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N)) = hAPP(int,nat,number_number_of(nat),N)) # label(fact_1876_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1155 (all X hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,zero_zero(nat))),X) = X) # label(fact_2671_real__root__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1156 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_4047_Im_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1157 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_450_four__x__squared) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1158 (all N_1 all N_7 all F ((all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_7)),hAPP(nat,nat,F,N_1)))))) # label(fact_1492_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1159 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2784_of__real__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1160 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D))))) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1161 (all X_a (real_n1866405975lgebra(X_a) -> (all R_4 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(X_a,real,norm_norm(X_a),X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X))),hAPP(real,real,inverse_inverse(real),R_4)))))))) # label(fact_2538_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1162 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_1591_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1163 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3121_mod__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1164 (all X_a (linordered_field(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1165 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3239_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1166 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 ti(int,Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3576_floor__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1167 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_4))))) # label(fact_671_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1168 (all X_a (number_ring(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_2603_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1169 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))) # label(fact_332_dvd__triv__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1170 (all X_a (real_n2089651433ebra_1(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),zero_zero(X_a)),sequentially)))))) # label(fact_4487_LIMSEQ__power__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1171 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_757_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1172 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> (exists K_2 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))))) # label(fact_3498_BseqD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1173 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),A_2))))))) # label(fact_4916_isCont__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1174 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,tan,X)) # label(fact_2256_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1175 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_3))))) # label(fact_2915_ResSet__finite) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1176 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_1299_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1177 (all A_1 all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3033_DeMoivre) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1178 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2032_minus__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1179 (all X_a (linord581940658strict(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1180 (all M all N all S_4 all S_3 all T_6 all T_5 all R_5 all R_4 all K_4 (ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)))))) # label(fact_3480_xzgcd__correct__aux1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1181 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_4975_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1182 (all A_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)))) # label(fact_3417_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1183 (all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),zero_zero(real))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),one_one(nat)),N_1)) = zero_zero(real)) # label(fact_4239_lemma__STAR__cos2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1184 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2020_minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1185 (all L all K ((zero_zero(int) = ti(int,K) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) & (ti(int,K) != zero_zero(int) -> (zero_zero(int) = ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K)) & (zero_zero(int) != ti(int,L) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(int,int,sgn_sgn(int),K)),hAPP(int,int,sgn_sgn(int),L))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L))))) # label(fact_4069_divmod__int__code) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1186 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5))))) # label(fact_4719_scaleR_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1187 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M))))) # label(fact_1329_less__add__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1188 (all X_a (real_normed_vector(X_a) -> (all K all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_3825_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1189 (all R_4 all A_1 all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)),N) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),N)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3158_DeMoivre2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1190 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4609_LIM__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1191 (all A_1 all B all P_5 all Q_3 hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),P_5)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),P_5)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)))) # label(fact_743_mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1192 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),zero_zero(nat)) = zero_zero(nat)) # label(fact_4806_min__0R) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1193 (all Z_1 hAPP(complex,real,norm_norm(complex),Z_1) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3018_cmod__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1194 (all X_a (topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4553_LIM__rabs) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1195 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_59_le__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1196 (all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) != zero_zero(int) -> (exists A_5 exists B_3 (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_5),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_3),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) = ti(int,B) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_5),B_3) = one_one(int))))) # label(fact_4777_gcd__coprime__exists__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1197 (all X_a all A_3 hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)) # label(fact_2778_Pow__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1198 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_559_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1199 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))))) # label(fact_2317_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1200 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4685_scaleR_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1201 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_2029_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1202 (all X_1 all Y_1 all P_1 ((-hBOOL(P_1) -> hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1))) & (hBOOL(P_1) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1)) = hAPP(int,nat,nat_1,X_1)))) # label(fact_1081_nat__if__cong) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1203 (all A_2 all B_1 all W_1 (B_1 = zero_zero(real) & hAPP(int,real,number_number_of(real),W_1) = A_2 <-> hAPP(int,complex,number_number_of(complex),W_1) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1))) # label(fact_2742_Complex__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1204 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3))))))) # label(fact_1518_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.60 1205 (all X_a (topological_space(X_a) -> (all K all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)))))) # label(fact_4446_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1206 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4599_cnj_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1207 (all X_a (comm_ring(X_a) & monoid_mult(X_a) -> (all Z all H all Ma hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),Ma))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma))))) # label(fact_4226_lemma__termdiff1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1208 (all Z_1 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1)) = Z_1) # label(fact_3000_complex__surj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1209 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)))) # label(fact_1825_finite__UnionD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1210 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_440_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1211 (all N_1 all X_1 exists T_4 (hAPP(real,real,sin,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4241_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1212 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))))) # label(fact_1031_neg__mod__sign) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1213 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))) # label(fact_2682_real__root__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1214 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2))))))) # label(fact_4084_of__real_Osums) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1215 (all X_a all X_b (t2_space(X_b) -> (all L_1 all F all L all A_3 (-hBOOL(hAPP(filter(X_a),bool,trivial_limit(X_a),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_1),A_3)) -> ti(X_b,L) = ti(X_b,L_1))))))) # label(fact_4767_tendsto__unique) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1216 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1456_power__odd__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1217 (all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_953_zmod__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1218 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1219 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,zero_zero(nat))),N) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_1354_power__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1220 (all P_4 hAPP(int,fun(int,bool),sRStar,P_4) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),P_4)))) # label(fact_1129_SRStar__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1221 (all A_1 hAPP(real,real,hAPP(real,fun(real,real),log,A_1),one_one(real)) = zero_zero(real)) # label(fact_2638_log__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1222 (all X_c all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S))))) # label(fact_4224_setsum__image__gen) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1223 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_2884_one__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1224 (all X_a (semiring_div(X_a) -> (all A_1 all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B)))) # label(fact_974_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1225 (all A_1 all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))))) # label(fact_3075_divmod__int__correct) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1226 (all X_a (real_normed_vector(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),S_3)))))))) # label(fact_1792_norm__add__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1227 (all X_a (dvd(X_a) -> (all A_1 all B all K_4 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_4) = ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)))))) # label(fact_337_dvdI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1228 (all X_1 X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_lessThan(real),X_1))) # label(fact_4327_Sup__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1229 (all Z_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N))))) # label(fact_2362_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1230 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),F_1) = one_one(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> one_one(nat) = hAPP(X_a,nat,F,X_2)))))) # label(fact_3938_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1231 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1232 (all A_2 all P_4 all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) # label(fact_1670_SetS__elems__finite) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1233 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)),A_1)))) # label(fact_3380_powr__divide) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1234 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_994_div__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1235 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1236 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2247_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1237 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_1),one_one(int)))) # label(fact_4572_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1238 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)))))) # label(fact_3623_RRset2norRR__correct1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1239 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1))))))) # label(fact_1727_diff__frac__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1240 (all D all I_1 (zero_zero(int) != ti(int,I_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),I_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),D)),hAPP(int,int,abs_abs(int),I_1)))))) # label(fact_1940_dvd__imp__le__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1241 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) <-> hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),one_one(real)) = X_1)) # label(fact_3379_powr__one__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1242 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2)),sequentially)))))) # label(fact_4468_of__real_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1243 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2)))))) # label(fact_599_mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1244 (all X_a (real_normed_algebra(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1245 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),K_4)),M)))) # label(fact_358_zcong__scalar) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1246 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))) # label(fact_1166_Euler__Criterion) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1247 (all X_a all X_b all C_1 all P_4 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,X_2),Y_2)))))) # label(fact_4062_splitE) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1248 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_696_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1249 (all X_a (field_char_0(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),field_char_0_Rats(X_a)))))) # label(fact_3702_Rats__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1250 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)))))) # label(fact_3956_setprod__delta) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1251 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3))))) # label(fact_1310_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1252 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1645_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1253 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1738_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1254 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,uminus_uminus(int),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)))) # label(fact_2146_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1255 (all X_a all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) # label(fact_3942_int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1256 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4072_suminf__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1257 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4594_LIM__rabs__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1258 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)))))) # label(fact_320_no__zero__divisors) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1259 (all X_a (real_normed_vector(X_a) -> (all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),B)))) # label(fact_4710_scaleR_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1260 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1633_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1261 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),P_5)))) # label(fact_3051_prime__g__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1262 (all K_4 hAPP(int,int,uminus_uminus(int),K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),K_4)) # label(fact_2160_mult__Min) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1263 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1473_even__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1264 (all X_a (ordere142940540dd_abs(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)))) # label(fact_1851_abs__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1265 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2)))))))))) # label(fact_3145_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1266 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3194_fact__gt__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1267 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1268 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2233_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1269 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y))))) # label(fact_1721_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1270 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4732_scaleR__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1271 (all K_4 min_1 != hAPP(int,int,bit0,K_4)) # label(fact_290_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1272 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),Y_1)))))) # label(fact_1143_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1273 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_439_zero__less__two) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1274 (all X_a (real_normed_field(X_a) -> (all F all X_1 all L ((exists G_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),G_1),X_1)) & hAPP(X_a,X_a,G_1,X_1) = ti(X_a,L) & (all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,F,Z_2)),hAPP(X_a,X_a,F,X_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G_1,Z_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Z_2),X_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),L)))))) # label(fact_4882_CARAT__DERIV) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1275 (all N hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = zero_zero(real)) # label(fact_2344_tan__npi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1276 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))))) # label(fact_267_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1277 (all M all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_2310_power__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1278 (all X_a (field_char_0(X_a) & field_inverse_zero(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3701_Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1279 (all X_a (comm_semiring_1(X_a) -> (all N all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N))))))) # label(fact_343_dvd__power__same) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1280 (all B all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),B),N)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Y_2)),B),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),N))))))) # label(fact_3478_zcong__lineq__unique) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1281 (all X_a (no_zero_divisors(X_a) -> (all A_1 all B (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) -> ti(X_a,B) = zero_zero(X_a) | zero_zero(X_a) = ti(X_a,A_1))))) # label(fact_319_divisors__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1282 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_1564_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1283 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1)))) # label(fact_3597_ceiling__add__of__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1284 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_3011_complex__Re__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1285 (all X_a (real_normed_vector(X_a) -> (all R_4 all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)),Xa_1)))) # label(fact_4698_scaleR__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1286 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_565_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1287 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_691_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1288 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (ti(int,X_2) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))) # label(fact_4637_bset_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1289 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),Q_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))))))) # label(fact_3095_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1290 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4449_divide_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1291 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1292 (all X_a (field_inverse_zero(X_a) & real_field(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2792_of__real__divide) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1293 (all X all Y all K_4 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y) -> (exists I_2 exists J_1 (Y = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),J_1) & X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2)))))) # label(fact_3426_prime__power__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1294 (all X_1 hAPP(rat,int,archim2085082626_floor(rat),X_1) = hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(rat,fun(int,bool),hAPP(fun(int,fun(rat,bool)),fun(rat,fun(int,bool)),combc(int,rat,bool),hAPP(fun(int,rat),fun(int,fun(rat,bool)),hAPP(fun(rat,fun(rat,bool)),fun(fun(int,rat),fun(int,fun(rat,bool))),combb(rat,fun(rat,bool),int),ord_less_eq(rat)),ring_1_of_int(rat))),X_1))),hAPP(fun(int,rat),fun(int,bool),hAPP(fun(rat,bool),fun(fun(int,rat),fun(int,bool)),combb(rat,bool,int),hAPP(rat,fun(rat,bool),ord_less(rat),X_1)),hAPP(fun(int,int),fun(int,rat),hAPP(fun(int,rat),fun(fun(int,int),fun(int,rat)),combb(int,rat,int),ring_1_of_int(rat)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int))))))) # label(fact_4147_floor__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1295 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,K_4)) # label(fact_1527_succ__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1296 (all X_a (linorder(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1)))) # label(fact_4817_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1297 (all X_a (real_vector(X_a) -> (all A_2 all X_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) <-> zero_zero(real) = A_2 | ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_4708_scaleR__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1298 (all N_1 all V_1 (hAPP(nat,nat,suc,N_1) = hAPP(int,nat,number_number_of(nat),V_1) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))) = N_1) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3884_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1299 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,uminus_uminus(int),D_1)),Ta)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)))) # label(fact_2145_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1300 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2288_sin__arccos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1301 (all X_a (sgn_if(X_a) -> ti(fun(X_a,X_a),sgn_sgn(X_a)) = sgn_sgn(X_a))) # label(tsy_c_Groups_Osgn__class_Osgn_1_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1302 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_3593_le__floor__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1303 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))) # label(fact_1314_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1304 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists R_2 exists A_4 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)) = Y)))) # label(fact_2726_polar__ex1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1305 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_3674_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1306 (all X_b all X_a (real_normed_vector(X_a) -> (all F all A_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),hAPP(fun(X_b,X_a),fun(X_b,real),hAPP(fun(X_a,real),fun(fun(X_b,X_a),fun(X_b,real)),combb(X_a,real,X_b),norm_norm(X_a)),F)),A_3)))))) # label(fact_4177_norm__setsum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1307 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N))) # label(fact_2307_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1308 (all X_a ti(fun(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a))),code_c600343653l_case(X_a)) = code_c600343653l_case(X_a)) # label(tsy_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1309 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))))) # label(fact_2357_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1310 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sin),X_1),hAPP(real,real,cos,X_1)))) # label(fact_2637_DERIV__sin) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1311 (all N (zero_zero(nat) != N -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_1653_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1312 (all L all U_1 hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),L)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)) # label(fact_4265_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1313 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_762_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1314 (all X_a (linorder(X_a) -> (all C_1 all D_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> (ti(X_a,A_2) = ti(X_a,C_1) & ti(X_a,B_1) = ti(X_a,D_1) <-> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1))))))) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1315 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L),hAPP(X_b,X_b,uminus_uminus(X_b),Ma))),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4587_LIM__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1316 (all X_a (sgn_if(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)))) # label(fact_2203_sgn0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1317 (all X_1 ((exists Y_2 ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)),one_one(int))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1469_odd__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1318 (all I_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_533_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1319 (all X_a (linordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_428_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1320 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),N_1)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),X_1)))))) # label(fact_1912_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1321 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_940_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1322 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3819_DERIV__sin__sin__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1323 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_690_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1324 (all Ma all N_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) <-> Ma = zero_zero(nat) & zero_zero(nat) = N_1)) # label(fact_543_add__is__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1325 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F))))))) # label(fact_3997_summable__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1326 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))))))) # label(fact_4950_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1327 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2366_sin__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1328 (all X_a (comm_semiring_1(X_a) -> (all X all N (one_one(X_a) = ti(X_a,X) | 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),dvd_dvd(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_462_dvd__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1329 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_3190_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1330 (all X_a (number_ring(X_a) -> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_173_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1331 (all A_2 all B_1 ((all D_3 (hAPP(nat,nat,suc,zero_zero(nat)) = D_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3296_coprime__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1332 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1582_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1333 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))) <-> ti(int,W_1) = ti(int,Z) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_167_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1334 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X) = ti(X_a,X)))) # label(fact_4956_Max_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1335 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_2348_natfloor__subtract) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1336 (all Ma all W_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> zero_zero(nat) = Ma) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> ti(int,W_1) = hAPP(nat,int,semiring_1_of_nat(int),Ma)) <-> Ma = hAPP(int,nat,nat_1,W_1))) # label(fact_1406_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1337 (all X_b all X_a all X_c all F all G all A_3 hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_3)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_3)) # label(fact_3844_image__image) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1338 (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]. 7.57/7.61 1339 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_384_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1340 (all X_a all X_b (comm_monoid_add(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)) = big_co1399186613setsum(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1341 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1578_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1342 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4549_mult__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1343 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4565_LIM__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1344 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X_1)) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) & ti(X_a,X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4093_sums__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1345 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1)))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))))) # label(fact_1425_zdiff__int__split) # label(axiom) # label(non_clause). [assumption]. 7.57/7.61 1346 (all A_2 all B_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1) = one_one(int) <-> (all D_3 (one_one(int) = ti(int,D_3) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_3)))))) # label(fact_4405_coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1347 (all X_b all X_a all R_3 all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_3),X_1),Y_1)))) # label(fact_3043_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1348 (all N_1 all Q_1 all P_1 ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_1,X_2)),hAPP(nat,nat,P_1,X_2)))) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),P_1)),Q_1)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),P_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))))) # label(fact_4326_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1349 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B))) # label(fact_2149_zmod__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1350 (all N_1 all S (hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> N_1 = hAPP(fun(int,bool),nat,finite_card(int),X_2))) -> hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),finite_card(int)),S) = hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),hAPP(nat,fun(fun(int,bool),nat),combk(nat,fun(int,bool)),N_1)),S))))) # label(fact_4418_card__setsum__aux) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1351 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4662_metric__LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1352 (all M hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))) # label(fact_1221_int__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1353 (all U all V all X all Y (Y = X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U)),V)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U)),Y))),V))))) # label(fact_1894_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1354 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls)))) # label(fact_154_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1355 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma)))) # label(fact_3619_RRset__gcd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1356 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N))) # label(fact_2859_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1357 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)) != ti(int,X) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)))))))) # label(fact_508_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1358 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_780_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1359 (all X_a (linordered_idom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),zero_zero(X_a))))))) # label(fact_1471_odd__power__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1360 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3494_Bseq__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1361 (all Y all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)))))) # label(fact_278_zpower__zdvd__prop2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1362 (all N_1 all Ma all F ((all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Ma)),hAPP(nat,nat,F,N_1))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,Ma)))))) # label(fact_1493_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1363 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> ti(int,X) = zero_zero(int) | ti(int,X) = one_one(int)))) # label(fact_185_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1364 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) | (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_3922_monoseq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1365 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2))),F)),zero_zero(X_b))),A_3))))) # label(fact_4185_setsum__restrict__set_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1366 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),A_2)) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),A_2))))))) # label(fact_3921_monoseq__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1367 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),N),M)) # label(fact_3542_minus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1368 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a)))))) # label(fact_1863_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1369 (all D_1 hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than,D_1) = hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combs(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int))))) # label(fact_4074_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1370 (all X_a (field_char_0(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),field_char_0_Rats(X_a)))))) # label(fact_3700_Rats__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1371 (all Ma all K all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K) <-> Ma = N_1 | K = zero_zero(nat))) # label(fact_553_mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1372 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_2839_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1373 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> Y = hAPP(real,real,sin,hAPP(real,real,arcsin,Y))))) # label(fact_2361_sin__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1374 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B))))) # label(fact_996_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1375 (all N hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2173_neg__zminus__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1376 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_434_mult__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1377 (all X_a all X all Y ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1378 (all X_a (division_ring(X_a) -> one_one(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),one_one(X_a)))) # label(fact_2516_inverse__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1379 (all X_a (linord626643107strict(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_277_convex__bound__lt) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1380 (all A_2 all B_1 (hAPP(int,int,abs_abs(int),B_1) = hAPP(int,int,abs_abs(int),A_2) <-> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1980_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1381 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_4100_mult__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1382 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4026_summable__geometric) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1383 (all X_a (metric_space(X_a) -> cauchy(X_a) = ti(fun(fun(nat,X_a),bool),cauchy(X_a)))) # label(tsy_c_SEQ_OCauchy_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1384 (all Ma all N_1 all P_1 ((all M_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),zero_zero(nat)))) -> ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_2),N_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Ma),N_1))))) # label(fact_3530_gcd__nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1385 (all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5) = one_one(int))))) # label(fact_3469_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1386 (all X_a (real_field(X_a) -> (all N_1 all X_1 all Y_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))))) # label(fact_4664_exp__series__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1387 (all X_a (sgn_if(X_a) -> (all X ((ti(X_a,X) != zero_zero(X_a) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),X)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),X))) & (zero_zero(X_a) = ti(X_a,X) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = zero_zero(X_a)))))) # label(fact_2232_sgn__if) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1388 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W)) # label(fact_2161_diff__int__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1389 (all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) != zero_zero(nat) -> (exists A_5 exists B_3 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_5),B_3) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = B & A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)))))) # label(fact_3312_gcd__coprime__exists__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1390 (all X_a all Q_1 all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4867_someI2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1391 (all A_2 (A_2 != zero_zero(nat) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),zero_zero(nat))))) # label(fact_890_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1392 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),X)),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(real,nat,natfloor,A_1))))) # label(fact_2331_le__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1393 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1)),zero_zero(real))) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_3511_dist__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1394 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_2956_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1395 (all N_1 hAPP(nat,nat,suc,N_1) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),N_1)))) # label(fact_3828_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1396 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,sin,X) -> (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2475_sin__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1397 (all N all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))))) # label(fact_2858_coprime__exp) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1398 (all X_a (real_normed_vector(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3317_CauchyI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1399 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4790_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1400 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2893_number__of__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1401 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2199_sgn__sgn) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1402 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_426_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1403 (all S_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_3),T_5)) -> T_5 != S_3)) # label(fact_519_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1404 (all K all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)))) # label(fact_207_zdvd__reduce) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1405 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),A_1)))) # label(fact_2519_inverse__divide) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1406 (all X hAPP(real,int,archim2085082626_floor(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,int,archim2085082626_floor(rat),X)) # label(fact_3748_real__floor__code) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1407 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4632_bset_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1408 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_386_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1409 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_3371_floor__subtract) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1410 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,cos,X))) # label(fact_2220_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1411 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = ti(X_a,Y_1) & ti(X_a,X_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))))))) # label(fact_106_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1412 (all X_a (ring_n68954251visors(X_a) -> (all A_2 all B_1 (zero_zero(X_a) = ti(X_a,B_1) | ti(X_a,A_2) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1) = zero_zero(X_a))))) # label(fact_321_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1413 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1)) # label(fact_135_zadd__0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1414 (all V hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) # label(fact_1112_nat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1415 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)))))) # label(fact_739_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1416 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_1534_semiring__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1417 (all Z1 all Z2 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W)) # label(fact_68_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1418 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2084_abs__power__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1419 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),X_1)))))))) # label(fact_4098_geometric__sums) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1420 (all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))) # label(fact_1209_dvd__1__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1421 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4007_summable__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1422 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S)))))))) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1423 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_583_le__cube) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1424 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1027_div__prop1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1425 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_928_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1426 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_1561_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1427 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_595_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1428 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)))))) # label(fact_4472_tendsto__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1429 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1176_transfer__morphismI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1430 (all K all Ma all N_1 (N_1 = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))) # label(fact_1250_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1431 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (exists C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_3)) & hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3) = ti(fun(X_a,bool),B_2) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_3))))))) # label(fact_3645_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1432 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_105_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1433 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) # label(fact_2053_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1434 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)))))) # label(fact_2027_minus__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1435 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2648_log__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1436 (all X_a (ring_1(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),ring_1_Ints(X_a)))))) # label(fact_3805_Ints__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1437 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1712_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1438 (all Y all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int)))) # label(fact_1458_tsub__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1439 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N)) # label(fact_1240_add__Suc__shift) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1440 (all P_1 all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4194_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1441 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4294_setsum__mono__zero__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1442 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2577_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1443 (all X all N hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N)) # label(fact_3334_real__of__int__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1444 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_71_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1445 (all X_a all X_b (real_normed_field(X_b) -> (all F all X_1 all F_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(X_a,fun(X_b,X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_a,fun(X_b,X_b)),combc(X_b,X_a,X_b),F),N_2)),X_1),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F_2,X_1),N_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),hAPP(fun(X_b,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(X_b,X_b)),combc(X_b,fun(X_a,bool),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),X_b),big_co1399186613setsum(X_a,X_b)),F)),S)),X_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),F_2,X_1)),S)))))))) # label(fact_4304_DERIV__setsum) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1446 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y))) # label(fact_2978_Im_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1447 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z_1)))) # label(fact_42_mult__number__of__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1448 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (ti(int,X_2) != ti(int,Ta) -> ti(int,Ta) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4639_aset_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1449 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_2),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1523_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1450 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1802_divide_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1451 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,real_1(nat),A_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),A_2))))) # label(fact_2345_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1452 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2477_odd__square) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1453 (all X_a (ordered_semiring(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_368_mult__mono_H) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1454 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2447_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1455 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1) != zero_zero(int)) # label(fact_166_odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1456 (all X_a (semiring_div(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)),A_1))))) # label(fact_1001_dvd__div__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1457 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all A_2 all B_1 all W_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1458 (all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_5)) & -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_5)))))) # label(fact_280_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1459 (all X_a (number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) <-> hAPP(int,X_a,number_number_of(X_a),X_1) = one_one(X_a))))) # label(fact_2503_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1460 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4575_LIM__mult__left__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1461 (all P_1 ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_1296_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1462 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))))))) # label(fact_2408_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1463 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1464 (all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),P_4),zOdd))))) # label(fact_1068_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1465 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,K_4)),L_4) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4))) # label(fact_63_mult__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1466 (all X all Y hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),X)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),Y)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2771_complex__inverse__complex__split) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1467 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_4),B_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1181_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1468 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_lessThan(X_a)) = ord_lessThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1469 (all X_a (topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,G,X_2))))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,G,X_2)),hAPP(X_a,real,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4776_real__LIM__sandwich__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1470 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3693_Rats__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1471 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))))) # label(fact_4369_gcd__greatest__iff__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1472 (all X all A_1 hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3359_powr__minus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1473 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3833_Bseq__realpow) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1474 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)))) # label(fact_1631_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1475 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),pi)) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2402_arcsin__pi) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1476 (all X_a (division_ring(X_a) -> (all A_2 all B_1 all C_1 (zero_zero(X_a) != ti(X_a,C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2)))))) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1477 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),sequentially)))))) # label(fact_4740_scaleR__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1478 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X))))) # label(fact_1049_StandardRes__lbound) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1479 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),Y))))) # label(fact_1884_abs__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1480 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3))))))) # label(fact_86_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1481 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,J_2),I_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3440_zgcd__commute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1482 (all A_1 all B hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A_1)),hAPP(int,int,sgn_sgn(int),B))) = hAPP(rat,rat,sgn_sgn(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3781_sgn__rat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1483 (all N_1 all Ma (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))) <-> N_1 = Ma))) # label(fact_1236_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1484 (all X_a (field_inverse_zero(X_a) -> (all X all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y))))) # label(fact_1720_add__frac__num) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1485 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1945_ln__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1486 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X))))) # label(fact_2707_real__root__pos__mult__exp) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1487 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4980_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1488 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),tan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2653_DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 7.57/7.62 1489 (all Y all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),zero_zero(int)),P_5)))))) # label(fact_456_zcong__zmult__prop3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1490 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_2 exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),X)))))) # label(fact_2409_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1491 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),zero_zero(int))))))) # label(fact_265_q__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1492 -(all T_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),T_4)) # label(fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1493 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2321_sin__add) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1494 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all L all Ma all F all G all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,B_1) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (ti(X_b,L) = ti(X_b,Ma) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),B_1)))))))))) # label(fact_4762_LIM__cong) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1495 (all X_a (semiring_div(X_a) -> (all D_1 all B_1 all C_1 all A_2 (ti(X_a,A_2) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,C_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_1),D_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),D_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))))) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1496 (all A_1 all B hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2150_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1497 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3812_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1498 (all X_b all X_a (real_n2089651433ebra_1(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),F)),A_2)))))) # label(fact_4904_isCont__of__real) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1499 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1085_mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1500 (all N zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),zero_zero(real))) # label(fact_2670_real__root__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1501 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),Xa_1)))) # label(fact_4713_scaleR__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1502 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_936_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1503 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) = ti(int,X_1))) # label(fact_910_StandardRes__SR__prop) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1504 (all N (N != zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N))) # label(fact_3287_coprime__minus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1505 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))))))) # label(fact_4520_LIMSEQ__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1506 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2264_arccos__ubound) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1507 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3)) # label(fact_705_real__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1508 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,B_1),A_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2855_coprime__commute) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1509 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_2422_odd__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1510 (all Z_1 hAPP(complex,complex,expi,Z_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),hAPP(complex,real,re,Z_1)))),hAPP(real,complex,cis,hAPP(complex,real,im,Z_1)))) # label(fact_3023_expi__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1511 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1512 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1824_psubset__card__mono) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1513 (all X all N hAPP(complex,complex,cnj,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),X),N)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,cnj,X)),N)) # label(fact_2943_complex__cnj__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1514 (all M hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),zero_zero(nat)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M)) # label(fact_3092_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1515 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_405_zero__le__power) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1516 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))) # label(fact_3990_suminf__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1517 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),X)),one_one(int)),P_5)))))) # label(fact_855_MultInv__prop2a) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1518 (all A_1 all R_4 all B all M all C all D all N hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),N)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),D))),N))) # label(fact_499_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1519 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4671_scaleR__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1520 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M))))) # label(fact_2492_fact__dvd) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1521 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(real,real,abs_abs(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),A_1)))) # label(fact_1859_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1522 (all X_a (power(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) -> (all A_2 all N_1 (zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1) <-> ti(X_a,A_2) = zero_zero(X_a) & zero_zero(nat) != N_1)))) # label(fact_414_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1523 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))))) # label(fact_3569_of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1524 (all K_4 zero_zero(rat) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),zero_zero(int))) # label(fact_3740_rat__number__collapse_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1525 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1))))) # label(fact_1237_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1526 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),Z_1),hAPP(complex,complex,cnj,Z_1)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,im,Z_1)))),ii)) # label(fact_2970_complex__diff__cnj) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1527 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(real,X_a,of_real(X_a),R_4)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,sgn_sgn(real),R_4))))) # label(fact_2801_sgn__of__real) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1528 (all P_5 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),zero_zero(int)))) # label(fact_3727_normalize__denom__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1529 (all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(complex,complex,inverse_inverse(complex),X)) # label(fact_2990_complex__inverse__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1530 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_518_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1531 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1900_abs__power2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1532 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3908_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1533 (all Ma all X_1 ((exists Y_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Ma),X_1)))) # label(fact_608_QuadRes__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1534 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_2521_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1535 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_394_mult__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1536 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,fact_fact(nat),X)) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,suc,X))) # label(fact_2491_Fact_Ofact__Suc) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1537 (all A_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = hAPP(real,real,uminus_uminus(real),A_1)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> hAPP(real,real,abs_abs(real),A_1) = A_1))) # label(fact_2110_abs__real__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1538 (all X_a (field(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2561_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1539 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)))))) # label(fact_2056_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1540 (all X_a (sgn_div_norm(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),X))),X) = hAPP(X_a,X_a,sgn_sgn(X_a),X)))) # label(fact_4725_sgn__div__norm) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1541 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) # label(fact_178_semiring__one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1542 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))) <-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4))))) # label(fact_1162_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1543 (all X_a (real_algebra_1(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,semiring_1_of_nat(real),N))))) # label(fact_2800_of__real__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1544 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,X)),zero_zero(real)))))) # label(fact_2277_tan__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1545 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1546 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4855_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1547 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2)))))) # label(fact_867_d22set__mem) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1548 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),A_3)))) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1549 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(real,real,abs_abs(real),R_4) = hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),R_4))))) # label(fact_2797_norm__of__real) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1550 (all M all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) -> hAPP(int,int,number_number_of(int),min_1) = ti(int,M) | one_one(int) = ti(int,M))) # label(fact_309_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1551 (all X_a (division_ring(X_a) -> (all N all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N))))) # label(fact_2553_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1552 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))) # label(fact_1689_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1553 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_480_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1554 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2546_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1555 (all K_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4)) # label(fact_131_add__Pls) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1556 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),re),A_2))) # label(fact_4894_Re_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1557 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3419_ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1558 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),X))) # label(fact_3246_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1559 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4)))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_4413_Rat__induct) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1560 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (zero_zero(X_b) != ti(X_b,L) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),hAPP(X_b,X_b,sgn_sgn(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4590_LIM__sgn) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1561 (all X_a fequal(X_a) = ti(fun(X_a,fun(X_a,bool)),fequal(X_a))) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1562 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4800_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1563 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)))))) # label(fact_3301_one__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1564 (all X_a (real_algebra_1(X_a) -> hAPP(real,X_a,of_real(X_a),one_one(real)) = one_one(X_a))) # label(fact_2786_of__real__1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1565 (all U all M all N all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N)))) # label(fact_750_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1566 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),one_one(int))) = one_frac(X_a)) # label(fact_3684_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1567 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))) <-> N_1 = zero_zero(nat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & zero_zero(X_a) != ti(X_a,X_1))))) # label(fact_2454_zero__less__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1568 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)) = ti(int,M))) # label(fact_992_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1569 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1635_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1570 (all X_a (semiring_1(X_a) -> (all Inc all I ti(X_a,I) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),zero_zero(nat)),I)))) # label(fact_4160_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1571 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4636_bset_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1572 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_741_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1573 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),M))))) # label(fact_360_zcong__zmult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1574 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),N) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_734_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1575 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_834_int__ge__induct) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1576 (all A_2 all D_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),A_2)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),D_1))))) # label(fact_4322_arith__series__nat) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1577 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(int,fun(X_a,int),combk(int,X_a),C_1)),X_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))))) # label(fact_4262_setsum__const) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1578 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L),X_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4737_scaleR__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1579 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (ti(int,B) != zero_zero(int) -> ti(int,R_5) = ti(int,R_4))))) # label(fact_1186_unique__remainder) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1580 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1581 (all X_a all F1 all Real1 all Real2 hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2) = hAPP(complex,X_a,hAPP(fun(real,fun(real,X_a)),fun(complex,X_a),complex_rec(X_a),F1),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2))) # label(fact_2758_complex_Orecs) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1582 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))) # label(fact_338_dvd__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1583 (all X_b all X_a all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),B_2)))) # label(fact_3655_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1584 (all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_188_power2__ge__self) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1585 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) <-> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4786_some__eq__ex) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1586 (all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N))) # label(fact_4355_gcd__add2__int) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1587 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4584_LIM__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1588 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))) # label(fact_1616_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1589 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4169_suminf__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1590 (all N_1 (zero_zero(nat) = N_1 <-> zero_zero(real) = hAPP(nat,real,real_1(nat),N_1))) # label(fact_2301_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1591 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1152_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1592 (all X_a ti(fun(int,X_a),number_of_frac(X_a)) = number_of_frac(X_a)) # label(tsy_c_Nitpick_Onumber__of__frac_res) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1593 (all X_a (real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_2017_divide_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1594 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_1337_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1595 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X)))) # label(fact_1874_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1596 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)))))) # label(fact_2015_minus__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1597 (all Ma (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),Ma) <-> hAPP(int,int,abs_abs(int),Ma) = one_one(int))) # label(fact_3464_zgcd__0__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1598 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) = ti(int,X_1))) # label(fact_1100_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1599 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_578_add__leD1) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1600 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1347_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1601 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)))))) # label(fact_4454_tendsto__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1602 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1258_even__times__anything) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1603 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_1655_le__funI) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1604 (all N zero_zero(real) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))) # label(fact_2420_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1605 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3541_plus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1606 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,X_1) = hAPP(quickcheck_code_int,int,quickcheck_int_of,Y_1))) # label(fact_3161_code__int_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1607 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_1854_abs__mult) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1608 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4071_suminf__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1609 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_542_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.57/7.63 1610 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1611 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M)) # label(fact_4957_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1612 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) | ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2000_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1613 (all P_1 all P1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P1,X_2)))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2844_minusinfinity) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1614 (all X_a (topological_space(X_a) -> (all F all K all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)))))) # label(fact_4443_LIMSEQ__offset) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1615 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat))))))))) # label(fact_4621_Cauchy__product) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1616 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3563_complex__Im__of__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1617 (all P (hBOOL(hAPP(bool,bool,fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1618 (exists X_2 ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & zero_zero(real) = hAPP(real,real,cos,Y_2) -> X_2 = Y_2)) & zero_zero(real) = hAPP(real,real,cos,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))) # label(fact_2249_cos__is__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1619 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_1944_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1620 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),P_5)))) # label(fact_3064_prime__g__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1621 (all X_1 ((exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) | (exists N_2 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) <-> zero_zero(real) = hAPP(real,real,cos,X_1))) # label(fact_2412_cos__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1622 (all F ((all I_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,I_2))),hAPP(nat,nat,F,I_2)))) -> (exists I_2 all K_1 hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1)) = hAPP(nat,nat,F,I_2)))) # label(fact_3552_weak__decr__stable) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1623 (all D all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1))) # label(fact_4383_coprime__lmult__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1624 (all K all L (hAPP(int,int,bit0,K) = hAPP(int,int,bit0,L) <-> ti(int,K) = ti(int,L))) # label(fact_92_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1625 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4785_someI__ex) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1626 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)))))) # label(fact_4469_LIMSEQ__minus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1627 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),M)))) # label(fact_420_zdvd__bounds) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1628 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2352_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1629 (all X_b all X_a all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))))) # label(fact_3638_imageI) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1630 (all A_2 all B_1 all C_1 (C_1 != zero_zero(real) -> (B_1 = A_2 <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),B_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),A_2)))) # label(fact_709_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1631 (all U_1 hAPP(nat,nat,suc,U_1) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),U_1))) # label(fact_4973_card__atMost) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1632 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D)))))))) # label(fact_4819_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1633 (all Z all W_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Z),W_1)) & Z != W_1 <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Z),W_1)))) # label(fact_3723_less__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1634 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real)))))) # label(fact_2698_real__root__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1635 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1))))))) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1636 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_3022_Re_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1637 (all N_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),hAPP(bool,fun(real,fun(real,real)),if(real),hAPP(nat,bool,even_odd_even(nat),N_1)),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1)) = zero_zero(real)) # label(fact_2471_lemma__STAR__sin) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1638 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,real,norm_norm(X_a),zero_zero(X_a)) = zero_zero(real))) # label(fact_1776_norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1639 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Y_2)),hAPP(real,real,F,X_1))))) -> L = zero_zero(real))))) # label(fact_2660_DERIV__local__max) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1640 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),min_1)))) # label(fact_3591_of__int__m1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1641 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) # label(fact_2147_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1642 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,tan,X)) = hAPP(real,real,tan,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2252_tan__minus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1643 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,A_2,zero_zero(nat)))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat)))))))))))) # label(fact_4523_summable__Leibniz_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1644 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4426_summable__Leibniz_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1645 (all X_a all X_b all F all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_2))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_3641_image__diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1646 (all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2141_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.63 1647 (all Z_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2927_complex__mod__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1648 (all X_a (field_inverse_zero(X_a) -> (all B_1 all C_1 all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2) <-> (zero_zero(X_a) = ti(X_a,C_1) -> ti(X_a,A_2) = zero_zero(X_a)) & (zero_zero(X_a) != ti(X_a,C_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1)))))) # label(fact_1686_divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1649 (all X all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B))))) # label(fact_3230_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1650 (all X_a (metric_space(X_a) -> (all X zero_zero(real) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),X)))) # label(fact_3516_dist__self) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1651 (all X_a all X all Y ti(X_a,X) = 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)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1652 (all X_a (linordered_idom(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_107_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1653 (all X_a (comple44059174attice(X_a) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3))))))) # label(fact_1763_complete__lattice__class_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1654 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)))))))) # label(fact_340_dvd__add) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1655 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arcsin,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2189_cos__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1656 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3625_ex__less__of__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1657 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_1),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),X_1)),A_2),P_4)))))))) # label(fact_3933_SetS__setprod__prop) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1658 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | zero_zero(nat) = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))))) # label(fact_348_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1659 (all N hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(nat,nat,fact_fact(nat),N))) # label(fact_2498_fact__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1660 (all X_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2449_odd__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1661 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4630_aset_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1662 (all X_b all X_a all X_c (real_normed_vector(X_c) -> (all F all A_2 all A_3 all S ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S)) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,I_2)),hAPP(X_a,X_c,A_2,I_2)),A_3)))) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),S)),hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),A_2),S)),A_3)))))) # label(fact_4763_tendsto__setsum) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1663 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3181_fact__mono__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1664 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1))))) # label(fact_1719_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1665 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),cos),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))))) # label(fact_2640_DERIV__cos) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1666 (all S (-hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (all M_2 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))))) # label(fact_3657_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1667 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)),A_1) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B)) # label(fact_3327_powr__powr__swap) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1668 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2610_one__le__inverse) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1669 (all X_b all X_a all R_3 all K all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),T_3)) -> K = hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(fun(X_b,bool),nat,finite_card(X_b),T_3)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S))))) # label(fact_4298_setsum__multicount) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1670 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))) <-> hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),N_1),Ma)))) # label(fact_3160_less__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1671 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)))) # label(fact_808_add__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1672 -(all S1 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),S1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))) # label(fact_283__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1673 (all X_a (real_normed_vector(X_a) -> (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X)))))) # label(fact_1779_norm__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1674 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1661_divide_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1675 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))))))) # label(fact_4087_sums__add) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1676 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))) <-> zero_zero(nat) != Ma | zero_zero(nat) != N_1)) # label(fact_3259_gcd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1677 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_1627_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1678 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W)) # label(fact_23_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1679 (all N all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) & (M = zero_zero(nat) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)))) # label(fact_719_mult__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1680 (all A_2 all B_1 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),A_3)) -> ti(int,A_2) = ti(int,B_1))))))) # label(fact_3620_RRset__zcong__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1681 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(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(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2579_right__inverse) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1682 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_1973_psubset__trans) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1683 (all X all A_1 hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),hAPP(real,real,ln,X))) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3382_powr__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1684 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B_1),A_2),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_313_zcong__sym) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1685 (all F all Y_1 all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),F),Y_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)))))) # label(fact_4105_sums__if) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1686 (all A_1 all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),one_one(int)))) # label(fact_354_zcong__1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1687 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_5)))))) # label(fact_264_q__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1688 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),uminus_uminus(real)))),sin))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),uminus_uminus(real)))),cos))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3918_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1689 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1690 (all N_1 hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) # label(fact_4317_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1691 (all X_a all F all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3)) # label(fact_4250_real__of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1692 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J)))) # label(fact_686_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1693 (all X_a (real_normed_algebra(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),S_3)))))))) # label(fact_1789_norm__mult__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1694 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N))) # label(fact_3263_gcd__add__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1695 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zEven))))) # label(fact_1364_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1696 (all X_1 all Y_1 (hAPP(real,real,sqrt,Y_1) = hAPP(real,real,sqrt,X_1) <-> X_1 = Y_1)) # label(fact_1610_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1697 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N)) # label(fact_2374_cos__npi2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1698 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2479_even__square) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1699 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2608_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1700 (all X_b all X_a all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_2))))))))))) # label(fact_4331_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1701 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2560_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1702 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_1597_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1703 (all N hAPP(nat,nat,size_size(nat),N) = N) # label(fact_2923_nat__size) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1704 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> (exists R_2 exists A_4 (Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) = X)))) # label(fact_2725_polar__ex2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1705 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma)),A_3) = hAPP(int,fun(int,bool),norRRset,Ma)))) # label(fact_3630_RRset2norRR__eq__norR) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1706 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),X_1),Y_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1707 (all X_a (mult_zero(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1708 (all X_a (monoid_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1709 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N))) # label(fact_2675_odd__real__root__pow) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1710 (all A_3 A_3 = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_3650_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1711 (all Z_1 all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))),one_one(int)),P_5)))) # label(fact_455_zcong__zpower__zmult) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1712 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1908_real__sqrt__ge__abs1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1713 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4292_setsum__mono3) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1714 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3249_gcd__mult__distrib__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1715 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)))))) # label(fact_754_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1716 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1273_even__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1717 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),zero_zero(X_a)),A_1)))) # label(fact_926_mod__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1718 (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]. 7.64/7.64 1719 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))) # label(fact_366_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1720 (all X_b all X_a all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))))) # label(fact_3642_finite__surj) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1721 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_3274_gcd__diff1__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1722 (all X_b all X_a all Q_1 all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4341_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1723 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X))))) # label(fact_3624_ex__of__int__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1724 (all X_a all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> ti(X_a,A_2) = ti(X_a,X_2))) -> hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,A_2)))) # label(fact_4789_some__equality) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1725 (all V_1 all N_1 (hAPP(int,nat,number_number_of(nat),V_1) = hAPP(nat,nat,suc,N_1) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))) = N_1) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3885_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1726 (all B_1 all A_2 all F all G all X_1 all D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),hAPP(real,real,G,X_1)),D_2)) -> (zero_zero(real) != D_2 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B_1)) -> Y_2 = hAPP(real,real,F,hAPP(real,real,G,Y_2)))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),hAPP(real,real,inverse_inverse(real),D_2)))))))))) # label(fact_4925_DERIV__inverse__function) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1727 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4649_bset_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1728 (all X_a (real_normed_vector(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)))) # label(fact_2201_sgn__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1729 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y)))) # label(fact_2126_arctan__lbound) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1730 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_1346_diff__Suc__1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1731 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),A_2))))))) # label(fact_4895_isCont__diff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1732 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))))) # label(fact_2506_exp__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1733 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),one_one(int)),P_5)))))) # label(fact_854_MultInv__prop2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1734 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3500_BseqI_H) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1735 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4548_LIM__mult) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1736 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))))))) # label(fact_803_inv__less__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1737 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)))))) # label(fact_4769_setprod_Ocong) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1738 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1545_le__funE) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1739 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1434_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1740 (all X_a (real_normed_field(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_4083_sums__minus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1741 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4822_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1742 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4397_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1743 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1)))))))))) # label(fact_4284_Maclaurin) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1744 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),A_2))))) # label(fact_4907_mult__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1745 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2132_arcsin__ubound) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1746 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = X)) # label(fact_2676_odd__real__root__power__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1747 (all P_4 hAPP(rat,int,archim2085082626_floor(rat),P_4) = hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),div_div(int)),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4027_rat__floor__code) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1748 (all A_1 (zero_zero(int) != ti(int,A_1) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),A_1))) # label(fact_984_zdiv__self) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1749 (all Nat_1 hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2921_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1750 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4738_LIM__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1751 (all X_a all X_b sum_Plus(X_a,X_b) = ti(fun(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool))),sum_Plus(X_a,X_b))) # label(tsy_c_Sum__Type_OPlus_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1752 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_140_mult__2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1753 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_373_mult__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1754 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_3117_mod__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1755 (all A_1 all B (zero_zero(nat) != B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),B)))) # label(fact_3261_gcd__le2__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1756 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))))) # label(fact_52_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1757 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_472_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1758 (all N all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),B)))))) # label(fact_202_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1759 (all X_a (monoid_mult(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N)))) # label(fact_341_power__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1760 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_924_mod__self) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1761 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),one_one(nat)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N_1))))))) # label(fact_612_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1762 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))) # label(fact_1690_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1763 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))),hAPP(int,int,fact_fact(int),N)) = hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3201_fact__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1764 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),X_1)),hAPP(int,int,number_number_of(int),Y_1))) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),Y_1)),hAPP(int,int,number_number_of(int),X_1)))) # label(fact_1038_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1765 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_4853_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1766 (all X all N all Y (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y),X)) -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q_4)) = X)))) # label(fact_1172_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1767 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),hAPP(complex,complex,inverse_inverse(complex),Y))) # label(fact_2755_complex__divide__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1768 (all X_b all X_a all B_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) & (-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = zero_zero(nat)))) # label(fact_3180_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1769 (all X_a (ab_group_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1770 (all X_a (division_ring(X_a) -> (all A_2 all B_1 (zero_zero(X_a) != ti(X_a,B_1) -> (ti(X_a,A_2) = ti(X_a,B_1) <-> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)))))) # label(fact_1696_right__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1771 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_3305_ceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1772 (all Ma all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),D_1) = zero_zero(nat) <-> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_1),Q_4) = Ma))) # label(fact_1104_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1773 (all K_4 zero_zero(rat) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),K_4),zero_zero(int)))) # label(fact_3708_Frct__code__post_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.64 1774 (all P_5 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)))) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) -> (zero_zero(int) = hAPP(product_prod(int,int),int,product_snd(int,int),P_5) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5)) & (hAPP(product_prod(int,int),int,product_snd(int,int),P_5) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))))) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5))))) # label(fact_4344_normalize__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1775 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_4813_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1776 (all X_a (ab_group_add(X_a) -> (all F all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4180_sumr__offset) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1777 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1439_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1778 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)))) # label(fact_2849_coprime__rmul2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1779 (all X_a (semiring_1(X_a) -> (all M hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))))) # label(fact_1218_of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1780 (all X_a all One all Times all A_2 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),zero_zero(nat)) = ti(X_a,One)) # label(fact_2840_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1781 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_233_power__even__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1782 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2551_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1783 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),Q_3),R_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),Q_3),hAPP(rat,rat,inverse_inverse(rat),R_4))) # label(fact_3717_divide__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1784 (all A_2 all C_1 all D_1 all B_1 (zero_zero(int) != ti(int,B_1) -> (zero_zero(int) != ti(int,D_1) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))))))) # label(fact_3784_le__rat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1785 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> X = hAPP(real,real,arccos,hAPP(real,real,cos,X))))) # label(fact_2259_arccos__cos) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1786 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1142_nat__add__distrib) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1787 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> (all D_3 (one_one(nat) = D_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)))))) # label(fact_2871_coprime) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1788 (all X_a (field_char_0(X_a) & number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),field_char_0_Rats(X_a)))))) # label(fact_3694_Rats__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1789 (all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,P_6)),K_3)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),K_3))))) # label(fact_4288_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1790 (all P_4 all N_1 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1))) <-> N_1 = one_one(nat) & hBOOL(hAPP(nat,bool,prime,P_4)))) # label(fact_3059_prime__exp) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1791 (all A_1 all C all D all B (zero_zero(int) != ti(int,B) -> (ti(int,D) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D))))) # label(fact_3786_diff__rat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1792 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)))))) # label(fact_1025_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1793 (all X_a (real_normed_vector(X_a) & inverse(X_a) -> (all F all A_2 all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)))),hAPP(X_a,X_a,F,A_2)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,A_2)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),A_2))),D_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4607_DERIV__LIM__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1794 (all M all D all R_4 (R_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),D) -> (exists Q_4 M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),R_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_4),D))))) # label(fact_1182_mod__eqD) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1795 (all X_a (linordered_idom(X_a) -> (all A_2 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2434_zero__le__power__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1796 (all R_4 all A_1 hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))) # label(fact_3170_Im__rcis) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1797 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_141_semiring__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1798 (all X_a all X_b (topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool))),tendsto(X_a,X_b)) = tendsto(X_a,X_b))) # label(tsy_c_Limits_Otendsto_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1799 (all X_a (comm_semiring_1(X_a) -> (all N all M all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),M)))))))) # label(fact_345_dvd__power__le) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1800 (all K all L (hAPP(int,int,bit1,L) = hAPP(int,int,bit1,K) <-> ti(int,L) = ti(int,K))) # label(fact_91_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1801 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),field_char_0_Rats(X_a))))) # label(fact_3695_Rats__1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1802 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1263_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1803 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))) # label(fact_550_mult__0__right) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1804 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_3999_mult__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1805 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3)))))) # label(fact_4774_setsum_Ocong) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1806 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)))))))) # label(fact_4012_summable__diff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1807 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y))))) # label(fact_1728_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1808 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_1042_div__add__self2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1809 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K)))) # label(fact_4313_finite__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1810 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,pred,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2910_number__of__pred) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1811 (all X_b all X_a all A_3 all B_2 hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),collect(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))) = hAPP(fun(X_b,bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool)),prod(X_a,X_b),A_3),B_2)) # label(fact_4159_Nitpick_Oprod__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1812 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3544_fact__lt) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1813 (all K all L ((exists N_2 L = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)))) # label(fact_1799_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1814 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & X_2 != C_1 -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,F,X_2)))))))))) # label(fact_4628_LIM__fun__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1815 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_962_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1816 (all X_1 all P_1 ((all A_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_4)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_4),one_one(int))))) -> hBOOL(hAPP(int,bool,P_1,A_4)))) -> hBOOL(hAPP(int,bool,P_1,X_1)))) # label(fact_832_d22set__induct__old) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1817 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3303_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1818 (all X_a (metric_space(X_a) -> (all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),B_1),sequentially)) -> ti(X_a,B_1) = ti(X_a,A_2)))))) # label(fact_4485_LIMSEQ__unique) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1819 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,ln,X)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y))))) # label(fact_3405_ln__powr) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1820 (all X_a (monoid_mult(X_a) -> (all Z_1 all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) = one_one(X_a)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))))))) # label(fact_3898_power__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1821 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),X))) # label(fact_4346_gcd__dvd1__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1822 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)))) # label(fact_570_le__add1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1823 (all X hAPP(real,real,cos,X) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X))) # label(fact_2391_cos__sin__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1824 (all F all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> K = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))))) # label(fact_2666_DERIV__const__ratio__const2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1825 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1453_even__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1826 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4535_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1827 (all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))))) # label(fact_2857_coprime__exp__imp) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1828 (all X_a (linordered_semiring(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_430_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1829 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3499_BseqI2_H) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1830 (all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) -> (exists N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) & -hBOOL(hAPP(nat,bool,P_1,N_2))))))) # label(fact_2738_exists__least__lemma) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1831 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real)))),suc))) = hAPP(real,real,ln,X_1)))) # label(fact_3977_ln__series) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1832 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N))))) # label(fact_1841_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1833 (all X_b all X_a (comm_monoid_mult(X_a) & ring_1(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),F),A_3))))) # label(fact_3929_of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1834 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))))) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1835 (all X_a (topological_space(X_a) -> ti(fun(X_a,filter(X_a)),at(X_a)) = at(X_a))) # label(tsy_c_Limits_Oat_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1836 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,A_2) = ti(X_a,C_1))))))) # label(fact_4196_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1837 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hAPP(nat,nat,suc,M) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_1233_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1838 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4586_divide_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1839 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1262_odd__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1840 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),X)))) # label(fact_4711_real__vector_Oscale__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1841 (all X_a all X_b (real_normed_field(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),Y_1)),A_3)))))) # label(fact_4456_divide_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1842 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) # label(fact_3222_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1843 (all N all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,exp(real),X)),N) = hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X))) # label(fact_2599_exp__real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1844 (all X_a (linordered_idom(X_a) -> (all A_1 all K_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_4))),zero_zero(X_a))) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_234_even__power__le__0__imp__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1845 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1095_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1846 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))))) # label(fact_2364_natceiling__add) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1847 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),B_1))))) # label(fact_871_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1848 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)))) # label(fact_737_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1849 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_2073_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1850 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))))) # label(fact_2077_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1851 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),L),Ma)),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4566_LIM__diff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1852 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> -(all K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) -> -(all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3501_BseqE) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1853 (all V zero_zero(real) = hAPP(complex,real,im,hAPP(int,complex,number_number_of(complex),V))) # label(fact_2979_complex__Im__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1854 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),X),Y))) # label(fact_3767_real__plus__code) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1855 (all A_1 all B hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_3107_div__int__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1856 (all Z_1 all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y))))) # label(fact_653_real__add__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1857 (all X_a (semiring_div(X_a) -> (all B all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),B)))) # label(fact_973_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1858 (all P_1 all A_2 all B_1 hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),zero_zero(nat)) = hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1)) # label(fact_3132_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1859 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3913_DERIV__cos__realpow2b) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1860 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M))))) # label(fact_204_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1861 (all X_a (ring_1(X_a) -> (all Z_1 all N hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),N)))) # label(fact_3566_of__int__power) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1862 (all X_a (metric_space(X_a) & comm_monoid_add(X_a) -> (all F hAPP(fun(nat,X_a),X_a,lim(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))) # label(fact_4328_suminf__eq__lim) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1863 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2665_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1864 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists K_1 ((exists X_2 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),X_2)))),K_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3491_Bseq__iff2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1865 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,N_2)))),X))))))) # label(fact_2723_ex__inverse__of__nat__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1866 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))))))) # label(fact_2883_floor__less__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1867 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_431_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1868 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),T_3)))))))) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1869 (all X_a (semiring_div(X_a) -> (all B all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_914_mod__div__equality2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1870 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))))))) # label(fact_3610_ceiling__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1871 (all K (hAPP(int,int,bit0,K) = pls <-> pls = ti(int,K))) # label(fact_120_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1872 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),of_real(X_a)),A_2))))) # label(fact_4903_of__real_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1873 (all B all A_1 (A_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),A_1)))) # label(fact_3260_gcd__le1__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1874 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z)))) # label(fact_84_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1875 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1))))) # label(fact_3827_bdd__nat__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1876 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1)))))))) # label(fact_2643_log__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1877 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),A_1)))) # label(fact_4399_gcd__le1__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1878 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)))))))) # label(fact_4489_Bseq__inverse) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1879 (all X hAPP(real,real,ln,hAPP(real,real,exp(real),X)) = X) # label(fact_2509_ln__exp) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1880 (all B_1 all A_2 all D_1 (ti(int,D_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),B_1)) & (all E (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),D_1)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_1)))) # label(fact_4395_gcd__unique__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1881 (all M all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_347_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1882 (all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),K_4)),M)))) # label(fact_989_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1883 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_2)),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))))) # label(fact_3799_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1884 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)))))) # label(fact_4473_tendsto__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1885 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3755_minus__rat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1886 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,X_a,number_number_of(X_a),V) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))))))) # label(fact_1514_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1887 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))))) # label(fact_2649_log__divide) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1888 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)))))) # label(fact_2505_aux4) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1889 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N))) # label(fact_2873_coprime__plus1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1890 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,sin,X)))) # label(fact_2316_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1891 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists R_2 ((all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_2)),zero_zero(real))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_4629_LIM__fun__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1892 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4573_LIM__mult__right__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1893 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X_1)))))) # label(fact_4987_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1894 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4631_aset_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1895 (all X_1 all N_1 (zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))))) # label(fact_198_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1896 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N)))) # label(fact_349_power__mult) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1897 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Z)))) # label(fact_1431_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1898 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4736_scaleR_OLIM__right__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1899 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_500_zcong__def) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1900 (all F all A_2 all B_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,A_2)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),A_2)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),B_1))) # label(fact_1800_lemma__MVT) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1901 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2050_minus__add) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1902 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),zero_zero(int)),P_5)))))) # label(fact_845_MultInv__prop3) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1903 (all N all M all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),M)))) # label(fact_4348_coprime__exp2__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1904 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1848_abs__divide) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1905 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all R_4 all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_4693_of__real_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1906 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))) # label(fact_4775_setsum__0_H) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1907 (all A_2 all Ma all X_1 (ti(int,X_1) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3932_Bnor__prod__power) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1908 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2))))) # label(fact_4109_cnj_Osums) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1909 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))))) # label(fact_269_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1910 (all X hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X))) # label(fact_2935_cnj_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1911 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1))))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1912 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_3751_minus__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1913 (all N N = hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N))) # label(fact_2295_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1914 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))))) # label(fact_251_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1915 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_402_zero__less__one) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1916 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2835_xt4) # label(axiom) # label(non_clause). [assumption]. 7.64/7.65 1917 (all X_a (field_char_0(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),field_char_0_Rats(X_a))))))) # label(fact_3697_Rats__power) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1918 (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)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1563_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1919 (all N all M all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),R_4)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)),R_4)))))) # label(fact_4393_divides__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1920 (all E_1 all B all D all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E_1),B)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),E_1))))) # label(fact_4358_coprime__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1921 (all Z (Z = zero_zero(complex) <-> zero_zero(complex) = hAPP(complex,complex,cnj,Z))) # label(fact_2930_complex__cnj__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1922 (all Z_1 hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z_1)) = ti(int,Z_1)) # label(fact_2143_zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1923 (all C all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),N) -> (exists R_2 exists S_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),S_1),N) = B & A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),R_2),N)))))) # label(fact_3425_coprime__pow) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1924 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))))) # label(fact_498_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1925 (all M all R_4 all S_3 all T_5 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_3),T_5)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N) -> ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N))))) # label(fact_3082_xzgcd__linear) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1926 (all A_2 all C_1 all D_1 all B_1 (zero_zero(int) != ti(int,B_1) -> (ti(int,D_1) != zero_zero(int) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))))))) # label(fact_3779_less__rat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1927 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),A_2)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4486_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1928 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1)),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1053_div__prop2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1929 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))))))) # label(fact_3133_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1930 (all X_a all A_3 ti(fun(X_a,bool),A_3) = hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))) # label(fact_2775_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1931 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_938_mod__add__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1932 (all A_1 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Y_2)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2))))) # label(fact_3090_bezout__prime) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1933 (all X_a (comm_semiring_1(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),zero_zero(X_a)),A_1)) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_329_dvd__0__left) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1934 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K_4)) # label(fact_678_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1935 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4017_summable__norm__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1936 (all X_a (ring_char_0(X_a) -> (all W_1 all Z (ti(int,Z) = ti(int,W_1) <-> hAPP(int,X_a,ring_1_of_int(X_a),W_1) = hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3574_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1937 (all X_a powp(X_a) = ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),powp(X_a))) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1938 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),F),A_3)))))) # label(fact_3937_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1939 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),R_4)),hAPP(int,rat,number_number_of(rat),S_3)))) # label(fact_3734_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1940 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,sin,X_1)))) # label(fact_4096_sin__converges) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1941 (all R_4 all X all Y hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),X)),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2811_complex__of__real__add__Complex) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1942 (all N ti(int,N) = hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,quickcheck_of_int,N))) # label(fact_3537_int__of__of__int) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1943 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 ((zero_zero(X_a) = ti(X_a,X_1) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))) & N_1 != zero_zero(nat) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))))))) # label(fact_2453_power__le__zero__eq) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1944 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2428_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1945 (all X_a complex_rec(X_a) = ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_rec(X_a))) # label(tsy_c_Complex_Ocomplex_Ocomplex__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1946 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat))) # label(fact_4112_nat__case__0) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1947 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_905_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1948 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))))) # label(fact_1075_zfact__prop) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1949 (all B_1 all D_1 all A_2 ((all E (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),D_1)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_2)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = D_1)) # label(fact_3241_gcd__unique__nat) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1950 (all X_c all X_a all X_b all C_1 all P_4 all Q_2 (ti(product_prod(X_a,X_b),Q_2) = ti(product_prod(X_a,X_b),P_4) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),Q_2) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),P_4))) # label(fact_3995_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1951 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),nat,finite_card(int),A_3) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))) # label(fact_3668_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1952 (all X_a (comple44059174attice(X_a) -> (all V_1 all U_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U_1),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),U_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)))))))) # label(fact_1765_complete__lattice__class_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1953 (all V_1 all N_1 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_3893_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1954 (all X_a all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_2804_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1955 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))),Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),Y)),X))))))) # label(fact_2407_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1956 (all X_a (semiring_1(X_a) -> ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1957 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) <-> N_1 = Ma))) # label(fact_746_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1958 (all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) -> (exists X_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),one_one(int)),N)))))) # label(fact_3479_zcong__lineq__ex) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1959 (all X_a (ring_1(X_a) -> (all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),Z_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3568_of__int__minus) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1960 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_4761_scaleR__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1961 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N) = X))) # label(fact_2709_real__root__pow__pos2) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1962 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_429_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1963 (all X_a (semiring_div(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),one_one(X_a))))) # label(fact_966_div__by__1) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1964 (all N all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N) -> N = M))) # label(fact_873_mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1965 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2093_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1966 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),zero_zero(int))))) # label(fact_3383_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1967 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),B))))))) # label(fact_344_power__le__dvd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1968 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_1))))))))))) # label(fact_4651_metric__LIM__D) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1969 (all D all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (ti(int,C) = ti(int,B) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),D),M)))))) # label(fact_315_zcong__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1970 (all P_5 all Q_3 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,P_5),Q_3) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),P_5),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),P_5),Q_3))) # label(fact_3080_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1971 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),hAPP(X_a,X_a,F,X_1)),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),G),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_3),D_2)))))))) # label(fact_3862_DERIV__chain_H) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1972 (all X_b all X_c all X_a combb(X_b,X_c,X_a) = ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a))) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1973 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,G,X_1)))),Ma))))) # label(fact_3854_DERIV__fun__cos) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1974 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2803_Pow__mono) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1975 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_1260_Parity_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1976 (all V_3 all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_1515_div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.64/7.66 1977 (all X_a (comm_monoid_add(X_a) -> (all K all F (zero_zero(X_a) = hAPP(nat,X_a,F,zero_zero(nat)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))))) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1978 (all X_a (banach(X_a) -> (all F all C_1 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C_1)) | hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4055_ratio__test__lemma2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1979 (all P_1 all A_2 all B_1 all N_1 hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_1)) = hAPP(product_prod(real,real),product_prod(real,real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(product_prod(real,real),product_prod(real,real)),product_prod_case(real,real,product_prod(real,real)),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))))),combb(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),real),combs(real,product_prod(real,real),product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real))))),combs(real,fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),real),combs(real,product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),real),hAPP(fun(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),combb(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))),real),if(product_prod(real,real)))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool)),hAPP(fun(fun(real,product_prod(real,real)),fun(real,bool)),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool))),combb(fun(real,product_prod(real,real)),fun(real,bool),real),hAPP(fun(product_prod(real,real),bool),fun(fun(real,product_prod(real,real)),fun(real,bool)),combb(product_prod(real,real),bool,real),P_1)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(real,real),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combc(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real))),real),combs(real,real,product_prod(real,real))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real)))),hAPP(fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real))))),combb(fun(real,real),fun(real,fun(real,product_prod(real,real))),real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combb(real,fun(real,product_prod(real,real)),real),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),combi(real))))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))) # label(fact_4053_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1980 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),Ma))))) # label(fact_356_zcong__zmult__prop1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1981 (all A_1 hAPP(real,complex,cis,hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,cis,A_1))) # label(fact_3030_cis__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1982 (all X_a all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1921_DiffI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1983 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)))) # label(fact_4408_normalize__stable) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1984 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,X_2))),hAPP(nat,X_a,C_1,hAPP(nat,nat,suc,X_2))) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2)))) # label(fact_4118_diffs__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1985 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_4821_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1986 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3)) # label(fact_97_zadd__assoc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1987 (all S (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,S)) <-> (all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))))) # label(fact_3662_nat__set__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1988 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(P_2) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1)))) # label(fact_545_conj__le__cong) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1989 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_560_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1990 (all X hAPP(real,complex,of_real(complex),X) = hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X))) # label(fact_2945_complex__cnj__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1991 (all X hAPP(complex,complex,uminus_uminus(complex),X) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),X))) # label(fact_2763_complex__i__mult__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1992 (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,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1445_of__nat__less__two__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1993 (all B_1 hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1) = hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combs(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(fun(int,int),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_4035_adjust__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1994 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),J_2))) # label(fact_699_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1995 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_2))))) # label(fact_1749_Union__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1996 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all R_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4734_scaleR__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1997 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A_1),X)) # label(fact_4673_real__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1998 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1580_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 1999 (all B all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,hAPP(real,fun(real,real),log,B),X))))) # label(fact_3418_log__powr) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2000 (all K_4 ((zero_zero(quickcheck_code_int) = K_4 -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = zero_zero(int)) & (zero_zero(quickcheck_code_int) != K_4 -> (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(quickcheck_code_int) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)) = hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4)) & (zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_3157_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2001 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2)),sequentially)))) # label(fact_4506_cnj_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2002 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))),hAPP(real,real,uminus_uminus(real),X)))))) # label(fact_2119_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2003 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3401_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2004 (all Z_1 hAPP(complex,complex,cnj,hAPP(complex,complex,cnj,Z_1)) = Z_1) # label(fact_2938_complex__cnj__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2005 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2585_exp__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2006 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),X)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(int,X_a,number_number_of(X_a),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X))))))) # label(fact_2113_abs__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2007 (all M all N all K_4 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)))) # label(fact_3453_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2008 (all A_1 all B (hAPP(rat,product_prod(int,int),quotient_of,A_1) = hAPP(rat,product_prod(int,int),quotient_of,B) -> A_1 = B)) # label(fact_3720_quotient__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2009 (all L_4 hAPP(int,int,bit0,L_4) != min_1) # label(fact_291_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2010 (all X_a (real_normed_vector(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,sgn_sgn(real),R_4)),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4721_sgn__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2011 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1249_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2012 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,number_number_of(int),min_1)))) # label(fact_1150_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2013 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),G))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),hAPP(X_a,X_a,uminus_uminus(X_a),E_3))))))))) # label(fact_3816_DERIV__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2014 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> ti(int,Z_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)))) # label(fact_1378_nat__0__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2015 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1) <-> ti(X_a,D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1))))) # label(fact_490_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2016 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,re,X)),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2998_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2017 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N))))) # label(fact_2356_less__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2018 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2030_minus__mult__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2019 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_64_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2020 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),pi)) & (all Y_2 (hAPP(real,real,cos,Y_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) -> Y_2 = X_2)) & Y = hAPP(real,real,cos,X_2)))))) # label(fact_2248_cos__total) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2021 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_1251_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2022 (all Ma all No_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,Ma)),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),No_1)))))) # label(fact_1833_lemma__f__mono__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2023 (all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> (exists N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_2) = L_4))) # label(fact_2733_le__Suc__ex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2024 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_568_zspecial__product) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2025 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_1964_DiffD1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2026 (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7)))))) # label(fact_1482_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2027 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4979_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2028 (all N ti(int,N) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N))) # label(fact_3324_floor__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2029 (all X_a (real_algebra_1(X_a) & number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),W) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,number_number_of(real),W))))) # label(fact_2785_of__real__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2030 (all X_a (ring_1(X_a) -> one_one(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),one_one(int)))) # label(fact_3585_of__int__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2031 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))) # label(fact_3002_Re_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.68/7.66 2032 (all X_a all X_b all X_c all F ti(fun(product_prod(X_a,X_b),X_c),F) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b)))) # label(fact_4013_split__eta) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2033 (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),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)))))) # label(fact_2063_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2034 (all X_a all G all B_1 all F all A_2 all Net (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),Net)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),B_1),Net)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,real),fun(X_a,complex),hAPP(fun(X_a,fun(real,complex)),fun(fun(X_a,real),fun(X_a,complex)),combs(X_a,real,complex),hAPP(fun(X_a,real),fun(X_a,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(X_a,real),fun(X_a,fun(real,complex))),combb(real,fun(real,complex),X_a),complex_1),F)),G)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),Net))))) # label(fact_4505_tendsto__Complex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2035 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,B_1) <-> ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B_1))))) # label(fact_2043_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2036 (all D_1 hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(fun(int,bool),fun(int,bool)),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combb(fun(int,bool),fun(int,bool),int),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int)))) = hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than2,D_1)) # label(fact_4075_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2037 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),zero_zero(X_a))))) # label(fact_964_div__by__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2038 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))) # label(fact_1668_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2039 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_1862_abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2040 (all N_1 all Ma (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma) = one_one(nat) <-> N_1 = one_one(nat) & one_one(nat) = Ma)) # label(fact_725_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2041 (all X_a all X_b (ordere779506340up_add(X_b) & semiring_1(X_b) -> (all F all K_3 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),K_3)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),K_3))))))) # label(fact_4296_setsum__bounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2042 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_1206_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2043 (all A_2 all B_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd))))) # label(fact_1367_even__plus__odd__prop2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2044 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all R_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4735_scaleR__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2045 (all K_4 hAPP(int,int,number_number_of(int),K_4) = hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),K_4))) # label(fact_3163_int__of__number) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2046 (all D all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1))) # label(fact_3271_coprime__lmult__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2047 (all M all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,suc,J_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))))) # label(fact_1392_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2048 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2966_cnj_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2049 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),B_1)),A_3))))))) # label(fact_4726_scaleR_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2050 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_639_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2051 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> N = hAPP(real,nat,natfloor,X)))) # label(fact_2363_natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2052 (all X_a (division_ring(X_a) -> (all B all A_1 all C (zero_zero(X_a) != ti(X_a,C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) = ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C) = ti(X_a,A_1)))))) # label(fact_1692_divide__eq__imp) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2053 (all X_a (power(X_a) -> ti(fun(X_a,fun(nat,X_a)),power_power(X_a)) = power_power(X_a))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2054 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3021_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2055 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2033_minus__mult__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2056 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X1_1)),U))))))) # label(fact_2590_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2057 (all R_4 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),R_4) = hAPP(real,real,abs_abs(real),R_4)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> R_4 = hAPP(real,real,abs_abs(real),R_4)))) # label(fact_2111_real__abs__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2058 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2059 (all X_a (metric_space(X_a) -> (all Y all Z_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1))))))) # label(fact_3507_dist__triangle__alt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2060 (all X hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2973_complex__Im__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2061 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),X),Y))) # label(fact_3768_real__minus__code) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2062 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))))))) # label(fact_502_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2063 (all X_a (real_algebra(X_a) -> (all X all A_1 all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4675_mult__scaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2064 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_2869_coprime__divprod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2065 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(int,int,number_number_of(int),V) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V))))) # label(fact_2872_floor__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2066 (all X all Y all N (N != zero_zero(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_728_divides__exp2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2067 (all X_a all C_1 all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2191_ComplI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2068 (all R_4 all A_1 hAPP(real,real,abs_abs(real),R_4) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))))) # label(fact_2816_cmod__complex__polar) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2069 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)))) -> ((all T1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T1),S)) -> (all T2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T2),S)) -> (ti(fun(X_a,bool),T1) != ti(fun(X_a,bool),T2) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T2)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))))))))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),S)) = hAPP(fun(fun(X_a,bool),bool),X_b,hAPP(fun(fun(X_a,bool),X_b),fun(fun(fun(X_a,bool),bool),X_b),big_co1399186613setsum(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F)),S))))))) # label(fact_4310_setsum__UNION__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2070 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_2))))) # label(fact_546_imp__le__cong) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2071 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_2952_mult__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2072 (all X_b all X_a (comm_monoid_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4220_setsum__addf) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2073 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_2868_divides__mul) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2074 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & X_1 != Y_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_622_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2075 (all X_a (number(X_a) -> number_number_of(X_a) = ti(fun(int,X_a),number_number_of(X_a)))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2076 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) = hAPP(X_a,X_a,uminus_uminus(X_a),X_1) <-> ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_2954_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2077 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)))))) # label(fact_3570_of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2078 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4309_setsum__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2079 (all X_a all X_c all X_b (real_normed_vector(X_c) & topological_space(X_b) -> (all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,X_2)),X_1)))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),A_3)),X_1))))))) # label(fact_4926_isCont__setsum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2080 (all Z all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1138_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2081 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X))))) # label(fact_2618_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2082 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all P_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),P_1)),F)),zero_zero(X_b))),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),P_1))))))) # label(fact_4186_setsum__restrict__set_H_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2083 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,X_1))))) # label(fact_4850_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2084 (all X_a (real_normed_field(X_a) -> (all Db all F all G all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),hAPP(X_a,X_a,G,X_1)),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),Db)))))))) # label(fact_3861_DERIV__chain2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2085 (all R_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_4)) -> -(all S_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),S_1)) -> (all T_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),T_4)) -> R_4 != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),S_1),T_4))))))) # label(fact_3731_obtain__pos__sum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2086 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)))) # label(fact_836_aux______3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2087 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K))))) # label(fact_51_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2088 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_660_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2089 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),P_4)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),P_4)) = hAPP(int,nat,nat_1,A_2)))) # label(fact_3204_Bnor__prime) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2090 (all X_1 all Y_1 (X_1 = zero_zero(real) & Y_1 = one_one(real) <-> ii = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1))) # label(fact_2766_Complex__eq__i) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2091 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4642_bset_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2092 (all A_1 all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)))) # label(fact_2180_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2093 (all A_2 all B_1 (zero_zero(complex) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) <-> zero_zero(real) = B_1 & zero_zero(real) = A_2)) # label(fact_2740_Complex__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2094 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1084_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2095 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),zero_zero(real)),sequentially)))) # label(fact_4500_zeroseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2096 (all N_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),N_1) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,N_1))) # label(fact_4121_cos__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2097 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(nat,nat,suc,zero_zero(nat)))) <-> Ma = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1323_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2098 (all X_b (semiring(X_b) & number(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_95_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2099 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M))) # label(fact_3093_divmod__nat__base) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2100 (all X_b all X_a all F all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_b),combs(X_a,bool,bool)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_b),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_a,X_b),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,X_b),fun(X_a,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool)))),combb(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),X_b),combb(X_b,bool,X_a)),fequal(X_b))),F)))),P_1))))))) # label(fact_4423_finite__image__set) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2101 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),A_2))))) # label(fact_4915_scaleR__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2102 (all A_1 all B all C all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (exists K_1 hAPP(int,int,abs_abs(int),A_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N)))))) # label(fact_3476_int__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2103 (all X_a refl(X_a) = ti(fun(fun(product_prod(X_a,X_a),bool),bool),refl(X_a))) # label(tsy_c_Nitpick_Orefl_H_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2104 (all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),M)) -> ti(int,A_1) = zero_zero(int))))) # label(fact_452_zcong__zless__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2105 (all A_1 all B all X (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3228_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2106 (all N_1 all Ma (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),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1)),Ma)) <-> N_1 = one_one(nat)))) # label(fact_505_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2107 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_378_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2108 (all Ma all N_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_4538_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2109 (all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V))) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))))) # label(fact_1432_expand__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2110 (all Nat all Nat_5 (Nat_5 = Nat <-> hAPP(nat,nat,suc,Nat_5) = hAPP(nat,nat,suc,Nat))) # label(fact_1215_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2111 (all X_a (number_ring(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X))))) # label(fact_2457_Parity_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2112 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),one_one(real)))) # label(fact_1840_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2113 (all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1161_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2114 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_760_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2115 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1)))) # label(fact_4816_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2116 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2557_divide__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2117 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1))))) # label(fact_3787_Fract__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2118 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X zero_zero(X_a) != hAPP(X_a,X_a,exp(X_a),X)))) # label(fact_2537_exp__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2119 (all I_1 all J_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),I_1))) # label(fact_554_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2120 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1122_mod__le__divisor) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2121 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) = ti(int,A_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_3)))))) # label(fact_189_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2122 (all Z_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)) = ti(int,Z_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1))))) # label(fact_1376_int__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2123 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4670_scaleR__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2124 (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),abs_abs(real)),A_2))) # label(fact_4913_isCont__abs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2125 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)))))) # label(fact_3886_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2126 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_1380_zdiff__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2127 (all X exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_2)))) # label(fact_2732_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2128 (all X (hAPP(real,real,sin,X) = zero_zero(real) -> hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X)) = one_one(real))) # label(fact_2337_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2129 (all X_a all P_3 all X_2 (hBOOL(hAPP(X_a,bool,P_3,X_2)) -> hBOOL(hAPP(X_a,bool,P_3,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_3))))) # label(fact_4783_tfl__some) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2130 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_1617_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2131 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2681_real__root__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2132 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))),one_one(int)),P_4)))))) # label(fact_3934_wset__zcong__prod__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2133 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)) & hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))))))) # label(fact_3703_Rats__dense__in__real) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2134 (all X_1 (hAPP(real,real,sqrt,X_1) = zero_zero(real) <-> zero_zero(real) = X_1)) # label(fact_1613_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2135 (all X_1 hAPP(real,real,sin,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) # label(fact_3970_sin__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2136 (all X_b all X_a all F1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4039_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2137 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1)))) # label(fact_4958_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2138 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2139 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2))))) # label(fact_2135_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2140 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)) # label(fact_1253_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2141 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int)))))) # label(fact_3791_Fract__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2142 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) <-> Ma = N_1 | K = zero_zero(nat))) # label(fact_552_mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2143 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3221_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2144 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = ti(int,X_1))) # label(fact_1465_even__div__2__prop2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2145 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (zero_zero(real) != hAPP(real,real,cos,Y) -> (zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) -> hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)))))))) # label(fact_2268_tan__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2146 (all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5))))) # label(fact_842_MultInv__prop1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2147 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2120_aux5) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2148 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),zero_zero(real)),sequentially))))) # label(fact_4429_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2149 (all X_a (linordered_idom(X_a) -> (all X all W (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_2444_power__even__abs__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2150 (all X_b all X_a (minus(X_a) -> (all A_3 all B_2 all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_2,X_1)) = hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_2),X_1)))) # label(fact_2964_minus__apply) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2151 (all X_a (banach(X_a) -> (all F all N_4 all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C_1),one_one(real))) -> ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4054_ratio__test) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2152 (all X_a (real_div_algebra(X_a) -> (all X (zero_zero(real) != X -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)))))) # label(fact_2807_nonzero__of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2153 (all N_1 all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3894_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2154 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) # label(fact_955_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2155 (all Z_1 all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z_1)),W)) # label(fact_2140_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2156 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3522_Cauchy__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2157 (all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_1))) & hBOOL(hAPP(int,bool,P_1,X_2)))))))) # label(fact_4643_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2158 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4620_DERIV__D) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2159 (all X_a all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4784_someI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2160 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (X_1 = one_one(real) <-> zero_zero(real) = hAPP(real,real,ln,X_1)))) # label(fact_1948_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2161 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)))) # label(fact_2848_coprime__lmul2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2162 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) <-> hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) # label(fact_2195_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2163 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1)))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))) # label(fact_3974_lemma__sin__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2164 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y)) # label(fact_2278_arctan) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2165 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_1389_Suc__pred) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2166 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4672_real__vector_Oscale__scale) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2167 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,X)))) # label(fact_2617_ln__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2168 (all I_1 ((zero_zero(int) != ti(int,I_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> one_one(int) = hAPP(int,int,sgn_sgn(int),I_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> hAPP(int,int,sgn_sgn(int),I_1) = hAPP(int,int,uminus_uminus(int),one_one(int)))) & (zero_zero(int) = ti(int,I_1) -> zero_zero(int) = hAPP(int,int,sgn_sgn(int),I_1)))) # label(fact_2258_zsgn__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2169 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2133_negative__zle) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2170 (all X_b all X_a all X_c all F all X_1 hAPP(X_c,X_a,F,hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),X_1)) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(product_prod(X_b,X_c),product_prod(X_b,X_a),hAPP(fun(X_c,X_a),fun(product_prod(X_b,X_c),product_prod(X_b,X_a)),product_apsnd(X_c,X_a,X_b),F),X_1))) # label(fact_4067_snd__apsnd) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2171 (all X_a (power(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_1308_power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2172 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B))))) # label(fact_882_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2173 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all W_1 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1))))))))) # label(fact_1746_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2174 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X))))) # label(fact_3567_of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2175 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),J_2))) # label(fact_3429_zgcd__zdvd2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2176 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = one_one(X_a))))) # label(fact_1695_divide__self) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2177 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4603_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2178 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4151_setprod__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2179 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_2))))) # label(fact_3635_image__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2180 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2431_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2181 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))) # label(fact_1349_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2182 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,tan,X_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)))))) # label(fact_2285_lemma__tan__total) # label(axiom) # label(non_clause). [assumption]. 7.68/7.67 2183 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3924_monoseq__realpow) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2184 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3))))))) # label(fact_41_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2185 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (zero_zero(X_a) != hAPP(X_a,X_a,F,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))),D_2)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))))))))))) # label(fact_3877_DERIV__inverse_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2186 (all X_a (real_normed_vector(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),A_1)),B))),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Y)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4722_scaleR_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2187 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) = ti(X_a,B)))) # label(fact_2049_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2188 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1611_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2189 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3622_RRset2norRR__correct2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2190 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1114_le__mod__geq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2191 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2197_ComplE) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2192 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))) = hAPP(X_a,X_a,exp(X_a),X_1)))) # label(fact_4751_exp__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2193 (all X_a (number(X_a) -> (all W_1 all X_1 (ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_90_number__of__reorient) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2194 (all W_1 all Z ((exists N_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2)) = ti(int,Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)))) # label(fact_1306_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2195 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),R_1),sequentially))) # label(fact_4437_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2196 (all Z all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3706_SupInf_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2197 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))) # label(fact_1094_nat__div__distrib) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2198 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2881_zero__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2199 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(real,real,ln,X)) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X))) # label(fact_2630_log__base__10__eq1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2200 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N) # label(fact_587_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2201 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) # label(fact_531_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2202 (all X_a (metric_space(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))))) # label(fact_3510_zero__le__dist) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2203 (all M all K_4 all N (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N))) # label(fact_4385_gcd__mult__cancel__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2204 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_1424_realpow__two__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2205 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3182_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2206 (all W hAPP(int,complex,ring_1_of_int(complex),W) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_3584_complex__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2207 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)))) # label(fact_3368_ceiling__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2208 (all K_4 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),zero_zero(int)))) # label(fact_1293_int__less__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2209 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_1246_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2210 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,nat_1,X)) = hAPP(int,real,real_1(int),X))) # label(fact_3394_real__nat__eq__real) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2211 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2961_compl__less__swap1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2212 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2213 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B))))) # label(fact_1039_div__mult__self1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2214 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2163_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2215 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,abs_abs(X_a),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_1850_abs__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2216 (all X all Y (X = Y -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_626_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2217 (all A_2 all B_1 all C_1 all X_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C_1),hAPP(int,nat,nat_1,X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) = one_one(int) -> (exists K_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)) = ti(int,A_2))))))) # label(fact_3474_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2218 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B))))) # label(fact_3118_mod__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2219 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),hAPP(X_a,X_a,abs_abs(X_a),K))))))) # label(fact_1845_dvd__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2220 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(X_a,int,F,I_2)),X_1) = one_one(int))) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3)),X_1))) # label(fact_4414_setprod__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2221 (all X_a all G all A_3 hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),A_3) = hAPP(complex,complex,cnj,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3))) # label(fact_4247_cnj_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2222 (all Y all X exists R_2 exists A_4 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)))) # label(fact_3492_polar__Ex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2223 (all X_1 ((exists A_4 exists B_4 ti(int,X_1) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) <-> hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X_1)))) # label(fact_755_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2224 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_761_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2225 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4952_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2226 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_1958_equalityD1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2227 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))) # label(fact_4135_suminf__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2228 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,X_1)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),X_1))),D_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)))))) # label(fact_4601_DERIV__iff2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2229 (all A_1 all B all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4)) # label(fact_921_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2230 (all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,A_1)),C)) # label(fact_1419_div__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2231 (all Z_1 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W),Z_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W)) # label(fact_704_real__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2232 (all T_1 comple44059174attice(filter(T_1))) # label(arity_Limits_Ofilter___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2233 (all N_1 all X_1 exists T_4 (hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4270_Maclaurin__exp__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2234 (all X_a (archim1804426504_field(X_a) -> (all X exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),X_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),one_one(int))))) & (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Y_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y_2),one_one(int))))) -> ti(int,X_2) = ti(int,Y_2))))))) # label(fact_3617_floor__exists1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2235 (all X_1 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X_1)),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) = hAPP(real,real,exp(real),X_1)) # label(fact_3975_exp__first__two__terms) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2236 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X)))) # label(fact_4937_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2237 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int))) # label(fact_65_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2238 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4407_gcd__int__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2239 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> ti(X_a,A_1) = ti(X_a,B))))) # label(fact_2523_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2240 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))))) # label(fact_2350_natceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2241 (all A_1 all N all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) # label(fact_4362_gcd__exp__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2242 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))))) # label(fact_2082_abs__le__D2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2243 (all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_951_zdiv__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2244 (all X_a (linord1278240602ring_1(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_457_convex__bound__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2245 (all N hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N)) # label(fact_3007_complex__Re__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2246 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_36_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2247 (all X_a (real_vector(X_a) -> (all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),X)),Xa_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1))))) # label(fact_4687_scaleR__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2248 (all Z all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z))),Ma)))) # label(fact_1970_dvd__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2249 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2250 (all K_4 hAPP(int,rat,ring_1_of_int(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int))) # label(fact_3744_of__int__rat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2251 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1))))) # label(fact_3865_bdd__nat__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2252 (all X all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),N)))) # label(fact_1941_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2253 (all A_3 hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = hAPP(fun(nat,bool),nat,finite_card(nat),A_3)) # label(fact_3651_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2254 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less))))) # label(fact_3485_pair__lessI2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2255 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3348_powr__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2256 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_1))))))))) # label(fact_4519_LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2257 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(Q) | hBOOL(P))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2258 (all A_1 all B all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),N)) # label(fact_3441_zgcd__power__distrib) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2259 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real))))) # label(fact_2346_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2260 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) <-> hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1) = hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1))))) # label(fact_4962_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2261 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N))))) # label(fact_3054_prime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2262 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),X_a),lim(X_a)) = lim(X_a))) # label(tsy_c_SEQ_Olim_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2263 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int)) = hAPP(nat,rat,semiring_1_of_nat(rat),K_4)) # label(fact_3742_of__nat__rat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2264 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M)))) # label(fact_1339_diff__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2265 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_2898_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2266 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(nat,fun(real,real),root,M),X))))) # label(fact_2673_real__root__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2267 (all X_a (comm_ring_1(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X))))) # label(fact_2439_minus__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2268 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)))) # label(fact_307_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2269 (all N_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),sin_coeff),N_1) = hAPP(nat,real,cos_coeff,N_1)) # label(fact_4116_sin__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2270 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1587_order__le__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2271 (all X_a (number_ring(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))),Z_1)))) # label(fact_2045_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2272 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3547_fact__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2273 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_2117_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2274 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1496_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2275 (all X_b all X_a (linordered_field(X_a) -> (all F all A_3 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))) # label(fact_3948_abs__setprod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2276 -(all S_1 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),S_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))))) # label(fact_196__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2277 (all X_1 all Y_1 (Y_1 = X_1 <-> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_1))) # label(fact_1485_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2278 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> (K_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),K_4))))))) # label(fact_1385_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2279 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3692_Rats__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2280 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> N = one_one(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)))) # label(fact_3071_prime__coprime) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2281 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))))) # label(fact_3198_card__Plus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2282 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2717_DERIV__real__root) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2283 (all X_b (number(X_b) & semiring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C))))) # label(fact_96_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2284 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)))))) # label(fact_3621_RRset2norRR__correct) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2285 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),K_4) = zero_zero(rat)) # label(fact_3739_rat__number__collapse_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2286 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2702_real__root__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2287 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2288 (all Y_3 all Y_1 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),Y_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),hAPP(nat,real,Y_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_4431_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2289 (all X_a (group_add(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2290 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),M))) # label(fact_972_StandardRes__prop1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2291 (all Z_1 hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1))) # label(fact_3009_Re__sgn) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2292 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))))))) # label(fact_2879_floor__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2293 (all X_a all F all C_1 all H ((all N_2 hAPP(nat,X_a,F,N_2) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2)) -> hAPP(nat,X_a,F,zero_zero(nat)) = ti(X_a,C_1))) # label(fact_4332_def__nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2294 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3600_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2295 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))))) # label(fact_3119_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2296 (all X_a (metric_space(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3505_dist__triangle2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2297 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))) # label(fact_4212_abs__setsum__abs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2298 (all M hAPP(int,int,abs_abs(int),M) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M)) # label(fact_3451_zgcd__0__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2299 (all X_a member(X_a) = ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a))) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2300 (all P_1 all Ma all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1))) <-> N_1 = zero_zero(nat) & hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) | (exists Q_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_4)),Ma)) & hBOOL(hAPP(nat,bool,P_1,Q_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_4)))))))) # label(fact_1443_split__div_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2301 (all Z_1 all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),Z_1)),M)))) # label(fact_363_zcong__zpower) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2302 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_783_add__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2303 (all N_1 all Ma hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),Ma) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N_1))),Ma)) # label(fact_4833_min__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2304 (all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),X_3))))) # label(fact_4844_vanishes__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2305 (all R_4 exists X_2 (R_4 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) & (all Y_2 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) = R_4 & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) = one_one(int) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2))) -> X_2 = Y_2)) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) = one_one(int) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2))))) # label(fact_4410_quotient__of__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2306 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aq),Ar))) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Bq),Br))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aq),Bq)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C)))))))) # label(fact_3097_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2307 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3910_DERIV__sin__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2308 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),A_2))))) # label(fact_4914_scaleR__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2309 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))) # label(fact_4499_summable__Leibniz_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2310 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),A_6)),B)))) # label(fact_4715_scaleR_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2311 (all X_a (linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)))))))) # label(fact_4820_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2312 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),S),T_3)))))) # label(fact_3036_Diff__infinite__finite) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2313 (all Z_1 hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_4854_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2314 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))) # label(fact_266_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2315 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1098_div__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2316 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_4836_min__leastL) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2317 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_1546_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2318 (all X_a (real_vector(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a))))) # label(fact_4702_scaleR__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2319 (all X one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),zero_zero(real))) # label(fact_3351_powr__zero__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2320 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3257_gcd__red__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2321 (all N all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N)),K_4)))) # label(fact_663_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2322 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_162_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2323 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_2822_of__real_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2324 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_2950_times_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2325 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1622_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.68 2326 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))))) # label(fact_150_less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2327 (all X_a all X_1 ti(X_a,X_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1))) # label(fact_4788_some__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2328 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2231_sgn__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2329 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),N)) # label(fact_1437_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2330 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2062_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2331 (all A_3 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists X_2 (hBOOL(hAPP(int,bool,P_2,X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),X_2))))))) <-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))))) # label(fact_4875_cppi) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2332 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_1575_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2333 (all X_a (real_normed_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_2035_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2334 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1665_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2335 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2336 (all K_4 all L_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3711_Frct__code__post_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2337 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3903_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2338 (all X hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2290_sin__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2339 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) != zero_zero(X_a) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X_1))))))) # label(fact_1787_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2340 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_611_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2341 (all X hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(real,real,exp(real),one_one(real))),X) = hAPP(real,real,ln,X)) # label(fact_2644_log__ln) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2342 (all X_c all X_a all X_b all Z all C_1 all P_4 ((all A_4 all B_4 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4))))) # label(fact_4057_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2343 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))) # label(fact_617_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2344 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2828_minf_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2345 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_181_less__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2346 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2780_PowD) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2347 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1649_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2348 (all X_a (field_inverse_zero(X_a) -> (all Z_1 all X all Y (zero_zero(X_a) != ti(X_a,Y) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))) # label(fact_1718_add__num__frac) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2349 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,one_one(int)),M) = one_one(int)) # label(fact_3434_zgcd__1__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2350 (all M all K_4 all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4353_gcd__add__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2351 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_503_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2352 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_3_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2353 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all Sa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),Sa),sequentially)) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)))))) # label(fact_4496_sums__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2354 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),cnj),A_2))) # label(fact_4892_cnj_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2355 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),one_one(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))))),R_1),sequentially))) # label(fact_4498_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2356 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_2864_floor__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2357 (all Ma all N_1 hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_max(nat)),N_1))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),Ma),hAPP(nat,nat,suc,N_1))) # label(fact_4955_max__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2358 (all A_2 all B_1 (ti(int,B_1) = ti(int,A_2) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),zero_zero(int))))) # label(fact_353_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2359 (all B all X all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)))))) # label(fact_3235_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2360 (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),sequentially)))) # label(fact_4471_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2361 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)))) # label(fact_2729_z3div__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2362 (all Ma all N_1 (hAPP(nat,nat,suc,zero_zero(nat)) = N_1 & Ma = zero_zero(nat) | Ma = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = zero_zero(nat) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) # label(fact_1324_add__is__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2363 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))) # label(fact_2104_number__of__Min) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2364 (all A_1 all B all C (ti(int,C) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3752_mult__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2365 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all D_3 all I_2 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),D_3),I_2))) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),D_3),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),I_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3556_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2366 (all Z all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Z),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> Z = hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))) # label(fact_3713_Sup__eq__maximum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2367 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1644_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2368 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a))))))) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2369 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))))) # label(fact_312_dvd__trans) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2370 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N))) = zero_zero(real)) # label(fact_2296_sin__npi2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2371 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)) = hAPP(nat,nat,suc,N)) # label(fact_1343_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2372 (all X_c all X_b all X_a all P_4 all F all G all Q_2 ((all X_2 all Y_2 (ti(product_prod(X_a,X_b),Q_2) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F),P_4) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),Q_2)))) # label(fact_4771_split__cong) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2373 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_809_diff__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2374 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,Y) = ti(X_a,X)))))) # label(fact_1549_order__antisym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2375 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1)))) # label(fact_139_semiring__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2376 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arctan),X_1))) # label(fact_4888_isCont__arctan) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2377 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_782_add__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2378 (all T_2 all T_1 (comple44059174attice(T_1) -> comple44059174attice(fun(T_2,T_1)))) # label(arity_fun___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2379 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,number_number_of(int),min_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),min_1)),B))) # label(fact_1047_div__eq__minus1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2380 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4616_Im_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2381 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1030_neg__mod__conj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2382 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2987_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2383 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2989_Im_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2384 (all X_1 ((exists Y_2 X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2442_even__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2385 (all A_1 (hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),zero_zero(int)) = zero_zero(int) & hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),zero_zero(int)) = ti(int,A_1))) # label(fact_908_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2386 (all X_a (ring_1(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),ring_1_Ints(X_a))))))) # label(fact_3851_Ints__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2387 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),zero_zero(nat)),X)) # label(fact_3253_gcd__0__left__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2388 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),zero_zero(int))))))) # label(fact_1057_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2389 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_475_number__of__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2390 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),min_1)),B)) # label(fact_1066_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2391 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2))))))) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2392 (all Code_numeral all Code_numeral_5 (Code_numeral_5 = Code_numeral <-> hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral) = hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_5))) # label(fact_2939_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2393 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_640_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2394 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1628_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2395 (all X all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M))),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),X)),M)) # label(fact_2151_zminus__zmod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2396 (all X_a (linordered_semidom(X_a) -> (all K all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,P_6)),K_3)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),K_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),K_3)))))))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2397 (all P_1 all N_1 ((exists M_2 (hBOOL(hAPP(nat,bool,P_1,M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) <-> (exists X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))) & hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4537_ex__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2398 (all X_b all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),Q_1),Y_2)))))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1))),Q_1)))))))) # label(fact_4422_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2399 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),B)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_2))))))))) # label(fact_1914_lemma__interval) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2400 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),pls)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)))))) # label(fact_1430_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2401 (all A_1 all P_5 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = hAPP(int,int,number_number_of(int),min_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = one_one(int))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = zero_zero(int)))) # label(fact_607_Legendre__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2402 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Y_1)))))) # label(fact_48_le__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2403 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(X_a,int,archimedean_ceiling(X_a),R_4) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R_4)))))) # label(fact_3355_floor__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2404 (all X_a (real_n1866405975lgebra(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2511_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2405 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_634_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2406 (all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3)))) # label(fact_3628_RsetR__fin) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2407 (all X_b (number(X_b) & monoid_mult(X_b) -> (all W hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,X_b,number_number_of(X_b),W)) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_168_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2408 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b)) = lex_prod(X_a,X_b)) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2409 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))))) # label(fact_1623_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2410 (all R_4 all S_3 all T_5 all R_5 all S_4 all M all T_6 all N (ti(int,R_5) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) = ti(int,R_4) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5))),N))))) # label(fact_968_xzgcda__linear__aux2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2411 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_569_le__add2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2412 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int)) = hAPP(int,rat,ring_1_of_int(rat),K_4)) # label(fact_3745_Fract__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2413 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,X_1) <-> ti(int,Y_1) = ti(int,X_1))))) # label(fact_1105_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2414 (all Q_3 -(all A_4 all B_4 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) = Q_3 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4))))) # label(fact_4412_Rat__cases) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2415 (all R_4 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4691_Im_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2416 (all C_1 (zero_zero(rat) = C_1 <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(rat,fun(nat,rat),combk(rat,nat),C_1))))) # label(fact_4843_vanishes__const) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2417 (all A_1 all B all Q_3 all R_4 (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4)))))) # label(fact_1197_divmod__int__relI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2418 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arccos),X_1))))) # label(fact_4921_isCont__arccos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2419 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)))))) # label(fact_3234_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2420 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_1867_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2421 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_374_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2422 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> ti(fun(fun(nat,X_a),X_a),suminf(X_a)) = suminf(X_a))) # label(tsy_c_Series_Osuminf_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2423 (all A_2 all B_1 all Q_2 all R_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_2)),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),hAPP(int,int,uminus_uminus(int),Q_2)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),Q_2)),one_one(int)))),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B_1),R_1))))))) # label(fact_2183_zminus1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2424 (all A_1 all B ((zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2170_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2425 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),one_one(real)))) # label(fact_2208_cos__le__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2426 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1555_le__funD) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2427 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 Y = hAPP(real,real,exp(real),X_2)))) # label(fact_2718_exp__total) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2428 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_1),B)) | zero_zero(nat) = B)) # label(fact_723_divides__ge) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2429 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)))) # label(fact_2748_complex__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2430 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1433_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2431 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),G),S)),Ma)))) # label(fact_4333_setsum__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2432 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_1282_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2433 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1))) = zero_zero(X_a)))))) # label(fact_4606_setsum__cl__ivl__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2434 (all X_a (real_algebra_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X))))) # label(fact_2795_of__real__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2435 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))))))) # label(fact_3601_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2436 (all X_a (real_algebra_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(real,X_a,of_real(X_a),X)),N) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_2789_of__real__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2437 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1222_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2438 (all X_a all X_b all T_5 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),T_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),T_5)) = ti(product_prod(X_a,X_b),T_5)) # label(fact_3129_surjective__pairing) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2439 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),zero_zero(real))))) # label(fact_4917_isCont__root__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2440 (all Ma all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_597_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2441 (all X_a (number_ring(X_a) & field(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_2587_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2442 (all X_a (semiring_1(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),zero_zero(X_a))))) # label(fact_2554_iszero__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2443 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),combi(X_a)),A_2))))) # label(fact_4899_isCont__ident) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2444 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2148_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2445 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> ti(X_a,A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2529_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2446 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(int,X_b,number_number_of(X_b),V) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))))))) # label(fact_4989_max__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2447 (all X all Y all Xa_1 all Ya hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1648_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2448 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_784_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2449 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> Y = X))) # label(fact_633_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2450 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2451 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,number_number_of(int),min_1)) = zero_zero(int)) # label(fact_1037_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2452 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1223_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2453 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))))))))) # label(fact_3996_powser__insidea) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2454 (all X_b all X_a all P_5 ti(product_prod(X_a,X_b),P_5) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_5))) # label(fact_3130_pair__collapse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.69 2455 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_851_MultInv__zcong__prop2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2456 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))),X)))))))) # label(fact_2719_ex__inverse__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2457 (all C_1 all X_1 all Ta all A_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),D_1))),Ta)))))) # label(fact_208_zdvd__period) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2458 (all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),K_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M))),K_4) = one_one(nat))) # label(fact_1418_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2459 (all R_4 hAPP(real,complex,of_real(complex),R_4) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_4),zero_zero(real))) # label(fact_2791_complex__of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2460 (all Ma all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),Ma),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N_1))),Ma)) # label(fact_4832_min__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2461 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = Y -> X = zero_zero(real))) # label(fact_1646_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2462 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3906_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2463 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_416_power__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2464 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X))))) # label(fact_2037_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2465 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2244_cos__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2466 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),A_2))))) # label(fact_2230_sgn__1__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2467 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1156_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2468 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),pls)))) # label(fact_54_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2469 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3390_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2470 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))) # label(fact_4208_setsum__infinite) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2471 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),hAPP(int,int,uminus_uminus(int),J_2)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3443_zgcd__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2472 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))))) # label(fact_635_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2473 (all X_a (semiring_div(X_a) & number(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(int,X_a,number_number_of(X_a),Y_1)),hAPP(int,X_a,number_number_of(X_a),X_1)))))) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2474 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1462_even__div__2__l) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2475 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1225_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2476 (all N hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N) # label(fact_1228_nat__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2477 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))))))) # label(fact_2014_less__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2478 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_3336_real__of__int__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2479 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_4758_scaleR__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2480 (all X_a (comm_semiring_1(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2481 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_2051_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2482 (all X_a (ring_1(X_a) -> ring_1_of_int(X_a) = ti(fun(int,X_a),ring_1_of_int(X_a)))) # label(tsy_c_Int_Oring__1__class_Oof__int_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2483 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_768_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2484 (all X_a all A_2 all F all V_1 all N_1 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)))) # label(fact_4108_nat__case__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2485 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_3850_Re_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2486 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2306_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2487 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1))) = zero_zero(X_a)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(nat,X_a,F,N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2488 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))),hAPP(real,real,F,X_1))))))))))) # label(fact_2662_DERIV__pos__inc__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2489 (all X_a (real_n2089651433ebra_1(X_a) -> (all X all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N)))))) # label(fact_1794_norm__power__ineq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2490 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2491 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_74_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2492 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (zero_zero(X_a) != ti(X_a,A_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a)))))))) # label(fact_3688_nonzero__Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2493 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natceiling,X) = zero_zero(nat))) # label(fact_1899_natceiling__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2494 (all X_a all X_b all F all G all P_4 hAPP(product_prod(X_a,X_b),nat,hAPP(fun(X_b,nat),fun(product_prod(X_a,X_b),nat),hAPP(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat)),product_prod_size(X_a,X_b),F),G),P_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,F,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4))),hAPP(X_b,nat,G,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_4)))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3122_prod__size__simp) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2495 (all X_b all X_a (real_normed_vector(X_b) & real_normed_field(X_a) -> (all F all K_3 all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> ((all H_1 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,F,H_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),K_3),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4626_lemma__termdiff4) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2496 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))))) # label(fact_3103_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2497 (all X_a (power(X_a) & semiring_0(X_a) -> (all W ((zero_zero(nat) = hAPP(int,nat,number_number_of(nat),W) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W)) = one_one(X_a)) & (zero_zero(nat) != hAPP(int,nat,number_number_of(nat),W) -> zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W))))))) # label(fact_262_power__0__left__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2498 (all X_a (number_ring(X_a) & field(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1733_divide__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2499 (all X_a (real_algebra_1(X_a) -> (all R_4 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),one_one(X_a)) = hAPP(real,X_a,of_real(X_a),R_4)))) # label(fact_4699_of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2500 (all Real1_1 all Real2_1 zero_zero(nat) = hAPP(complex,nat,complex_size,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1))) # label(fact_2751_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2501 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)))))) # label(fact_1382_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2502 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_1552_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2503 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2576_one__less__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2504 (all M all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)))) # label(fact_1393_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2505 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))))) # label(fact_4946_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2506 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),L_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,ring_1_of_int(rat),K_4)),hAPP(int,rat,ring_1_of_int(rat),L_4))) # label(fact_3746_Fract__of__int__quotient) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2507 (all K_4 hAPP(int,int,bit1,hAPP(int,int,pred,K_4)) = hAPP(int,int,pred,hAPP(int,int,bit0,K_4))) # label(fact_2901_pred__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2508 (all Ma all N_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1) <-> N_1 = zero_zero(nat) & Ma = zero_zero(nat))) # label(fact_3255_gcd__zero__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2509 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X))))) # label(fact_1897_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2510 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = ti(int,X))) # label(fact_1454_two__times__even__div__two) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2511 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3438_zgcd__assoc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2512 (all B all A_1 (ti(int,B) != zero_zero(int) | ti(int,A_1) != zero_zero(int) -> (exists C_4 exists D_3 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),C_4) = ti(int,A_1) & hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_4),D_3) = one_one(int) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),D_3) = ti(int,B))))) # label(fact_3484_make__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2513 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_4703_scaleR_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2514 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)))) # label(fact_1269_even__times__either) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2515 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) # label(fact_1086_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2516 (all N ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int))))))) # label(fact_827_zfact_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2517 (all X_a (real_normed_vector(X_a) -> (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),Y)))) -> ti(X_a,X) = zero_zero(X_a)))))) # label(fact_1785_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2518 (all A_1 all B ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))) # label(fact_1067_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2519 (all X_a (real_normed_field(X_a) -> (all G all Db all F all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Db),hAPP(X_a,X_a,F,X_1)))))))))) # label(fact_3817_DERIV__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2520 (all P_1 all N_1 all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),K))) <-> (K != zero_zero(nat) -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,J_1)))))) & (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,N_1))))) # label(fact_1133_split__mod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2521 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N))) # label(fact_4380_gcd__mult__distrib__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2522 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3594_less__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2523 (all X_1 ((exists Y_2 X_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2441_odd__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2524 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_149_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2525 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))))) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2526 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1)) = ti(X_a,X_1)) # label(fact_4787_some__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2527 (all X_c all X_b all X_a product_apsnd(X_c,X_b,X_a) = ti(fun(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b))),product_apsnd(X_c,X_b,X_a))) # label(tsy_c_Product__Type_Oapsnd_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2528 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_3311_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2529 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_759_add__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2530 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),Y_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))),sequentially))))))) # label(fact_4438_LIMSEQ__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2531 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_1855_abs__mult__self) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2532 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_436_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2533 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4809_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2534 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),zero_zero(int))) -> zero_zero(int) = hAPP(int,int,fact_fact(int),M))) # label(fact_3188_fact__neg__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2535 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_1416_div__geq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2536 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_444_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2537 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y)) # label(fact_2260_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2538 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_2071_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2539 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_2021_neg__equal__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2540 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_2593_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2541 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))))) # label(fact_751_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2542 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1743_divide__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2543 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))) # label(fact_4396_gcd__ge__0__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2544 (all A_2 (one_one(nat) = A_2 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))))) # label(fact_896_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2545 (all V_1 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls))))) # label(fact_212_le__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2546 (all X_a all X_b all X_c all F all X_1 hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1)) = hAPP(product_prod(X_a,X_c),X_a,product_fst(X_a,X_c),X_1)) # label(fact_4065_fst__apsnd) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2547 (all K_4 all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)),M)),N)) # label(fact_1111_mod__mult__self3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2548 (all X_a (semiring_div(X_a) -> ti(fun(X_a,fun(X_a,X_a)),div_div(X_a)) = div_div(X_a))) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2549 (all X_a (comm_semiring_1(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_335_dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2550 (all X_1 ((exists N_2 hAPP(int,real,real_1(int),N_2) = X_1) <-> hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1)) = X_1)) # label(fact_3325_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2551 (all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (exists P_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_1)) & hBOOL(hAPP(int,bool,zprime,P_6)))))) # label(fact_473_zprime__factor__exists) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2552 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1)))) # label(fact_148_add__numeral__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2553 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2))))) # label(fact_1828_card__seteq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2554 (all X all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N) = hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))) # label(fact_3333_power__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2555 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))))) # label(fact_1285_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2556 (all X_a (semiring_char_0(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)) != zero_zero(X_a)))) # label(fact_2486_of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2557 (all X_a all X_b (real_normed_field(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> (zero_zero(X_b) != ti(X_b,B_1) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),B_1)),A_3)))))))) # label(fact_4452_tendsto__divide) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2558 (all X_a (real_normed_field(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))))) # label(fact_1790_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2559 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X))))) # label(fact_2312_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2560 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) = zero_zero(nat) -> N = M))) # label(fact_658_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2561 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> ((all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K)))))) # label(fact_1007_split__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2562 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4633_bset_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2563 (all M all N -(all Q_4 all R_2 -hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_4),R_2))))) # label(fact_3104_divmod__nat__rel__ex) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2564 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)))) # label(fact_3384_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2565 (all X_b all X_a (semiring_1(X_a) -> (all F all A_3 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3)))) # label(fact_4171_of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2566 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)))))) # label(fact_3609_floor__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2567 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3589_of__int__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2568 (all X_a (semiring_1(X_a) -> (all Z (zero_zero(X_a) = ti(X_a,Z) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),Z)))))) # label(fact_2555_iszero__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2569 (all X_a (metric_space(X_a) -> the(X_a) = ti(fun(fun(X_a,bool),X_a),the(X_a)))) # label(tsy_c_HOL_OThe_0_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2570 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_2596_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2571 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B) = zero_zero(int)) # label(fact_907_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2572 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),M)))) # label(fact_362_zcong__shift) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2573 (all X_a (real_normed_vector(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),A_1)),B) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4697_scaleR_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2574 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),V) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),V))))) # label(fact_3565_of__int__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2575 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> ti(X_a,A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_1860_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2576 (all N hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))) # label(fact_2381_fact__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2577 (all X_a (semiring_1(X_a) -> semiri532925092at_aux(X_a) = ti(fun(fun(X_a,X_a),fun(nat,fun(X_a,X_a))),semiri532925092at_aux(X_a)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2578 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = M) # label(fact_1350_div__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2579 (all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),X_1)))) # label(fact_4104_sums__if_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2580 (all X_a all X_b (real_normed_algebra(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),A_2)),A_3)))))) # label(fact_4476_mult__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2581 (all A_1 all B all C (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = ti(int,C) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) # label(fact_483_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2582 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),one_one(nat)))),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),N_2))))))) # label(fact_2406_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2583 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N))) # label(fact_4963_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2584 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_412_one__le__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2585 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_613_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2586 (all M all N (N = M | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_567_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2587 (all P_1 all Y_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1)))))))) # label(fact_4394_gcd__cases__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2588 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_530_le__refl) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2589 (all X hAPP(real,real,exp(real),X) = hAPP(real,real,abs_abs(real),hAPP(real,real,exp(real),X))) # label(fact_2532_abs__exp__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2590 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_4876_fin__bijRl) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2591 (all X_a all X_b all A_2 all B_1 all A_8 all B_7 all R_1 all Sa (hBOOL(hAPP(fun(product_prod(X_b,X_b),bool),bool,hAPP(product_prod(X_b,X_b),fun(fun(product_prod(X_b,X_b),bool),bool),member(product_prod(X_b,X_b)),hAPP(X_b,product_prod(X_b,X_b),hAPP(X_b,fun(X_b,product_prod(X_b,X_b)),product_Pair(X_b,X_b),B_1),B_7)),Sa)) & ti(X_a,A_8) = ti(X_a,A_2) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_2),A_8)),R_1)) <-> hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_8),B_7))),hAPP(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool)),lex_prod(X_a,X_b),R_1),Sa))))) # label(fact_3487_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2592 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2737_ex__le__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2593 (all X_a all X_b (real_normed_vector(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),X_1)),A_3)))))) # label(fact_4727_scaleR__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2594 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),H)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3)))))) # label(fact_3954_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2595 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4694_scaleR__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2596 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_557_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2597 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1))))) # label(fact_2335_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2598 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma) -> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),norRRset,Ma))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),Y_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_2),hAPP(int,fun(int,bool),norRRset,Ma))) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),X_2),Ma))))))) # label(fact_3614_norR__mem__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2599 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1818_finite__code) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2600 (all X_a (real_algebra(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),Y)))) # label(fact_4677_mult__scaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2601 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_592_zdiff__power2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2602 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))))) # label(fact_1200_inv__inv__aux) # label(axiom) # label(non_clause). [assumption]. 7.68/7.70 2603 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M)) # label(fact_956_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2604 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)))) # label(fact_4862_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2605 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aq),Ar))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Bq),Br))) -> (ti(int,C) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aq),Bq)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C)))))))) # label(fact_1196_zadd1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2606 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),one_one(nat)))) # label(fact_2853_coprime__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2607 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),int_lcm,X),Y)) # label(fact_3631_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2608 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))) = hAPP(int,int,fact_fact(int),N))) # label(fact_3202_fact__reduce__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2609 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))))) # label(fact_1870_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2610 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),M)))) # label(fact_3192_fact__ge__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2611 (all X_a (linordered_idom(X_a) -> (all X all Y all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2421_power__mono__odd) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2612 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4)) # label(fact_523_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2613 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_62_mult__Pls) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2614 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1097_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2615 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != ti(int,P_5) -> (ti(int,P_5) != hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)))))) # label(fact_274_prime__g__5) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2616 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3912_DERIV__cos__realpow2a) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2617 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a)) = finite_finite_1(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2618 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_556_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2619 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4653_LIM__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2620 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),one_one(int))) <-> hAPP(int,int,abs_abs(int),X_1) = one_one(int))) # label(fact_1931_zdvd1__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2621 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),B_2)) # label(fact_1963_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2622 (all Z_1 hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,re,Z_1))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_3017_complex__add__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2623 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1594_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2624 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all I all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,I)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)))))))) # label(fact_3953_dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2625 (all M all N hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) # label(fact_3126_mod__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2626 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a)))) -> hAPP(X_a,int,archim2085082626_floor(X_a),X) = ti(int,Z_1)))))) # label(fact_3605_floor__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2627 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))) <-> hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),N_1),Ma)))) # label(fact_3159_less__eq__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2628 (all X_c all X_b all X_a all Q_1 all F all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2)) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),F,X_2),Y_2))))) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(product_prod(X_b,X_a),X_c,hAPP(fun(X_b,fun(X_a,X_c)),fun(product_prod(X_b,X_a),X_c),product_prod_case(X_b,X_a,X_c),F),P_4)))))) # label(fact_4126_exE__realizer) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2629 (all X_1 all Y_1 (Y_1 != X_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))) # label(fact_655_real__less__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2630 (all X_b all X_a (comm_monoid_mult(X_a) -> (all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),one_one(X_a))),A_3) = one_one(X_a)))) # label(fact_3947_setprod__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2631 (all A_1 all B hAPP(complex,complex,cnj,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2948_complex__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2632 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> (ti(X_a,B_1) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a))))))))) # label(fact_3689_nonzero__Rats__divide) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2633 (all X_a all X_b (real_normed_algebra(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Y_1)),A_3)))))) # label(fact_4475_mult__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2634 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))) # label(fact_171_number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2635 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)))) # label(fact_3677_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2636 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,tan,X)))))) # label(fact_2270_tan__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2637 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_4)),J_2)) # label(fact_742_diff__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2638 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,number_number_of(int),min_1))) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != one_one(int) # label(fact_468__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2639 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_863_minf_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2640 (all L (ti(int,L) = min_1 <-> min_1 = hAPP(int,int,bit1,L))) # label(fact_286_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2641 (all X_a all X_b (minus(X_b) -> (all A_3 all B_2 all X_2 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_2,X_2)) = hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_2),X_2)))) # label(fact_2963_fun__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2642 (all M all N ((N != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)) & (hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = N -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_1352_mod__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2643 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4580_LIM__offset__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2644 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_401_not__one__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2645 (all X_a all X_b all B_2 all F all A_3 ((exists AA (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA) = ti(fun(X_a,bool),B_2) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_3)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))))) # label(fact_3634_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2646 (all X_a (order(X_a) -> ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),strict_mono(nat,X_a)) = strict_mono(nat,X_a))) # label(tsy_c_Orderings_Oorder_Ostrict__mono_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2647 (all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)) = hAPP(int,nat,nat_1,U_1)) # label(fact_4258_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2648 (all X_a (real_normed_field(X_a) -> (all K all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),combk(X_a,X_a),K)),X_1),zero_zero(X_a)))))) # label(fact_3840_DERIV__const) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2649 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,fact,N)) = hAPP(nat,nat,fact,hAPP(nat,nat,suc,N))) # label(fact_3546_fact_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2650 (all X_a all A_3 all B_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less(filter(X_a)),A_3),B_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),B_2)) & -hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),B_2),A_3)))) # label(fact_4510_less__filter__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2651 (all X_a (metric_space(X_a) -> (all X all Y hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3518_dist__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2652 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))),X)))) # label(fact_1045_zdiv__leq__prop) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2653 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_1265_even__sum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2654 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)))))) # label(fact_2850_coprime__mul) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2655 (all X_a (semiring_1(X_a) -> (all M all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N)))) # label(fact_1292_of__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2656 (all X_a all X_1 all Y_1 all F (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))))) # label(fact_3319_in__measure) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2657 (all Y (Y != zero_zero(code_code_numeral) -> -(all Code_numeral_1 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_1) != Y))) # label(fact_2971_code__numeral_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2658 (all X_a all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)) -> ((all M_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),M_3),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),M_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)))))) # label(fact_1829_finite__Union) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2659 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K) <-> N_1 = Ma)))) # label(fact_673_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2660 (all X_a (number_ring(X_a) -> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_174_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2661 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2597_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2662 (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_1584_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2663 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X))))) # label(fact_2798_of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2664 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W))))) # label(fact_137_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2665 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2666 (all Z_1 hAPP(real,real,sqrt,hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_3013_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2667 (all X_1 hAPP(rat,product_prod(int,int),quotient_of,X_1) = hAPP(fun(product_prod(int,int),bool),product_prod(int,int),the(product_prod(int,int)),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool),hAPP(fun(rat,bool),fun(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool)),combb(rat,bool,product_prod(int,int)),hAPP(rat,fun(rat,bool),fequal(rat),X_1)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),rat),hAPP(fun(product_prod(int,int),fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),rat)),combs(product_prod(int,int),int,rat),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat)),hAPP(fun(int,fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat))),combb(int,fun(int,rat),product_prod(int,int)),fract),product_fst(int,int))),product_snd(int,int))))),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),bool),hAPP(fun(int,bool),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),bool)),combb(int,bool,product_prod(int,int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))),product_snd(int,int)))),hAPP(int,fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(int,bool)),fun(int,fun(product_prod(int,int),bool)),combc(product_prod(int,int),int,bool),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool))),combb(int,fun(int,bool),product_prod(int,int)),fequal(int)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),int),hAPP(fun(product_prod(int,int),fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),int)),combs(product_prod(int,int),int,int),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int))),combb(int,fun(int,int),product_prod(int,int)),gcd_gcd(int)),product_fst(int,int))),product_snd(int,int)))),one_one(int)))))) # label(fact_4409_quotient__of__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2668 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1))))))) # label(fact_3998_summable__mult2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2669 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_685_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2670 (all N N != hAPP(nat,nat,suc,N)) # label(fact_1216_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2671 (all N one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))),N)) # label(fact_4356_coprime__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2672 (all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat)))) = hAPP(nat,nat,fact_fact(nat),M)) & (M = zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,fact_fact(nat),M)))) # label(fact_2500_fact__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2673 (all X_b all X_a all A_1 all B all A_6 all B_5 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_5) -> -(ti(X_a,A_1) = ti(X_a,A_6) -> ti(X_b,B_5) != ti(X_b,B)))) # label(fact_3137_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2674 (all J_2 all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4)),M)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)))) # label(fact_465_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2675 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_801_mult__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2676 (all X_1 (one_one(real) = hAPP(real,real,exp(real),X_1) <-> zero_zero(real) = X_1)) # label(fact_2569_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2677 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))))) # label(fact_902_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2678 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))))) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2679 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption]. 7.68/7.71 2680 (all Nat_3 hAPP(nat,nat,suc,Nat_3) != zero_zero(nat)) # label(fact_1226_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2681 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),zero_zero(nat)) = X) # label(fact_3254_gcd__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2682 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),Y_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_2415_even__sum__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2683 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))))))) # label(fact_1935_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2684 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2685 (all D all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int))) # label(fact_4382_coprime__rmult__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2686 (all X hAPP(complex,real,re,X) = hAPP(complex,real,re,hAPP(complex,complex,cnj,X))) # label(fact_2995_complex__Re__cnj) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2687 (all X_a (real_normed_vector(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B))))) # label(fact_4695_scaleR_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2688 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a))) # label(fact_1288_of__nat__1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2689 (all N all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))) # label(fact_682_diff__add__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2690 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> (zero_zero(X_a) != hAPP(X_a,X_a,G,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(X_a,X_a,G,X_1))))))))))) # label(fact_3811_DERIV__divide) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2691 (all Z_3 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_3)) -> (hAPP(int,nat,nat_1,Z) = hAPP(int,nat,nat_1,Z_3) <-> ti(int,Z_3) = ti(int,Z))))) # label(fact_1108_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2692 (all X_b all X_c all X_a all F all P_4 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),P_4) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),P_4)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),P_4))) # label(fact_3991_prod__case__beta) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2693 (all X_a all C_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,int),fun(X_a,int),hAPP(fun(int,int),fun(fun(X_a,int),fun(X_a,int)),combb(int,int,X_a),hAPP(int,fun(int,int),times_times(int),C_1)),F)),A_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3)))) # label(fact_4252_setsum__const__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2694 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)))))) # label(fact_3783_zero__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2695 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1567_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2696 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3397_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2697 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> (exists M_2 N_1 = hAPP(nat,nat,suc,M_2)))) # label(fact_1322_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2698 (all X (zero_zero(real) != X -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),X) = one_one(real))) # label(fact_2592_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2699 (all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)))) # label(fact_4253_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2700 (all B all A_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1770_real__average__minus__second) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2701 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) # label(fact_1128_posDivAlg__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2702 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3112_div__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2703 (all X_a all A_2 all P_1 ((exists X_2 ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> ti(X_a,X_2) = ti(X_a,Y_2))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,A_2)))) # label(fact_4868_some1__equality) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2704 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all Rn all Sn_1 all Tn_1 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn_1),Tn_1)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) -> (ti(int,R_5) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) -> (ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) -> ti(int,Rn) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn_1),N))))))) # label(fact_3085_xzgcda__linear) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2705 (all X_5 all Y_4 hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2404_sin__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2706 (all X_a all F all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3)) # label(fact_3941_real__of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2707 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1))) # label(fact_894_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2708 (all P_1 all I (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,I))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),zero_zero(int))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all N_2 (hAPP(nat,int,semiring_1_of_nat(int),N_2) = ti(int,I) -> hBOOL(hAPP(nat,bool,P_1,N_2)))))) # label(fact_1405_split__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2709 (all X_a (monoid_mult(X_a) -> (all Y all P_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),P_5))),Y) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),P_5)))))) # label(fact_1412_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2710 (all X_a all A_2 all R_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2))))) # label(fact_2919_accp__downward) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2711 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,im,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)))) # label(fact_4049_Im_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2712 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat)))) # label(fact_889_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2713 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))))) # label(fact_1141_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2714 (all B all A_1 all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),C))) # label(fact_4364_gcd__int_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2715 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_14_zero__eq__power2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2716 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_1949_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2717 (all X_a finite_psubset(X_a) = ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a))) # label(tsy_c_Wellfounded_Ofinite__psubset_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2718 (all X_a (linordered_ring(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))))) # label(fact_109_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2719 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),P_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b))))) # label(fact_4143_split__paired__The) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2720 (all X_a (linordered_semidom(X_a) -> (all N all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),R_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),R_4),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),R_4),hAPP(nat,nat,suc,N))),R_4))))))) # label(fact_1403_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2721 (all X_a (real_normed_algebra(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_1811_mult_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2722 (all X_a (comm_ring_1(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X))))) # label(fact_2438_minus__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2723 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)))) # label(fact_1759_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2724 (all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),X_2),M)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),Y_2),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M)) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),M)))))) # label(fact_616_zcong__zless__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2725 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)))))) # label(fact_177_less__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2726 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)))))) # label(fact_1966_ln__le__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2727 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))) = hAPP(int,nat,nat_1,N_1))) # label(fact_3809_card__bdd__int__set__l) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2728 (all X_a all C_2 all A_3 ((all X_4 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_4),C_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),C_2)))) # label(fact_2730_Union__least) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2729 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_33_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2730 (all Z_1 ((all N_2 ti(int,Z_1) != hAPP(nat,int,semiring_1_of_nat(int),N_2)) -> -(all N_2 hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2))) != ti(int,Z_1)))) # label(fact_3526_int__cases) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2731 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,cos,X_2)) # label(fact_3971_lemma__cos__ext) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2732 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1274_not__odd__impl__even) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2733 (all X_a all X_b (comm_monoid_mult(X_b) -> big_co302546470etprod(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co302546470etprod(X_a,X_b)))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2734 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),sequentially)))))) # label(fact_4729_scaleR__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2735 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)))))) # label(fact_339_dvd__mult__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2736 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2614_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2737 (all X ((X = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),X) = zero_zero(real)) & (zero_zero(real) != X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),X))))) # label(fact_2227_real__sgn__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2738 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K))) <-> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))))) # label(fact_1008_split__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2739 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3)) -> ti(X_a,D_2) = ti(X_a,E_3)))))) # label(fact_2633_DERIV__unique) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2740 (all W all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2))) # label(fact_69_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2741 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1227_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2742 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4022_summable__cos) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2743 (all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),A_1)) # label(fact_1769_real__average__minus__first) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2744 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,A_2)),A_3)))) # label(fact_4509_Re_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2745 (all M all K_4 all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M))))) # label(fact_3290_coprime__dvd__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2746 (all P_5 all Q_3 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3))) -> one_one(nat) = P_5 | one_one(nat) = Q_3)) # label(fact_3055_prime__product) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2747 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_2019_minus__divide__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2748 (all X_a (field_inverse_zero(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1)),N)))) # label(fact_1698_power__one__over) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2749 (all V_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) <-> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_2911_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2750 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),hAPP(nat,int,semiring_1_of_nat(int),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))),hAPP(nat,int,semiring_1_of_nat(int),Y)))) # label(fact_3211_bezw__aux) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2751 (all X_a (ring_1(X_a) -> (all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> -(all Z_2 hAPP(int,X_a,ring_1_of_int(X_a),Z_2) != ti(X_a,Q_2)))))) # label(fact_4345_Ints__cases) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2752 (all I all M_1 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3873_card__less__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2753 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_789_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2754 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),R_4) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),R_4))) # label(fact_1667_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2755 (all A_1 all B ((hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = zero_zero(int)) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_2171_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.68/7.71 2756 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3834_bdd__int__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2757 (all N_1 all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))))) # label(fact_4282_Maclaurin2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2758 (all X_1 hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(real,fun(int,bool),hAPP(fun(int,fun(real,bool)),fun(real,fun(int,bool)),combc(int,real,bool),hAPP(fun(int,real),fun(int,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(int,real),fun(int,fun(real,bool))),combb(real,fun(real,bool),int),ord_less_eq(real)),ring_1_of_int(real))),X_1))),hAPP(fun(int,real),fun(int,bool),hAPP(fun(real,bool),fun(fun(int,real),fun(int,bool)),combb(real,bool,int),hAPP(real,fun(real,bool),ord_less(real),X_1)),hAPP(fun(int,int),fun(int,real),hAPP(fun(int,real),fun(fun(int,int),fun(int,real)),combb(int,real,int),ring_1_of_int(real)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int)))))) = hAPP(real,int,archim2085082626_floor(real),X_1)) # label(fact_4146_floor__real__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2759 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_2)),X_1))))) # label(fact_2343_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2760 (all X_a (division_ring(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),A_1)))) # label(fact_1658_divide__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2761 (all Ma all N_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) <-> hAPP(int,int,number_number_of(int),min_1) = ti(int,N_1) & ti(int,Ma) = hAPP(int,int,number_number_of(int),min_1) | one_one(int) = ti(int,N_1) & one_one(int) = ti(int,Ma))) # label(fact_308_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2762 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N)),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),N))) -> ti(int,N) = hAPP(real,int,archimedean_ceiling(real),X)))) # label(fact_3415_ceiling__eq3) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2763 (all A_1 all C all D all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) != ti(int,D) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3785_add__rat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2764 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_798_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2765 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_4943_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2766 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2767 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)))))) # label(fact_4791_dvd_Ostrict__monoI) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2768 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sqrt),X_1))) # label(fact_4889_isCont__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2769 (all A_1 hAPP(complex,real,re,hAPP(real,complex,cis,A_1)) = hAPP(real,real,cos,A_1)) # label(fact_3026_Re__cis) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2770 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))) # label(fact_1978_ln__div) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2771 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),A_2)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))))) # label(fact_3366_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2772 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_425_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2773 (all Y Y = hAPP(real,real,tan,hAPP(real,real,arctan,Y))) # label(fact_2254_tan__arctan) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2774 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_2957_compl__mono) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2775 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M_2 hAPP(nat,int,semiring_1_of_nat(int),M_2) != ti(int,Z_1)))) # label(fact_1488_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2776 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_856_int__gr__induct) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2777 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),X_1)))) # label(fact_422_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2778 (all A_2 all B_1 hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,fun(int,int)),fun(int,fun(int,bool)),hAPP(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),combb(fun(int,int),fun(int,bool),int),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),fequal(int),A_2))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),B_1)))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),B_1))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),B_1))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),zero_zero(int))))))) = hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1)) # label(fact_4031_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2779 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N)) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N)))))) # label(fact_1837_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2780 (all M all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_1))) # label(fact_4804_min__diff) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2781 (all X_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1))) = X_1) # label(fact_3867_card__bdd__nat__set__l) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2782 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_843_wset__mem) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2783 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1568_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2784 (all X_b all X_a all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> -(all X_2 all Y_2 -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2))))) # label(fact_3146_exE__realizer_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2785 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1710_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2786 (all A_1 all B all C all D hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D))) # label(fact_2745_complex__add) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2787 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3540_times__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2788 (all F (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),zero_zero(real)),sequentially)))) # label(fact_4482_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2789 (all N_1 all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3895_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2790 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Y))) # label(fact_3245_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2791 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,Y_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)))))) # label(fact_1468_neg__one__power__parity) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2792 (all B_2 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),B_2)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),X_2))))))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & hBOOL(hAPP(int,bool,P_2,X_2)))))))))) # label(fact_4873_cpmi) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2793 (all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),X))),X) = hAPP(complex,complex,sgn_sgn(complex),X)) # label(fact_4742_complex__sgn__def) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2794 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_792_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2795 (all A_1 all B hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B))) # label(fact_3028_cis__mult) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2796 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)))) # label(fact_777_add__0) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2797 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_322_mult__zero__right) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2798 (all Sa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Sa)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),powr),real_1(nat))),hAPP(real,real,uminus_uminus(real),Sa))),zero_zero(real)),sequentially)))) # label(fact_4493_LIMSEQ__neg__powr) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2799 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4102_divide_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2800 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,sqrt,X) -> X = zero_zero(real)))) # label(fact_1621_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2801 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),Y))) # label(fact_4347_gcd__dvd2__int) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2802 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1101_mod__less__divisor) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2803 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))))) # label(fact_2501_fact__reduce__nat) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2804 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,re,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_3008_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2805 (all A_1 all B (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_647_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2806 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3240_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2807 (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_630_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.68/7.72 2808 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))))) # label(fact_829_wset__inv__mem__mem) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2809 (all N all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_1267_odd__pow) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2810 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_3308_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2811 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_156_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2812 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),hAPP(int,int,number_number_of(int),K_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3712_Frct__code__post_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2813 (all X_a (real_normed_algebra(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1788_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2814 (all X_a (real_normed_vector(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_4759_scaleR_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2815 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y))) # label(fact_2936_cnj_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2816 (all X_a (ring(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))))) # label(fact_729_mult__diff__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2817 (all N_1 all Ma (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) <-> N_1 = zero_zero(nat) & Ma = zero_zero(nat))) # label(fact_2155_negative__eq__positive) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2818 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A_1))))) # label(fact_904_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2819 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_1 all W_1 all A_2 ((hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_2)) & (hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2820 (all X_a (real_normed_field(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),zero_zero(X_a)),sequentially)))))) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2821 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) != zero_zero(X_a))))) # label(fact_2528_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2822 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_4818_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2823 (all X_a all X_b (metric_space(X_b) -> (all G all Ma all F all L all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_a,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,real)),combs(X_a,X_b,real),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,real)),hAPP(fun(X_b,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,real))),combb(X_b,fun(X_b,real),X_a),dist_dist(X_b)),F)),G)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),L),Ma)),A_3))))))) # label(fact_4457_tendsto__dist) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2824 (all X hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X)) # label(fact_1904_real__sqrt__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2825 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,sqrt,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2054_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2826 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),Y_1)))))) # label(fact_2047_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2827 (all X_a pow(X_a) = ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),pow(X_a))) # label(tsy_c_Set_OPow_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2828 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,nat,F,X_2) = zero_zero(nat))) <-> zero_zero(nat) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),F_1)))) # label(fact_4254_setsum__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2829 (all N (one_one(nat) != N -> (exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),N)))))) # label(fact_3088_prime__factor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2830 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))))) # label(fact_3409_real__of__int__div2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2831 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))) # label(fact_838_wset__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2832 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))))) # label(fact_32_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2833 (all X_a (real_normed_algebra(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_878_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2834 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),one_one(int))),zEven)))) # label(fact_1400_odd__minus__one__even) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2835 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arcsin),X_1))))) # label(fact_4922_isCont__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2836 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) | X_1 = Y_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_654_less__eq__real__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2837 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> ((all X_2 exists D_3 ((all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))))))) # label(fact_3205_lemma__BOLZANO) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2838 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya)))) # label(fact_1664_divide_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2839 (all M all N all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)))) # label(fact_3215_gcd__dvd__prod__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2840 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all I_2 all J_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),I_2),J_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))),J_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3555_upto_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2841 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1705_frac__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2842 (all X_a (banach(X_a) & real_normed_field(X_a) -> hAPP(X_a,X_a,exp(X_a),zero_zero(X_a)) = one_one(X_a))) # label(fact_2583_exp__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2843 (all X_a (semiring_1(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),one_one(X_a))))) # label(fact_2562_not__iszero__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 2844 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,sin,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X))),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)) # label(fact_2400_sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2845 (all R_4 all A_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,cis,A_1)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) # label(fact_3173_rcis__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2846 (all X_a (banach(X_a) -> (all F ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),M_2)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M_2),N_2)))),E))))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4287_summable__Cauchy) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2847 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (X != zero_zero(real) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N))) & (X = zero_zero(real) -> zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_3420_powr__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2848 (all Ma all K all N_1 (Ma = N_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_525_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2849 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,uminus_uminus(int),A_4)),hAPP(int,int,uminus_uminus(int),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3553_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2850 (all N zero_zero(real) = hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_2982_complex__Im__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2851 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all X_1 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),hAPP(X_a,filter(X_a),at(X_a),X_1)))))) # label(fact_4561_LIM__const) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2852 (all N_1 all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),G)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,G,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))),Ma))))) # label(fact_3879_DERIV__fun__pow) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2853 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)))))) # label(fact_4463_LIMSEQ__imp__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2854 (all X_a (idom(X_a) -> (all X_1 all Y_1 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) = ti(X_a,X_1))))) # label(fact_2100_realpow__two__disj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2855 (all A_1 all B (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),one_one(int))))))) # label(fact_3792_rat__floor__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2856 (all M all N M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)) # label(fact_668_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2857 (all X_a (real_normed_vector(X_a) -> (all X ((zero_zero(X_a) != ti(X_a,X) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = one_one(real)) & (zero_zero(X_a) = ti(X_a,X) -> zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))))) # label(fact_2234_norm__sgn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2858 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1))))))) # label(fact_3881_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2859 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1901_power2__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2860 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),X))) # label(fact_4378_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2861 (all X_a all X_b all X_c all Q_1 all P_1 all Z (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z))) -> -(all X_2 all Y_2 (hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) = ti(product_prod(X_b,X_c),Z) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,X_2),Y_2))))))) # label(fact_4770_splitE2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2862 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))) # label(fact_1448_int__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2863 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 (hAPP(X_a,X_a,inverse_inverse(X_a),A_2) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2527_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2864 (all N exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_6),hAPP(nat,nat,suc,hAPP(nat,nat,fact,N)))))) # label(fact_3551_euclid__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2865 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y_1)))) # label(fact_2451_even__power__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2866 (all X_b all X_c all X_a (topological_space(X_a) & metric_space(X_b) & metric_space(X_c) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,hAPP(X_c,fun(X_c,real),dist_dist(X_c),hAPP(X_a,X_c,G,X_2)),Ma)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4656_metric__LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2867 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = ti(X_a,A_1))))) # label(fact_997_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2868 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4029_summable__exp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2869 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_787_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2870 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less)))) # label(fact_3486_pair__lessI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2871 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1979_ln__add__one__self__le__self2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2872 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_3299_ceiling__less__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2873 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,suc,X_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2417_even__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2874 (all I_1 hAPP(int,nat,nat_1,hAPP(quickcheck_code_int,int,quickcheck_int_of,I_1)) = hAPP(quickcheck_code_int,nat,quickcheck_nat_of,I_1)) # label(fact_3176_nat__of__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2875 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact,M)),hAPP(nat,nat,fact,N))))) # label(fact_3539_fact__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2876 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))),one_one(X_a))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X)))))))) # label(fact_3607_ceiling__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2877 (all K all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))))) # label(fact_604_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2878 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1817_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2879 (all A_1 all N all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))) -> (zero_zero(nat) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_727_divides__rev) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2880 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> zero_zero(nat) = K | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)))) # label(fact_748_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2881 (all X_2 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,cos_coeff,X_2)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,cos_coeff,X_2) = zero_zero(real)))) # label(fact_2480_cos__coeff__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2882 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),A_2)))))) # label(fact_4905_isCont__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2883 (all X all A_1 zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3322_powr__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2884 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)))) <-> Ma = zero_zero(nat) & zero_zero(nat) = N_1)) # label(fact_2165_int__zle__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2885 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)),one_one(int))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1))) # label(fact_4605_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2886 (all P_1 hAPP(fun(nat,bool),fun(nat,bool),collect(nat),P_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(fun(int,nat),fun(int,bool),hAPP(fun(nat,bool),fun(fun(int,nat),fun(int,bool)),combb(nat,bool,int),P_1),nat_1))))) # label(fact_3832_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2887 (all X_a (real_n1866405975lgebra(X_a) -> (all A_2 (zero_zero(X_a) != ti(X_a,A_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),inverse_inverse(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4547_LIM__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2888 (all X_1 all Y_1 (Y_1 = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_624_divides__antisym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2889 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_2)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))))) # label(fact_3364_le__floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2890 (all X_a (field_inverse_zero(X_a) -> (all X all Y all Z_1 all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Z_1),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),W))))) # label(fact_1660_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2891 (all X_a all X all Y (ti(X_a,Y) != ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2892 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2893 (all X (one_one(real) = hAPP(real,real,cos,X) -> zero_zero(real) = hAPP(real,real,sin,X))) # label(fact_2318_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2894 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3599_ceiling__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2895 (all B all A_1 (B != zero_zero(nat) | zero_zero(nat) != A_1 -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3291_div__gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2896 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_183_zadd__power3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2897 (all Y exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,tan,Y_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) -> X_2 = Y_2)) & Y = hAPP(real,real,tan,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2283_tan__total) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2898 (all X_b (ring(X_b) & number(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C))))) # label(fact_491_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2899 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))))) # label(fact_1069_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2900 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b)),the(product_prod(X_a,X_b))) = the(product_prod(X_a,X_b))) # label(tsy_c_HOL_OThe_2_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2901 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,B),A_1) = hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3750_inverse__rat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2902 (all X_a (metric_space(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_4488_LIMSEQ__imp__Cauchy) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2903 (all X_a (linorder(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))) = ord_min(X_a))) # label(fact_4834_dual__max) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2904 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)))))) # label(fact_4669_scaleR__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2905 (all X_a (ring_div(X_a) -> (all A_1 all B all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_2011_mod__minus__cong) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2906 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))))) # label(fact_2691_real__root__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2907 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),zero_zero(X_a)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),zero_zero(real)),sequentially)))))) # label(fact_4450_LIMSEQ__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2908 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Z_1))) # label(fact_3225_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2909 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2549_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2910 (all Qr_2 all M all N all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_1)) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_2)) -> Qr_1 = Qr_2))) # label(fact_3098_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2911 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_714_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2912 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))))) # label(fact_1911_natceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2913 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> one_one(X_b) = hAPP(X_a,X_b,G,X_2))) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)))))) # label(fact_4148_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2914 (all X_a mlex_prod(X_a) = ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a))) # label(tsy_c_Wellfounded_Omlex__prod_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2915 (all X_1 all N_1 all Y_1 ((exists Q1 exists Q2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q1))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),N_1))) # label(fact_1183_nat__mod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2916 (all X_a (ab_group_add(X_a) -> (all A_1 all C all B all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D))))) # label(fact_722_add__diff__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2917 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_767_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2918 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_73_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2919 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C)) # label(fact_1090_div__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2920 (all J_2 all A_1 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5))))))) # label(fact_852_aux______2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2921 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all F_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),F_1))))) # label(fact_4772_setprod__1_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2922 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)),M))))) # label(fact_484_zcong__zdiff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2923 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c)),product_prod_case(X_a,X_b,X_c)) = product_prod_case(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2924 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,X)) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X))) # label(fact_2657_log__base__10__eq2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2925 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) # label(fact_3358_powr__divide2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2926 (all A_1 all B hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2750_complex__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2927 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),A_2)))))) # label(fact_4901_isCont__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2928 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))))) # label(fact_676_dvd__diffD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2929 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))))) # label(fact_4516_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2930 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2038_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2931 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))))) # label(fact_677_dvd__diffD1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2932 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4141_mono__SucI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2933 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),hAPP(int,int,uminus_uminus(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_2144_zcong__zminus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2934 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4023_summable__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2935 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_862_pinf_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2936 (all X_a all N hAPP(int,X_a,number_of_frac(X_a),N) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),N),one_one(int)))) # label(fact_3685_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2937 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2058_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2938 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1596_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2939 (all N_1 all Ma (hAPP(nat,real,real_1(nat),Ma) = hAPP(nat,real,real_1(nat),N_1) <-> N_1 = Ma)) # label(fact_2292_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2940 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,A_1)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) # label(fact_2639_Log_Olog__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2941 (all X_a all Y_3 ti(fun(X_a,bool),Y_3) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3)) # label(fact_3845_image__ident) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2942 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2))))) # label(fact_4114_Re_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2943 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)))))) # label(fact_1446_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2944 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)))) # label(fact_1390_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2945 (all X_a (abs_if(X_a) -> (all A_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2098_abs__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2946 (all X_a (dense_linorder(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2947 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2948 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int)))))) # label(fact_509_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2949 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(P_1)))) # label(fact_644_dvd_Oless__imp__triv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2950 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),I_1))) # label(fact_3428_zgcd__zdvd1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2951 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))))) # label(fact_4754_scaleR_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2952 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3375_powr__mono2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2953 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1813_mult__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2954 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_4939_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2955 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X))))),X))))) # label(fact_2006_best__division__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2956 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N)) # label(fact_2373_cos__npi) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2957 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4578_LIM__isCont__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2958 (all X_a all X_b all X_c all X_d all Y -(all A_4 all B_4 all C_4 all D_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3))))) # label(fact_3149_prod__cases4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2959 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2246_cos__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2960 (all X_a (archim1727834104eiling(X_a) -> zero_zero(int) = hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)))) # label(fact_2863_floor__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2961 (all M all K_4 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = ti(int,K_4) -> (exists S_1 exists T_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N)))))) # label(fact_3482_zgcd__ex__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2962 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,tan,X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2286_tan__half) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2963 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_758_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2964 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N)) # label(fact_3266_coprime__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2965 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (zero_zero(X_b) != hAPP(X_a,X_b,F,A_2) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),A_2))))))) # label(fact_4912_isCont__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2966 (all X_a all F all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3))) # label(fact_4246_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2967 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))))) # label(fact_3360_real__of__int__div4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2968 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))))) # label(fact_2895_one__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2969 (all X_a (real_div_algebra(X_a) -> (all X all A_1 (A_1 != zero_zero(real) -> (ti(X_a,X) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))))) # label(fact_4743_nonzero__inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2970 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,sin,X)) # label(fact_2376_sin__periodic) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2971 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K)))))) # label(fact_3814_DERIV__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2972 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C)))) # label(fact_4965_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2973 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_3795_Rat__induct__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2974 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)))))) # label(fact_3987_mult__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2975 (all K_4 all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)),M))),N)) # label(fact_1395_mod__mult__self4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2976 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4130_monoI2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2977 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)))))) # label(fact_3608_less__floor__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2978 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_579_add__leE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2979 (all Z hAPP(fun(real,bool),real,hilbert_Eps(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z)))),cos))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z)))),sin))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),pi)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi))))) = hAPP(complex,real,arg,Z)) # label(fact_3926_arg__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2980 (all X_a (semiring_div(X_a) -> (all Ma all K all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),Ma),N_1)))))))) # label(fact_947_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2981 (all X_a (linordered_idom(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_1849_abs__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2982 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2570_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2983 (all X hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) # label(fact_3343_real__of__int__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2984 (all X_a (number_ring(X_a) & field(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1734_divide__Numeral1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2985 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3992_Product__Type_Oprod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2986 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a))) # label(fact_13_zero__power2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2987 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_1548_order__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2988 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3044_prime__dvd__power__two) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2989 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),min_1),K_4)) # label(fact_2908_add__Min) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2990 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2991 (all X_a (archim1727834104eiling(X_a) -> zero_zero(int) = hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)))) # label(fact_3279_ceiling__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2992 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y))) # label(fact_2944_complex__cnj__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 2993 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))))) # label(fact_2328_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2994 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)))) # label(fact_4533_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2995 (all B all A_1 (A_1 != zero_zero(nat) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2)))) # label(fact_3313_bezout__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2996 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3388_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2997 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3749_floor__Fract) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2998 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (ti(int,K) = hAPP(nat,int,F,I_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)))))))) # label(fact_2009_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 2999 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M)))))) # label(fact_662_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3000 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_1573_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3001 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_549_mult__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3002 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3350_powr__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3003 (all Q_3 all R_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),hAPP(int,int,uminus_uminus(int),R_4)) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) # label(fact_3072_negateSnd__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3004 (all R_4 all X hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(complex,complex,cnj,X))) # label(fact_4692_cnj_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3005 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> N = zero_zero(nat))) # label(fact_544_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3006 (all X_a all X_b all S all R_3 ((all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_3)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S)))) <-> ti(fun(product_prod(X_a,X_b),bool),S) = ti(fun(product_prod(X_a,X_b),bool),R_3))) # label(fact_4338_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3007 (all A_2 all B_1 all Ma (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),Ma) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3473_Bnor__mem__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3008 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hAPP(X_a,X_b,F,A_2) != zero_zero(X_b) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),A_2))))))) # label(fact_4911_isCont__sgn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3009 (all X_a (real_normed_field(X_a) & field_inverse_zero(X_a) -> (all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1783_norm__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3010 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),A_3))))))) # label(fact_4440_tendsto__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3011 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_927_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3012 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4101_mult__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3013 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y)) -> (exists X_2 (Y = hAPP(real,real,exp(real),X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y),one_one(real)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))))) # label(fact_2628_lemma__exp__total) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3014 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = ti(X_a,Sa))))) # label(fact_4089_sums__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3015 (all N_1 all Ma (hBOOL(hAPP(int,bool,nat_is_nat,Ma)) -> (hBOOL(hAPP(int,bool,nat_is_nat,N_1)) -> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(int,nat,nat_1,Ma)),hAPP(int,nat,nat_1,N_1))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Ma),N_1)))) # label(fact_4839_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3016 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_1559_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3017 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4597_Im_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3018 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> N = hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_1384_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3019 (all X_a all X_b all A_1 all B ti(X_a,A_1) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B))) # label(fact_3140_fst__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3020 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1))))) # label(fact_2181_neg__even__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3021 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2099_abs__of__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3022 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))))) # label(fact_1875_natfloor__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3023 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_389_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3024 (all X_a (linordered_idom(X_a) -> (all L_4 all K_4 (hAPP(X_a,X_a,abs_abs(X_a),K_4) = hAPP(X_a,X_a,abs_abs(X_a),L_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_4),K_4)))))) # label(fact_1847_dvd__if__abs__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3025 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2271_arccos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3026 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))) # label(fact_3629_Bnor__in__RsetR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3027 (all X_a (ab_semigroup_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3028 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3029 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)))))) # label(fact_4455_tendsto__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3030 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))) # label(fact_1852_abs__idempotent) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3031 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2430_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3032 (all I_1 all U all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),U)),K_4)) # label(fact_745_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3033 (all X all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),P_5)))))) # label(fact_3070_prime__coprime__lt) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3034 (all X_a (number_semiring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_145_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3035 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1))))) # label(fact_1902_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3036 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_788_add__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3037 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_1374_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3038 (all X_a (linordered_idom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_104_zero__le__power2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3039 (all R_4 all A_1 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2385_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3040 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2)))) # label(fact_1919_equalityI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3041 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1))))) # label(fact_3989_suminf__mult2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3042 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),one_one(int)) = one_one(int)) # label(fact_3433_zgcd__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3043 (all X_a (comm_ring(X_a) & monoid_mult(X_a) -> (all X_1 all N_1 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Y_1)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))))))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3044 (all A_2 all B_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B_1))))) # label(fact_3052_prime__divprod__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3045 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,N)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,N)))))) # label(fact_471_number__of1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3046 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_575_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3047 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_163_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3048 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_4),B_4))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1179_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3049 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_260_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3050 (all T_1 order(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3051 (all Z_1 all W hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W)))) # label(fact_3870_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3052 (all S ((all M_2 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3656_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3053 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))))))) # label(fact_276_power__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3054 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2572_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3055 (all X_a (power(X_a) -> (all A_1 one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),zero_zero(nat))))) # label(fact_415_power__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3056 (all P_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,abs_abs(rat),P_4)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),abs_abs(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4030_rat__abs__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3057 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,sin,X))),one_one(real)))) # label(fact_2319_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3058 zero_zero(int) = t -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) # label(fact_4_calculation_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3059 (all X_a (idom(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2) | ti(X_a,A_2) = ti(X_a,B_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2))))) # label(fact_2034_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3060 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4550_mult__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3061 (all D_1 all K all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> ((exists I_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2) = D_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),K)))))) # label(fact_3068_divides__primepow) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3062 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))))) # label(fact_333_dvd__triv__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3063 (all N all M all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),M)) = one_one(nat))) # label(fact_3216_coprime__exp2__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3064 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)))) # label(fact_4243_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3065 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_43_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3066 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1331_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3067 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2003_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3068 (all A_1 all B ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))) # label(fact_1077_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3069 (all X_a all G all A_3 hAPP(complex,real,re,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),A_3)) # label(fact_4249_Re_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3070 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))))) # label(fact_641_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3071 (all V_3 all K_4 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))),K_4)))) # label(fact_232_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3072 (all N (hAPP(int,int,number_number_of(int),min_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N))) # label(fact_606_neg__one__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3073 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_1033_pos__mod__conj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3074 (all Ma all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> (hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))))) # label(fact_2414_even__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3075 (all N all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),B) = one_one(int))) # label(fact_3449_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3076 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,im,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2983_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3077 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> N = M))) # label(fact_1231_less__SucE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3078 (all A_1 ((A_1 = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),A_1) = zero_zero(real)) & (zero_zero(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,sgn_sgn(real),A_1) = one_one(real)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),A_1))))) # label(fact_2228_sgn__real__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3079 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> (exists N_2 ti(int,Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_1220_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3080 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_2589_exp__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3081 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_582_le__square) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3082 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X_1),Y_1))))) # label(fact_2419_even__product__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3083 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_819_add__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3084 (all X_a (real_normed_vector(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),L),hAPP(nat,X_a,F,zero_zero(nat))))))))) # label(fact_4095_sums__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3085 (all X_a all A_2 all F all V_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_4157_nat__rec__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3086 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_331_power__commutes) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3087 (all X_a (ordered_ab_group_add(X_a) -> ord_gr676655987ssThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3088 (all K_4 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),K_4)),X))))) # label(fact_1013_int__div__less__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3089 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1714_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3090 (all N all I_1 ((I_1 != zero_zero(code_code_numeral) -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),I_1),one_one(code_code_numeral))),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N)) & (zero_zero(code_code_numeral) = I_1 -> N = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N)))) # label(fact_1487_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3091 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3))))) # label(fact_3797_mlex__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3092 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,sin,X_2)) # label(fact_3969_lemma__sin__ext) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3093 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))))))) # label(fact_1136_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3094 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_4 all B_4 all C_4 all D_3 all E all F_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3))))))) # label(fact_3151_prod__cases6) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3095 (all Y all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> Y = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),Y))))) # label(fact_3407_log__powr__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3096 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1993_arctan__ubound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3097 (all X all Y hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4371_abs__gcd__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3098 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Ys) != hAPP(list(X_a),nat,size_size(list(X_a)),Xs) -> Ys != Xs)) # label(fact_3557_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3099 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),one_one(real))))) # label(fact_1632_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3100 (all Ma all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X_1) = zero_zero(int))) # label(fact_1011_StandardRes__eq__zcong) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3101 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))))))) # label(fact_1676_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3102 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,P_1,I_2))))) & (ti(int,K) = zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))))) # label(fact_1055_split__zdiv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3103 (all X_a (dvd(X_a) & linorder(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_868_pinf_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3104 (all X_a (real_vector(X_a) -> scaleR_scaleR(X_a) = ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3105 (all X_a (power(X_a) -> (all M all N ((zero_zero(nat) != N -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N)) & (zero_zero(nat) = N -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N)))))) # label(fact_735_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3106 (all I all P_1 all K (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_2843_int__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3107 (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(X_a,X_a,sgn_sgn(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2211_sgn__greater) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3108 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_346_le__imp__power__dvd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3109 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3508_dist__triangle__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3110 (all A_1 all B hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) # label(fact_3116_mod__int__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3111 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)))) # label(fact_3445_zgcd__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3112 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4))))))) # label(fact_3927_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3113 (all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = one_one(nat)))) # label(fact_1535_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3114 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4857_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3115 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,hAPP(int,int,uminus_uminus(int),K_4)))) # label(fact_2906_minus__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3116 (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (X_1 != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2716_DERIV__odd__real__root) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3117 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),L)) # label(fact_4401_gcd__code__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3118 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_1557_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3119 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2445_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3120 (all K_4 hAPP(int,int,bit1,K_4) != pls) # label(fact_116_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3121 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4747_scaleR_OLIM__left__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3122 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),D_2))))))) # label(fact_3856_DERIV__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3123 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_779_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3124 (all X_b all X_a all Q_1 all Q_2 all P_1 all P_4 (hBOOL(hAPP(X_a,bool,P_1,P_4)) -> (hBOOL(hAPP(X_b,bool,Q_1,Q_2)) -> hBOOL(hAPP(X_b,bool,Q_1,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),P_4),Q_2)))) & hBOOL(hAPP(X_a,bool,P_1,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),P_4),Q_2))))))) # label(fact_3124_conjI__realizer) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3125 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_375_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3126 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))),one_one(int)),P_5)))))) # label(fact_811_inv__is__inv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3127 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> ti(X_a,B) = ti(X_a,A_1))))))) # label(fact_1373_power__inject__base) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3128 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2470_lemma__even__div2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3129 (all D_1 all A_2 all B_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1)) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),B_1) & one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),A_2))) # label(fact_3267_coprime__mul__eq__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3130 (all X_a (metric_space(X_a) -> (all X2_1 all X1_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X2_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3521_dist__triangle__half__l) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3131 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4714_scaleR__left__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3132 (all X_a (monoid_mult(X_a) & linordered_ring(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_2433_zero__le__even__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3133 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3495_Bseq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3134 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> one_one(real) = hAPP(real,real,sgn_sgn(real),X))) # label(fact_2221_real__sgn__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3135 (all Ma all K all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K),N_1) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma))))) # label(fact_3289_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3136 (all X_a ti(fun(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a))),nat_rec(X_a)) = nat_rec(X_a)) # label(tsy_c_Nat_Onat_Onat__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3137 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)))))) # label(fact_1709_divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.74 3138 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_1362_exp__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3139 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1821_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3140 (all X_a (real_normed_field(X_a) -> (all C_1 all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),X_1),C_1))))) # label(fact_2636_DERIV__cmult__Id) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3141 (all B all D all A_1 all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),C),D)))))) # label(fact_3233_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3142 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1816_card__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3143 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all W_1 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (zero_zero(X_a) = ti(X_a,C_1) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),W_1)) & (zero_zero(X_a) != ti(X_a,C_1) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))))) # label(fact_1724_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3144 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_3994_summable__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3145 (all X_a all X_b in_rel(X_a,X_b) = ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b))) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3146 (all Z_1 hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_2991_complex__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3147 (all X0 all F all R_3 ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X_2)))))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X0),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),suc)))),X0),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X0))))))))) # label(fact_4036_DERIV__power__series_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3148 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1739_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3149 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),C_1)),X_3)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C_1)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))))) # label(fact_4263_setsum__const2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3150 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)) = inverse_divide(X_a))) # label(tsy_c_Fields_Oinverse__class_Odivide_0_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3151 (all X_a (real_normed_algebra(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_4674_mult_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3152 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N)))))) # label(fact_1880_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3153 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_799_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3154 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1744_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3155 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2))))))) # label(fact_4079_sums__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3156 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1))))))) # label(fact_1605_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3157 (all Z_1 all W (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),Z_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W)))) # label(fact_656_real__le__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3158 (all A_1 all C hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),C) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),A_1)) # label(fact_3741_eq__rat_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3159 (all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,I_1)),N) = hAPP(nat,nat,hAPP(int,fun(nat,nat),nat_aux,I_1),N)) # label(fact_1170_nat__aux__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3160 (all N all D (ti(int,D) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),D)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),D))))) # label(fact_3395_real__of__int__div) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3161 (all X_a (linordered_semidom(X_a) -> (all X all Y (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> ti(X_a,Y) = ti(X_a,X))))))) # label(fact_102_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3162 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_4)) & (all M_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M_2),P_4)) -> one_one(int) = ti(int,M_2) | ti(int,P_4) = ti(int,M_2))) <-> hBOOL(hAPP(int,bool,zprime,P_4)))) # label(fact_273_zprime__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3163 (all V_1 all V_2 (hAPP(int,nat,number_number_of(nat),V_1) = hAPP(int,nat,number_number_of(nat),V_2) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> zero_zero(int) = hAPP(int,int,number_number_of(int),V_1)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> ti(int,V_1) = ti(int,V_2))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))))) # label(fact_1511_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3164 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),min_1)),B))) # label(fact_1064_zmod__minus1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3165 (all Z_4 all Z_1 all W_3 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)))))) # label(fact_56_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3166 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> (all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))))))) # label(fact_4644_LIM__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3167 (all X_a all X_b all X_1 all Y_1 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1))))) # label(fact_4780_Eps__split__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3168 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))))) # label(fact_1070_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3169 (all X (zero_zero(real) != hAPP(real,real,cos,X) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2627_tan__sec) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3170 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))))) # label(fact_1195_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3171 (all X_a (number_semiring(X_a) -> (all X all Y hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))))) # label(fact_169_power2__sum) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3172 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2693_real__root__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3173 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))) -> (zero_zero(X_a) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))))))) # label(fact_2548_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3174 (all Ma all N_1 (N_1 != zero_zero(nat) & zero_zero(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),N_1) = zero_zero(nat))) # label(fact_726_nat__power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3175 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) = hAPP(real,real,sin,X)) # label(fact_2392_sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3176 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3883_DERIV__cos__cos__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3177 (all X_1 all Y_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))))) # label(fact_3759_real__less__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3178 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))))) # label(fact_763_inv__inv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3179 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (ti(X_a,B_1) = ti(X_a,A_2) <-> ti(X_a,C_1) = ti(X_a,D_1)))))) # label(fact_773_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3180 (all A_1 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1))))) # label(fact_3058_prime__dvd__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3181 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U_1)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)) # label(fact_4542_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3182 (all X all Y (zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3276_gcd__non__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3183 (all X_a (real_n2089651433ebra_1(X_a) -> one_one(real) = hAPP(X_a,real,norm_norm(X_a),one_one(X_a)))) # label(fact_1781_norm__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3184 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_3))))) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3185 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))))))) # label(fact_435_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3186 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2489_fact__gt__zero__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3187 (all B all A_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (zero_zero(int) = ti(int,A_1) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) & (zero_zero(int) != ti(int,A_1) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))))))) # label(fact_3045_divmod__int__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3188 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3430_zgcd__zmult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3189 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_775_add__0__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3190 (all X_a (linordered_idom(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D)))))))) # label(fact_1866_abs__mult__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3191 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1600_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3192 (all X_a (comm_ring_1(X_a) -> (all X all N ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_2423_neg__power__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3193 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1))))))) # label(fact_4009_summable__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3194 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))) # label(fact_2074_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3195 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))))) # label(fact_78_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3196 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all C_1 all W_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_1747_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3197 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1))))))) # label(fact_1554_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3198 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_828_wset__mem__inv__mem) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3199 (all X_b all X_a all P all Q ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3200 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),X_1)))))) # label(fact_4920_isCont__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3201 (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2))))))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3202 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),X)))) # label(fact_4686_scaleR__minus__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3203 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),N))) # label(fact_3213_gcd__dvd2__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3204 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K_4))))) # label(fact_697_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3205 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2216_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3206 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1716_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3207 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))))))) # label(fact_103_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3208 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_646_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3209 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> R_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_3102_mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3210 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),one_one(nat)) = one_one(nat)) # label(fact_3251_gcd__1__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3211 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))))) # label(fact_1283_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3212 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),zero_zero(code_code_numeral))) # label(fact_3549_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3213 (all X all Y all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z_1))) # label(fact_98_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3214 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1))))) = ti(int,N_1))) # label(fact_3808_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3215 (all Ma all N_1 ((exists K_1 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_571_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3216 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),N))) # label(fact_1119_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3217 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2040_number__of__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3218 (all X_a (ring_1(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_3587_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3219 (all X_a all X_c all X_b all F all X_1 all Y_1 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),hAPP(X_c,X_b,F,Y_1)) = hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),hAPP(X_c,product_prod(X_a,X_c),hAPP(X_a,fun(X_c,product_prod(X_a,X_c)),product_Pair(X_a,X_c),X_1),Y_1))) # label(fact_4064_apsnd__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3220 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))))))) # label(fact_3302_ceiling__le__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3221 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))))) # label(fact_2184_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3222 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))) -> zero_zero(nat) = one_one(nat)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)))) # label(fact_1830_card_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3223 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2313_sin__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3224 (all X_a (linordered_idom(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_2202_sgn__0__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3225 (all L (pls = ti(int,L) <-> pls = hAPP(int,int,bit0,L))) # label(fact_121_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3226 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1741_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3227 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> Y = hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2403_arcsin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3228 (all M all N hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)),N)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) # label(fact_922_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3229 (all Code_numeral_4 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_4)) # label(fact_2946_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3230 (all N all A_1 all B all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),A_1)))))) # label(fact_201_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3231 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_987_neg__mod__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3232 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> N = M))) # label(fact_526_le__antisym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3233 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5))))) # label(fact_4717_scaleR_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3234 (all V all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))) # label(fact_25_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3235 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1))))) # label(fact_4433_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3236 (all P_1 ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))))) # label(fact_1107_ex__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3237 (all X_5 all Y_4 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(real,real,cos,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2251_cos__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3238 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X)) # label(fact_1640_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3239 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))))))) # label(fact_1700_divide__le__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3240 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),B)))) # label(fact_4398_gcd__le2__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3241 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_1598_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3242 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(int,real,number_number_of(real),min_1)),X)))) # label(fact_4724_scaleR__minus1__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3243 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sin),X_1))) # label(fact_4890_isCont__sin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3244 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y))) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2323_sin__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3245 (all Z_1 hAPP(int,real,ring_1_of_int(real),Z_1) = hAPP(complex,real,re,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3571_complex__Re__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3246 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N)) # label(fact_4961_max__0L) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3247 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all L all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4879_isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3248 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)))) # label(fact_529_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3249 (all W hAPP(int,int,ring_1_of_int(int),W) = hAPP(int,int,number_number_of(int),W)) # label(fact_3583_int__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3250 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)))) # label(fact_1957_equalityD2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3251 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_1210_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3252 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2933_complex__cnj__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3253 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)))) # label(fact_1907_natfloor__add__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3254 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z_1))))) # label(fact_151_add__number__of__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3255 (all A_1 (hBOOL(hAPP(nat,bool,prime,A_1)) -> hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),A_1))))) # label(fact_3063_prime__impl__zprime__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3256 (all X_b all X_a all F all A_3 all B_2 (ti(fun(X_a,bool),B_2) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3) -> hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) # label(fact_3640_image__Pow__surj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3257 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_382_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3258 (all S ((exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_4318_finite__nat__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3259 (all P_5 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,sgn_sgn(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(rat,product_prod(int,int),quotient_of,P_5)))),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,sgn_sgn(rat),P_5))) # label(fact_3719_rat__sgn__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3260 (all C all A_1 all B (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (C = B -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_645_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3261 (all W hAPP(int,rat,hAPP(int,fun(int,rat),fract,W),one_one(int)) = hAPP(int,rat,number_number_of(rat),W)) # label(fact_3747_rat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3262 (all X_a (number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),ring_1_Ints(X_a)))))) # label(fact_3843_Ints__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3263 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4)) # label(fact_581_add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3264 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) = hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3265 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1034_pos__mod__sign) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3266 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) # label(fact_2092_minus__real__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3267 (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,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> zero_zero(X_a) != ti(X_a,A_2))))) # label(fact_11_zero__less__power2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3268 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),X))) # label(fact_2615_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3269 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> ti(X_a,L_2) = hAPP(fun(nat,X_a),X_a,lim(X_a),X_3))))) # label(fact_4494_limI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3270 (all X_a (ring_1(X_a) -> (all P_1 all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> ((all Z_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))) -> hBOOL(hAPP(X_a,bool,P_1,Q_2))))))) # label(fact_4415_Ints__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3271 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,tan,X)) # label(fact_2266_tan__periodic) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3272 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_a,bool)),isCont(X_a,X_b)) = isCont(X_a,X_b))) # label(tsy_c_Lim_OisCont_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3273 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2)),sequentially)))) # label(fact_4512_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3274 (all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4073_suminf__0__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3275 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2134_negative__zless) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3276 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)))))) # label(fact_4470_LIMSEQ__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3277 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4370_gcd__red__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3278 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,cos,X) = zero_zero(real) -> (exists N_2 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2))))))) # label(fact_2476_cos__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3279 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)))))) # label(fact_4880_isCont__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3280 (all N hAPP(nat,nat,fact_fact(nat),N) != zero_zero(nat)) # label(fact_2483_fact__nonzero__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3281 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1))))) # label(fact_342_one__dvd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3282 (all Z_1 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W)))) # label(fact_24_zle__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3283 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3197_dvd__fact__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.75 3284 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3353_powr__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3285 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2534_abs__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3286 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,suc,N) = M))) # label(fact_1248_le__SucE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3287 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3288 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2960_compl__less__swap2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3289 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4))))))) # label(fact_4604_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3290 (all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),U)))) # label(fact_1766_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3291 (all K_4 all L_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4)))) # label(fact_2722_pdivmod__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3292 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_4760_scaleR__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3293 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),B),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Q_3),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)))))))) # label(fact_3096_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3294 (all X hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),zero_zero(nat))) # label(fact_3035_bezw__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3295 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> zero_zero(X_a) = hAPP(real,X_a,of_real(X_a),zero_zero(real)))) # label(fact_2782_of__real_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3296 (all X_b all X_a (real_vector(X_a) -> (all G all A_3 all X_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,real),fun(X_b,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(X_b,real),fun(X_b,fun(X_a,X_a))),combb(real,fun(X_a,X_a),X_b),scaleR_scaleR(X_a)),G)),X_1)),A_3) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3)),X_1)))) # label(fact_4731_scaleR__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3297 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),Ma)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,fact_fact(nat),Ma)),hAPP(nat,nat,fact_fact(nat),N_1)))) # label(fact_4612_fact__div__fact) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3298 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4865_vanishesI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3299 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),A_2))))) # label(fact_4897_divide_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3300 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_747_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3301 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_1333_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3302 (all X_a (metric_space(X_a) -> (all X all Y -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),zero_zero(real)))))) # label(fact_3515_dist__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3303 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)))) # label(fact_1139_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3304 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_370_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3305 (all M all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M))))) # label(fact_424_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3306 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))))))))) # label(fact_488_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3307 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all R_4 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X))))) # label(fact_4676_mult__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3308 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_960_zcong__zmod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3309 (all X_1 all A_2 (zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),hAPP(real,real,uminus_uminus(real),A_2)) <-> X_1 = A_2)) # label(fact_2088_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3310 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)) = ord_min(X_a))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3311 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_318_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3312 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) = zero_zero(X_a))))) # label(fact_776_double__zero__sym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3313 (all A_1 -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))))) # label(fact_893_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3314 (all X_a all X_b all X_1 all Y_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1)))) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)) # label(fact_4142_The__split__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3315 (all X_a (division_ring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)) = inverse_divide(X_a))) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3316 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2))))))) # label(fact_4667_scaleR__right_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3317 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4648_bset_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3318 (all P_1 all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((N_1 = Ma -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma)))))) # label(fact_520_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3319 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2968_cnj_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3320 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_886_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3321 (all X_a (linorder(X_a) & number(X_a) -> (all V_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_50_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3322 (all Q_3 ((Q_3 = zero_zero(rat) -> zero_zero(rat) = hAPP(rat,rat,sgn_sgn(rat),Q_3)) & (zero_zero(rat) != Q_3 -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> one_one(rat) = hAPP(rat,rat,sgn_sgn(rat),Q_3)) & (-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(rat,rat,sgn_sgn(rat),Q_3))))) # label(fact_3716_sgn__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3323 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_2512_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3324 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),X)) # label(fact_4372_gcd__idem__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3325 (all Y all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = Y)) # label(fact_3237_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3326 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1266_even__difference) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3327 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4225_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3328 (all X_a all X_b product_Pair(X_a,X_b) = ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b))) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3329 (all X_a all X_b all B_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> -(all X_2 (ti(X_a,B_1) = hAPP(X_b,X_a,F,X_2) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))))) # label(fact_3964_imageE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3330 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1))))) # label(fact_3436_zgcd__greatest__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3331 (all N all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),A_1)))))) # label(fact_3069_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3332 (all B all A_1 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1))))) # label(fact_350_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3333 (all N hAPP(int,int,uminus_uminus(int),N) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),N)))) # label(fact_3373_floor__minus__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3334 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S)))))) # label(fact_3963_setprod__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3335 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_824_add__less__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3336 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = ti(X_a,B)))) # label(fact_2048_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3337 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(Q) | -hBOOL(P))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3338 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y))))) # label(fact_1199_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3339 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) = ti(fun(X_a,bool),A_3)) # label(fact_2193_double__complement) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3340 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))))) # label(fact_3837_Ints__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3341 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,W_1)),zero_zero(int))))) # label(fact_157_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3342 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) <-> Y_1 = X_1))) # label(fact_2672_real__root__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3343 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1089_mod__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3344 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) | zero_zero(nat) = N)) # label(fact_872_divides__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3345 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_3848_cnj_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3346 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_1413_Suc__pred_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3347 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4)) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> hAPP(nat,nat,suc,J_1) != K_4)))) # label(fact_1543_Suc__lessE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3348 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int)))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1))) # label(fact_3676_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3349 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1244_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3350 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)))))) # label(fact_4453_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3351 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1634_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3352 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_146_number__of__Pls) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3353 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))) # label(fact_3374_ceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3354 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))))) # label(fact_2793_of__real__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3355 (all X_a (ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a))))) # label(fact_731_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3356 (all A_1 all B all C all D hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D))) # label(fact_2747_complex__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3357 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2836_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3358 (all N all M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4)) -> (exists M_2 M_4 = hAPP(nat,nat,suc,M_2)))) # label(fact_1524_Suc__le__D) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3359 (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_516_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3360 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> zero_zero(nat) != N_1)) # label(fact_537_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3361 (all X_a (topological_space(X_a) -> (all L all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),X_1),sequentially)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),L)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),L))),X_1),sequentially))))))) # label(fact_4480_LIMSEQ__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3362 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4982_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3363 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd))))) # label(fact_970_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3364 (all X_a all F all A_3 all N_1 (hAPP(nat,nat,suc,N_1) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) -> (exists X_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)))))) # label(fact_4301_setsum__SucD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3365 (all X_a (real_normed_vector(X_a) -> (all G all F all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially))))))) # label(fact_4447_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3366 (all X_a (real_normed_vector(X_a) -> ti(fun(fun(nat,X_a),bool),bseq(X_a)) = bseq(X_a))) # label(tsy_c_SEQ_OBseq_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3367 (all Code_numeral_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,code_c271388182l_size,Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(code_code_numeral,nat,code_c271388182l_size,hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2))) # label(fact_2926_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3368 (all X_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4306_pos__summable) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3369 (all N all A_1 hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))),A_1)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)))) # label(fact_3034_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3370 (all V_1 all K all A_2 all B_1 (B_1 != A_2 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),V_1),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,V_1,A_2)),hAPP(real,real,V_1,B_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,V_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_2),B_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2658_DERIV__const__average) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3371 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y))) # label(fact_4373_gcd__abs__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3372 (all X_b all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))))) # label(fact_3643_card__image__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3373 (all X_1 -(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1277_even__odd__conj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3374 (all X_a (comm_monoid_add(X_a) & power(X_a) -> (all X_1 all Y_1 all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4175_lemma__realpow__rev__sumr) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3375 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))) & hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4070_summable__le2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3376 (all X_1 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,X_1)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),X_1)),N_1))))) # label(fact_4162_Maclaurin__sin__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3377 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C)) # label(fact_1080_div__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3378 (all W all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2))) # label(fact_482_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3379 (all N all M all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N))))) # label(fact_3408_lemma__floor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3380 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4910_mult_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3381 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))))) # label(fact_1888_natceiling__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3382 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_1541_order__refl) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3383 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (zero_zero(X_a) != ti(X_a,A_2) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),sequentially))))))) # label(fact_4483_LIMSEQ__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3384 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))))) # label(fact_3385_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3385 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),X) = X) # label(fact_3219_gcd__idem__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3386 (all X_a (semiring_div(X_a) -> (all K_4 all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M))))))) # label(fact_950_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3387 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2010_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3388 (all Ma all N_1 (one_one(nat) = N_1 & one_one(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = one_one(nat))) # label(fact_588_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3389 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)),P_5))))))) # label(fact_1079_Euler__part3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3390 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)))) # label(fact_1965_DiffD2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3391 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(int,int,number_number_of(int),min_1)),P_5))))))) # label(fact_1076_Euler__part1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3392 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = M -> zero_zero(nat) = M | N = one_one(nat))) # label(fact_600_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3393 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1704_frac__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3394 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_3339_real__of__int__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3395 (all Ma (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1153_mod2__gr__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3396 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1898_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3397 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_1074_mod__div__decomp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3398 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & Y = hAPP(real,real,tan,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))))) # label(fact_2282_tan__total__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3399 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)))))) # label(fact_3602_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3400 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N)))) # label(fact_2876_coprime__minus1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3401 (all X hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2980_Im_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3402 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1553_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3403 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))))) # label(fact_874_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3404 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_4752_exp__converges) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3405 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3813_bdd__int__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3406 (all X_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),X_1))))) # label(fact_4290_suminf__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3407 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))))) # label(fact_1257_Parity_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3408 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),Y)))) # label(fact_3446_zgcd__geq__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3409 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))),zero_zero(X_a)))))) # label(fact_2096_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3410 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3411 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4796_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3412 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))) <-> ti(X_a,Y_1) != ti(X_a,X_1))))) # label(fact_3514_dist__nz) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3413 (all B all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))) # label(fact_2647_log__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3414 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X))))) # label(fact_1974_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3415 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1834_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3416 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1642_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3417 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))) # label(fact_669_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3418 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),B_1)) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),B_1)))))))) # label(fact_1762_Sup__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3419 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))),X))))) # label(fact_2629_reals__Archimedean) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3420 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1585_order__less__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3421 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_4848_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3422 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_538_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3423 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> (exists N_2 exists F_3 ti(fun(X_a,bool),A_3) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))))) # label(fact_4127_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3424 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> summable(X_a) = ti(fun(fun(nat,X_a),bool),summable(X_a)))) # label(tsy_c_Series_Osummable_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3425 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_912_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3426 (all X hAPP(real,nat,natfloor,X) = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))) # label(fact_2860_natfloor__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3427 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,int,uminus_uminus(int),B_1))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (ti(int,A_2) = zero_zero(int) | ti(int,B_1) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1)) & (-(ti(int,A_2) = zero_zero(int) | ti(int,B_1) = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1))))))) # label(fact_3919_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3428 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),B_1)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat)))))) # label(fact_3794_Fract__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3429 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all B_2 all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (B_2 = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I)),B_2))))))))) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3430 (all X_a (real_algebra_1(X_a) -> of_real(X_a) = ti(fun(real,X_a),of_real(X_a)))) # label(tsy_c_RealVector_Oof__real_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3431 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3880_card__bdd__int__set__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3432 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_771_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3433 (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_1592_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3434 (all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))) -> -(all M_2 all N_2 (zero_zero(nat) != N_2 -> (hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),M_2)),hAPP(nat,real,real_1(nat),N_2)) = hAPP(real,real,abs_abs(real),X_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_2),N_2) != one_one(nat)))))) # label(fact_3679_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3435 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_1083_div__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3436 (all X_a (comm_semiring_1(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))) # label(fact_336_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3437 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))) = hAPP(int,nat,phi,P_5))) # label(fact_1173_phi__prime) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3438 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(int,int,fact_fact(int),X)) = hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)))) # label(fact_3199_transfer__nat__int__factorial) # label(axiom) # label(non_clause). [assumption]. 7.75/7.76 3439 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,uminus_uminus(rat),P_4))) # label(fact_4028_rat__uminus__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3440 (all X_a all C_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> (ti(X_a,C_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) -> hBOOL(hAPP(X_a,bool,P_1,C_1))))) # label(fact_4778_exE__some) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3441 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))))) # label(fact_26_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3442 (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) <-> (all J_1 exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,X_3,M_2)),hAPP(nat,real,X_3,N_2)))),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,J_1))))))))))) # label(fact_3314_Cauchy__iff2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3443 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3444 (all X hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)) = hAPP(real,real,abs_abs(real),X)) # label(fact_1872_real__sqrt__abs2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3445 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4935_max__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3446 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))))) # label(fact_1193_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3447 (all X_a (comm_semiring_0(X_a) & monoid_mult(X_a) -> (all X_1 all Y_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4174_lemma__realpow__diff__sumr) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3448 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1495_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3449 (all X_a (ring_1(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_2121_power__minus1__even) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3450 (all X_a all Q_1 all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4337_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3451 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2))))) # label(fact_3790_zero__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3452 (all Z all Ma ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> zero_zero(nat) = Ma) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,Z)),Ma)))) # label(fact_1449_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3453 (all A_2 all B_1 ((all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) <-> D_3 = one_one(nat))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3265_coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3454 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))))) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y))) # label(fact_3114_bezw__non__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3455 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) = hAPP(real,real,arctan,X)) # label(fact_1831_arctan__half) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3456 (all D_2 all X_1 (zero_zero(real) != X_1 -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D_2) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),D_2)))))) # label(fact_2655_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3457 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_649_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3458 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,hAPP(real,real,G,X_1))),Ma))))) # label(fact_3859_DERIV__fun__sin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3459 (all X_a all X_b combk(X_a,X_b) = ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3460 (all X_a all A_3 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)),X_2)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))))) # label(fact_4871_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3461 (all X all M hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2365_cos__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3462 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),P_4),zOdd)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1050_Euler_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3463 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4436_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3464 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all B_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B_1),X_1) <-> ti(X_a,X_1) = zero_zero(X_a) | A_2 = B_1)))) # label(fact_4704_scaleR__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3465 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3774_rat__number__expand_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3466 (all J all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),P_4)) -> hBOOL(hAPP(nat,bool,P_1,J))))))) # label(fact_1481_mod__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3467 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B)))) # label(fact_906_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3468 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1551_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3469 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),F),A_3)))))) # label(fact_4305_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3470 (all Ma all K all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> ((exists S_1 exists T_4 hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_1),T_4)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,Ma),N_1)) <-> ti(int,K) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1)))) # label(fact_3475_xzgcd__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3471 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4805_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3472 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3131_Bolzano__bisect__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3473 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_4110_nat__case__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3474 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = one_one(X_a))))) # label(fact_2223_sgn__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3475 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),hAPP(int,fun(int,bool),norRRset,Ma))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),Ma)))))) # label(fact_4156_aux__some) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3476 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3477 (all Real1 all Real2 all Real1_2 all Real2_2 (Real2 = Real2_2 & Real1_2 = Real1 <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_2),Real2_2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2))) # label(fact_2739_complex_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3478 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_1677_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3479 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M))))) # label(fact_670_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3480 (all Y_1 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3916_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3481 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1)) = hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1))) # label(fact_3169_Re__rcis) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3482 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4461_LIMSEQ__Suc__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3483 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_327_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3484 (all M all N (ti(int,N) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,M),N)),one_one(rat)))) # label(fact_3789_Fract__add__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3485 (all X_a (comm_ring_1(X_a) -> (all X ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = one_one(X_a)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))))))) # label(fact_2437_minus__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3486 (all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1169_mod__exhaust__less__4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3487 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))))) # label(fact_1360_exp__mono__lt) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3488 (all X_a (order(X_a) -> ord_atLeastAtMost(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastAtMost(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3489 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),M)) | M = N | M = zero_zero(nat))) # label(fact_610_divides__cases) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3490 (all X_a (linord581940658strict(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))))))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3491 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> zero_zero(X_a) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_2)),A_2))))) # label(fact_3907_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3492 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))))) # label(fact_2429_even__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3493 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> zero_zero(X_a) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))))) # label(fact_3968_suminf__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3494 (all X_a (sgn_div_norm(X_a) -> scaleR_scaleR(X_a) = ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3495 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3855_Bseq__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3496 (all M all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_2311_real__of__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3497 (all X_1 all Y_1 (Y_1 = hAPP(real,real,uminus_uminus(real),X_1) <-> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1) = zero_zero(real))) # label(fact_2089_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3498 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1962_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3499 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),min_1) = hAPP(int,int,succ,K_4)) # label(fact_1530_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3500 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3501 (all X_a all X_b all X_c all Y -(all A_4 all B_4 all C_4 hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4)) != ti(product_prod(X_a,product_prod(X_b,X_c)),Y))) # label(fact_3147_prod__cases3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3502 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) # label(fact_2192_Compl__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3503 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))))) # label(fact_572_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3504 (all A_1 all B all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3))) # label(fact_3758_normalize__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3505 (all Z (hAPP(int,int,abs_abs(int),Z) = one_one(int) <-> one_one(int) = ti(int,Z) | ti(int,Z) = hAPP(int,int,number_number_of(int),min_1))) # label(fact_1943_abs__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3506 (all K (min_1 = hAPP(int,int,bit1,K) <-> ti(int,K) = min_1)) # label(fact_285_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3507 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)))))) # label(fact_2650_log__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3508 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))) # label(fact_2103_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3509 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3611_le__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3510 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_1348_zdiv__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3511 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2495_of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3512 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))) # label(fact_4543_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3513 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4986_le__maxI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3514 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all B_1 all C_1 all W_1 (hAPP(int,X_a,number_number_of(X_a),W_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) <-> (ti(X_a,C_1) = zero_zero(X_a) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)) & (zero_zero(X_a) != ti(X_a,C_1) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))))) # label(fact_1725_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3515 (all X_a (dist_norm(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3503_dist__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3516 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W_1)))))) # label(fact_1506_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3517 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))))))) # label(fact_4002_summable__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3518 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_695_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3519 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_393_mult__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3520 (all X_b all X_a (topological_space(X_a) & power(X_b) & real_normed_algebra(X_b) -> (all N_1 all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),L),N_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4556_LIM__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3521 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1))))) # label(fact_3985_divide_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3522 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hAPP(X_a,X_b,F,X_2) = zero_zero(X_b) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = zero_zero(X_b)))))) # label(fact_3950_setprod__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3523 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> -(-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma))))) # label(fact_2413_odd__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3524 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,C) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))))))) # label(fact_1198_zmult1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3525 (all X_a (metric_space(X_a) -> (all X all Y all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),X)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),Y))))))) # label(fact_3504_dist__triangle3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3526 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))) # label(fact_1167_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3527 (all X all Y all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),M) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),M) = one_one(nat))) # label(fact_3292_invertible__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3528 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))))) # label(fact_2787_of__real_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3529 (all X_a (divisi14063676e_zero(X_a) & real_n1866405975lgebra(X_a) -> (all A_1 hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2510_norm__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3530 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3) <-> A_3 = B_2)))) # label(fact_3664_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3531 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1737_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3532 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2)) -> (N_1 = Ma <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)))))) # label(fact_413_power__inject__exp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3533 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K))))) # label(fact_3820_DERIV__sin__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3534 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4552_mult__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3535 (all X_a (linorder(X_a) -> (all Ma all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ma),N_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Ma)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),N_1))))))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3536 (all N N != hAPP(nat,nat,suc,N)) # label(fact_1217_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3537 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) -> ti(fun(product_prod(X_a,X_b),X_c),G) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F))) # label(fact_4329_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3538 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2568_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3539 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2060_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3540 (all N ti(int,N) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N))) # label(fact_3340_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3541 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),hAPP(int,int,abs_abs(int),D)))) # label(fact_1926_zdvd__self__abs1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3542 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) <-> ti(X_a,C_1) = ti(X_a,B_1))))) # label(fact_770_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3543 (all X_a all X_b (topological_space(X_b) -> (all K all A_3 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),A_3))))) # label(fact_4460_tendsto__const) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3544 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)))) # label(fact_3454_zgcd__zmult__eq__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3545 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_3577_of__int__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3546 (all X_a (division_ring(X_a) -> ti(fun(X_a,X_a),inverse_inverse(X_a)) = inverse_inverse(X_a))) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3547 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_49_less__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3548 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = X))) # label(fact_2708_real__root__pos2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3549 (all M all N all R_5 all R_4 all S_4 all S_3 all T_6 all T_5 all K_4 ((exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4)))) # label(fact_3477_xzgcd__correct__aux2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3550 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(nat,nat,suc,N)))))) # label(fact_1361_divides__rexp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3551 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_144_even__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3552 (all X_a (comple1803745165norder(X_a) -> (all A_2 all S (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),S))) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X_2)))))))) # label(fact_1767_less__Sup__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3553 (all X all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),X)),hAPP(nat,real,real_1(nat),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),D))),hAPP(nat,real,real_1(nat),D))))) # label(fact_2372_real__of__nat__div__aux) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3554 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4611_LIM__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3555 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),B_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),A_2)),Ma))))) # label(fact_357_zcong__zmult__prop2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3556 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1)) # label(fact_230_nat__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3557 (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))) # label(fact_195__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3558 (all X_2 ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_2),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,sin_coeff,X_2)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,sin_coeff,X_2) = zero_zero(real)))) # label(fact_2478_sin__coeff__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3559 (all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_497_dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3560 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | ti(int,X) = ti(int,Y))) # label(fact_93_zless__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3561 (all P_1 all N_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))) # label(fact_3128_Bolzano__bisect__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3562 (all X_a (ring_1(X_a) & real_normed_vector(X_a) -> (all C_1 all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),C_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))))) # label(fact_4107_diffs__equiv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3563 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_823_add__le__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3564 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_4406_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3565 (all N (N != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))) # label(fact_1459_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3566 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_933_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3567 (all Ma (Ma != zero_zero(nat) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat)),Ma)))))) # label(fact_3842_finite__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3568 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1)))) # label(fact_3372_ceiling__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3569 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3134_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3570 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))) # label(fact_3321_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3571 (all W all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),W))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z_1))) = hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)))) # label(fact_1942_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3572 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3775_rat__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3573 (all N_1 all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,N_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(nat,bool,P_1,N_1))))) # label(fact_1654_nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3574 (all X all Y (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1259_anything__times__even) # label(axiom) # label(non_clause). [assumption]. 7.75/7.77 3575 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),D_2))))))) # label(fact_3863_DERIV__cmult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3576 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4))))) # label(fact_1232_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3577 (all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)))) # label(fact_1036_zmod__zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3578 (all X_b all X_a (real_normed_algebra(X_b) & metric_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4577_LIM__mult__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3579 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,X)),one_one(real)))) # label(fact_2300_sin__le__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3580 (all X all Y zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2399_sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3581 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_1905_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3582 (all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,L_4))) # label(fact_495_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3583 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1457_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3584 (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,sgn_sgn(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2212_sgn__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3585 (all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_4858_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3586 (all K_3 all K all F ((all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),K_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),K),hAPP(nat,real,F,N_2))))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),F)))) # label(fact_4312_BseqI2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3587 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1588_leI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3588 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_2 hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_2))) = hAPP(X_a,X_a,exp(X_a),X_2)))) # label(fact_4750_lemma__exp__ext) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3589 (all R_4 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X))) # label(fact_4681_complex__Im__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3590 (all X_a all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) # label(fact_1823_card__infinite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3591 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_4978_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3592 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))))) # label(fact_3331_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3593 (all K_4 all I_1 all J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),J_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J_2),K_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),K_4))))) # label(fact_652_real__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3594 (all B_1 all C_1 all A_2 all D_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),D_1) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B_1),C_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A_2)),hAPP(int,int,abs_abs(int),C_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B_1)),hAPP(int,int,abs_abs(int),D_1)) <-> hAPP(int,int,abs_abs(int),D_1) = hAPP(int,int,abs_abs(int),C_1) & hAPP(int,int,abs_abs(int),B_1) = hAPP(int,int,abs_abs(int),A_2))))) # label(fact_4400_coprime__crossproduct__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3595 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3596 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) # label(fact_1429_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3597 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))))) # label(fact_257_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3598 (all X_c all X_a all X_b all F all A_2 all B_1 all A_3 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,A_2),B_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_c,bool),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(product_prod(X_a,X_b),bool),fun(X_c,bool)),image(product_prod(X_a,X_b),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)),A_3))))) # label(fact_3981_pair__imageI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3599 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1))))))) # label(fact_4085_divide_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3600 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_988_pos__mod__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3601 (all A_2 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),A_2)) -> (exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A_2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),N_2))))),R_1))))))) # label(fact_4056_suminf__exist__split) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3602 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3603 (all K_4 all L_4 ((zero_zero(int) = ti(int,L_4) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4)) & (ti(int,L_4) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_4))))) # label(fact_2720_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3604 (all X_a (division_ring(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,inverse_inverse(X_a),B)))))))) # label(fact_2611_inverse__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3605 (all X_a all X_c all X_b all F all X_1 all G (hAPP(X_c,X_b,G,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) = hAPP(X_c,X_b,F,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) <-> hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),G),X_1) = hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1))) # label(fact_4066_apsnd__eq__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3606 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2397_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3607 (all P_1 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))))) # label(fact_3831_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3608 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_400_zero__le__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.78 3609 (all X_1 all Y_1 (zero_zero(real) = Y_1 & X_1 = zero_zero(real) <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1)))) # label(fact_707_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3610 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),X_1),Y_1))))) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3611 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1556_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3612 (all X all Q_3 all N all R_4 (X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_3),N)),R_4) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X)))))) # label(fact_732_divides__div__not) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3613 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> zero_zero(nat) = N_1 & hAPP(nat,nat,suc,zero_zero(nat)) = Ma | hAPP(nat,nat,suc,zero_zero(nat)) = N_1 & Ma = zero_zero(nat))) # label(fact_1325_one__is__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3614 (all P_1 all A_2 all B_1 (-(-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) | (exists D_3 (-hBOOL(hAPP(nat,bool,P_1,D_3)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) = A_2))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))))) # label(fact_701_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3615 (all P_5 all R_4 all S_3 all Q_3 (zero_zero(int) != ti(int,Q_3) -> (zero_zero(int) != ti(int,S_3) -> (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),R_4),S_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),Q_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),P_5),S_3))))) # label(fact_3728_normalize__crossproduct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3616 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Z_2))))))))) # label(fact_4933_lemma__isCont__inj) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3617 (all X_a all X_b (topological_space(X_b) -> (all F all L all A_3 all A_7 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),A_7)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_7)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3))))))) # label(fact_4430_tendsto__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3618 (all K_4 hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,real,number_number_of(real),K_4)) # label(fact_3763_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3619 (all Ma all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)))) # label(fact_1971_int__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3620 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arccos,Y)),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2274_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3621 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_132_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3622 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4275_series__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3623 (all X_a (field(X_a) -> (all X_1 all W_1 all Z all Y_1 (zero_zero(X_a) != ti(X_a,Y_1) -> (zero_zero(X_a) != ti(X_a,Z) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W_1),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_1),Y_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1))))))) # label(fact_1691_frac__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3624 (all X_a all X_b all A_3 all B_1 all F all X_1 (hAPP(X_b,X_a,F,X_1) = ti(X_a,B_1) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)))))) # label(fact_3632_image__eqI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3625 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))) # label(fact_1893_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3626 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (one_one(nat) != B -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),one_one(nat)))))) # label(fact_2897_coprime__bezout__strong) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3627 (all X_b all X_a (real_normed_algebra(X_a) -> (all G all A_3 all Y_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),G)),Y_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1)))) # label(fact_4190_mult__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3628 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2))))))) # label(fact_3686_Rats__dense__in__nn__real) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3629 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M)) # label(fact_3452_zgcd__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3630 (all X all Y Y = hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2972_Im) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3631 (all X_1 all Y_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_623_dvd_Oless__le__not__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3632 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))) # label(fact_2687_real__root__divide) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3633 (all R_4 all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3726_normalize__denom__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3634 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1294_zero__zle__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3635 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_1318_zdvd__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3636 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B)))) # label(fact_977_mod__mult__self1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3637 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3448_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3638 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2280_arccos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3639 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real))) <-> zero_zero(nat) = N_1)) # label(fact_2315_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3640 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1707_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3641 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (zero_zero(nat) != N -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),M) = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_3066_prime__factor__lt) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3642 (all X hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),X)) = hAPP(int,int,fact_fact(int),hAPP(nat,int,semiring_1_of_nat(int),X))) # label(fact_3193_transfer__int__nat__factorial) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3643 (all X one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),one_one(nat))) # label(fact_3252_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3644 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1230_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3645 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))),one_one(real)))) # label(fact_3410_real__of__int__div3) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3646 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))))) # label(fact_1338_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3647 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_3986_suminf__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3648 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))) # label(fact_866_d22set__g__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3649 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_427_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3650 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | N_1 = Ma)) # label(fact_1238_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3651 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),K)))) # label(fact_300_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3652 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> M = N))) # label(fact_1235_less__antisym) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3653 (all Z_1 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z_1)) -> ti(int,W) = ti(int,Z_1)))) # label(fact_30_zle__antisym) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3654 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),U),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2118_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3655 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_2))))))) # label(fact_1764_Sup__subset__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3656 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_1574_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3657 (all X all Y ((Y = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = X) & (zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)))) # label(fact_3275_gcd__nat_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3658 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))))) # label(fact_3979_summable__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3659 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Z_2)) & hAPP(real,real,tan,Z_2) = X & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_2281_tan__total__pi4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3660 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_4034_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3661 (all N_1 hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_4934_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3662 (all N all K_4 all M (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),M) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),M)))) # label(fact_3431_zgcd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3663 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all X_3 all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),X_3),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (all S_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),S_2),A_2),sequentially)) & (all N_2 hAPP(nat,X_a,S_2,N_2) != ti(X_a,A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(nat,X_a),fun(nat,X_b),hAPP(fun(X_a,X_b),fun(fun(nat,X_a),fun(nat,X_b)),combb(X_a,X_b,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4655_LIMSEQ__SEQ__conv1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3664 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1304_zmult__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3665 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),X),Y))) # label(fact_3771_real__times__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3666 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> A_3 = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))) # label(fact_3666_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3667 (all W hAPP(int,complex,number_number_of(complex),W) = hAPP(complex,complex,cnj,hAPP(int,complex,number_number_of(complex),W))) # label(fact_2932_complex__cnj__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3668 (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))))))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3669 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)) # label(fact_3248_gcd__add1__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3670 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))) # label(fact_2465_even__dvd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3671 (all A_1 all N all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) -> (N != zero_zero(nat) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B))))) # label(fact_870_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3672 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))))) # label(fact_1652_Union__SetS__finite) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3673 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2314_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3674 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1))),hAPP(real,real,F,X_1))))))))))) # label(fact_2664_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3675 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4659_LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3676 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)))) # label(fact_2951_mult__idem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3677 (all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),zero_zero(int)),P_5)))))) # label(fact_281_zcong__zprime__prod__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3678 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> (exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),X)))))) # label(fact_3086_coprime__prime__dvd__ex) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3679 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)))))))) # label(fact_4088_sums__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3680 (all M all N hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1242_add__Suc__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3681 (all X_b all X_a (order(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2831_xt7) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3682 (all X_b all X_a (ab_group_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),minus_minus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4221_setsum__subtractf) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3683 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (ti(int,Ma) = one_one(int) & one_one(int) = ti(int,N_1) <-> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) = one_one(int)))) # label(fact_114_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3684 (all X_1 (X_1 = hAPP(real,real,exp(real),hAPP(real,real,ln,X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2600_exp__ln__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3685 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> zero_zero(int) != hAPP(int,int,fact_fact(int),N))) # label(fact_3191_fact__nonzero__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3686 (all X all N hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)))) # label(fact_2347_tan__periodic__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3687 (all A_2 hAPP(int,int,zfact,A_2) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),d22set,A_2))) # label(fact_3930_d22set__prod__zfact) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3688 (all W all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_1516_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3689 (all P_5 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5)) = hAPP(product_prod(int,int),rat,frct,P_5)) # label(fact_3778_Frct__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3690 (all K all N_1 all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4181_sumr__offset2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3691 (all B all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))))) # label(fact_4384_coprime__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3692 (all X_a (linordered_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))))) # label(fact_1871_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3693 (all X_a all F all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3) = hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3))) # label(fact_4251_real__of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3694 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_2041_minus__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3695 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),Y)) # label(fact_4375_gcd__abs1__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3696 (all A_1 all B hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),A_1)),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2746_complex__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3697 (all X all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))) # label(fact_3347_powr__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3698 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1335_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3699 (all X_1 all N_1 all Y_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y_1),N_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))))) # label(fact_993_zmod__eq__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3700 (all X_a (order(X_a) -> mono(nat,X_a) = ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),mono(nat,X_a)))) # label(tsy_c_Orderings_Oorder_Omono_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3701 (all P_4 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),P_4))) = hAPP(int,fun(int,bool),sr,P_4)) # label(fact_898_SR__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3702 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2880_zero__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3703 (all W ii != hAPP(int,complex,number_number_of(complex),W)) # label(fact_2762_complex__i__not__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3704 (all K_4 all A_1 all J_2 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5))))))) # label(fact_853_aux______4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3705 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_816_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3706 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))))) # label(fact_3661_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3707 (all X_a all R1_1 all R2_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,fun(X_a,bool)),bool),ord_less_eq(fun(X_a,fun(X_a,bool))),R1_1),R2_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R2_1)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R1_1))))) # label(fact_2913_accp__subset) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3708 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) # label(fact_3356_powr__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3709 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),X),P_5)))))) # label(fact_846_MultInv__prop4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3710 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),one_one(nat)))))))))) # label(fact_4504_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3711 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2605_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3712 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),A_3)) = ti(fun(X_a,bool),A_3)))) # label(fact_1997_double__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3713 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3714 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2130_arcsin__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3715 (all N all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_2156_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3716 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_2806_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3717 (all Y all X all P_5 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y))))) # label(fact_272_Euler_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3718 (all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),M)),K_4)))) # label(fact_1463_int__power__div__base) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3719 (all X_a (linordered_idom(X_a) -> (all A_1 all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)))))) # label(fact_1470_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3720 (all V_3 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))) # label(fact_1467_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3721 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),one_one(X_a))))) # label(fact_975_mod__by__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3722 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))))))) # label(fact_791_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3723 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),field_char_0_Rats(X_a))))) # label(fact_3691_Rats__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3724 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_458_power__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.78 3725 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_3))))))) # label(fact_3961_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3726 (all X_a (banach(X_a) & real_normed_field(X_a) -> exp(X_a) = ti(fun(X_a,X_a),exp(X_a)))) # label(tsy_c_Transcendental_Oexp_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3727 (all X one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2386_sin__cos__squared__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3728 (all N all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,Z_1)),N))) # label(fact_1146_nat__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3729 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K)),L)))) # label(fact_2902_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3730 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3731 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))))) # label(fact_1284_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3732 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2677_real__root__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3733 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))) # label(fact_3231_dvd__gcd__D2__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3734 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,B) != zero_zero(int) -> ti(int,Q_3) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_1191_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3735 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2496_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3736 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))) # label(fact_330_power__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3737 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3238_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3738 (all Z_1 hAPP(complex,complex,cnj,hAPP(int,complex,ring_1_of_int(complex),Z_1)) = hAPP(int,complex,ring_1_of_int(complex),Z_1)) # label(fact_3572_complex__cnj__of__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3739 (all X_b all X_a (field(X_a) -> (all F all A_3 all R_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),F)),R_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),R_1)))) # label(fact_4218_setsum__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3740 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_3106_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3741 (all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> hAPP(int,nat,nat_1,Z_1) = zero_zero(nat))) # label(fact_1507_neg__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3742 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_4835_min__leastR) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3743 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_2962_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3744 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Ma)),one_one(real)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),Ma)))) # label(fact_3393_int__le__real__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3745 (all K (hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),K))) <-> hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),K))))) # label(fact_3690_iszero__rat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3746 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_379_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3747 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3821_Ints__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3748 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),F),X_1)))))) # label(fact_4886_DERIV__isCont) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3749 (all X_a all A_3 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),fEx(fun(X_a,bool))),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,fun(X_a,bool))),fequal(fun(X_a,bool)))),uminus_uminus(fun(X_a,bool)))))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3)),pow(X_a)))))) # label(fact_4428_Pow__Compl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3750 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4593_LIM__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3751 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4006_of__real_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3752 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3753 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2243_cos__double__less__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3754 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1) = Ma))) # label(fact_749_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3755 (all X_a (ring_1(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),ring_1_Ints(X_a))))))) # label(fact_3858_Ints__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3756 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_941_mod__add__self1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3757 (all X_a (dvd(X_a) & linorder(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_861_minf_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3758 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 (hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))) <-> (all S_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) & (all N_2 hAPP(nat,real,S_2,N_2) != A_2) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4634_LIMSEQ__SEQ__conv) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3759 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)))) # label(fact_301_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3760 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))) | (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_3923_monoseq__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3761 (all X_a (real_n1866405975lgebra(X_a) -> (all X all N hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N)))) # label(fact_1782_norm__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3762 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1) = ti(X_a,C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1))))) # label(fact_489_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3763 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_4814_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3764 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),zero_zero(int))) -> (exists N_2 ti(int,X) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_2186_negD) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3765 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),one_one(int))) # label(fact_2905_pred__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3766 (all X_a nat_case(X_a) = ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a))) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3767 (all X_b all X_a (real_normed_field(X_a) & banach(X_b) -> (all G all F all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all H_1 all N_2 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(nat,X_b,hAPP(X_a,fun(nat,X_b),G,H_1),N_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,F,N_2)),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(X_a,X_b),hAPP(fun(fun(nat,X_b),X_b),fun(fun(X_a,fun(nat,X_b)),fun(X_a,X_b)),combb(fun(nat,X_b),X_b,X_a),suminf(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))))) # label(fact_4625_lemma__termdiff5) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3768 (all F all F_2 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),hAPP(real,real,F_2,X_2))))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),B_1)) & hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(real,real,F_2,Z_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Z_2))))))) # label(fact_2721_MVT2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3769 (all P_1 all N_1 all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),K))) <-> (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (K != zero_zero(nat) -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,I_2)))))))) # label(fact_1131_split__div) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3770 (all X_a (real_vector(X_a) -> (all A_1 all B all X (ti(X_a,X) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X) -> B = A_1))))) # label(fact_4705_scaleR__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3771 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3772 (all X_a all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_3))) # label(fact_1960_subset__refl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3773 (all K_4 hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))) # label(fact_1528_succ__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3774 (all X_a (real_normed_algebra(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_877_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3775 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi))) # label(fact_2326_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3776 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)))))) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3777 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1158_Int2_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3778 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1309_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3779 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),I),K)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),K))))))) # label(fact_4314_lessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3780 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_5),Q_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3))))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3781 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combb(product_prod(int,int),product_prod(int,int),int)),hAPP(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combs(int,int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),int),combc(int,int,product_prod(int,int))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,int),fun(int,fun(int,product_prod(int,int))),int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),times_times(int)),sgn_sgn(int))))),abs_abs(int)))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,inverse_inverse(rat),P_4))) # label(fact_4033_rat__inverse__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3782 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,ln,X)) = hAPP(real,real,ln,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)))) # label(fact_2355_ln__realpow) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3783 (all X_a (power(X_a) -> power_power(X_a) = hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),one_one(X_a)),times_times(X_a)))) # label(fact_2838_power__power__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3784 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3396_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3785 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2796_of__real_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3786 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),zero_zero(X_b))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),zero_zero(X_b))))))) # label(fact_4308_setsum__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3787 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3699_Rats__divide) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3788 (all I all K (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I)) | zero_zero(int) = ti(int,K))) # label(fact_1026_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3789 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))))) # label(fact_1793_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3790 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1680_divide__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3791 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))))) # label(fact_3413_less__floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3792 (all X_1 hAPP(real,real,ln,X_1) = hAPP(fun(real,bool),real,the(real),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),exp(real))),X_1))) # label(fact_4134_ln__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3793 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X))))) # label(fact_1951_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3794 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4615_Re_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3795 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = Q_3)) # label(fact_3101_div__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3796 (all X_2 hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)) = hAPP(nat,fun(nat,bool),ord_less(nat),X_2)) # label(fact_3815_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3797 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))))) # label(fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3798 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4))) # label(fact_532_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3799 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)))) # label(fact_3646_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3800 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_390_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3801 (all X_b all X_a (comm_monoid_mult(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),A_3))))) # label(fact_3946_setprod__timesf) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3802 (all Q_2 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_2)),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_2)))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1) = Q_2))) # label(fact_1442_split__div__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3803 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)))) # label(fact_2776_Pow__top) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3804 (all X_1 all Y_1 (Y_1 = X_1 <-> hAPP(complex,real,re,X_1) = hAPP(complex,real,re,Y_1) & hAPP(complex,real,im,Y_1) = hAPP(complex,real,im,X_1))) # label(fact_2996_complex__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3805 (all R all S_5 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R),hAPP(real,real,inverse_inverse(real),S_5)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R),S_5)) # label(fact_2564_real__divide__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3806 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4985_le__maxI2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3807 (all X_b all X_a (ring_1(X_a) -> (all F all A_3 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3)))) # label(fact_4170_of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3808 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))) # label(fact_268_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3809 (all A_1 all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2179_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3810 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = Ma & hAPP(nat,nat,suc,zero_zero(nat)) = N_1)) # label(fact_1326_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3811 (all X_1 hAPP(nat,nat,suc,X_1) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1)))) # label(fact_3829_card__bdd__nat__set__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3812 (all X_b all X_a (semiring_0(X_a) -> (all F all A_3 all R_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),R_1)))) # label(fact_4210_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3813 (all X_a all X_b all X_c all Z all C_1 all P_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),P_4))) -> -(all X_2 all Y_2 (hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) = ti(product_prod(X_b,X_c),P_4) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,X_2),Y_2))))))) # label(fact_4059_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3814 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3920_monoseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3815 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),Y))) # label(fact_4379_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3816 (all N_4 ((exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)))) # label(fact_3673_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3817 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))))) # label(fact_1336_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3818 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3108_div__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3819 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_1127_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3820 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_2),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_2826_dense__le__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3821 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2468_even__even__mod__4__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3822 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))))) # label(fact_1815_card__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3823 (all X_a (field(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1) = one_one(X_a))))) # label(fact_2580_field__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3824 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4663_LIM__I) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3825 (all Y (zero_zero(real) != Y -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2756_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3826 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))) # label(fact_3006_Re_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3827 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arcsin,hAPP(real,real,sin,X)) = X))) # label(fact_2398_arcsin__sin) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3828 (all X_a (division_ring(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> (ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))) # label(fact_1693_eq__divide__imp) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3829 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2818_of__real_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3830 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sin,X)),zero_zero(real)))))) # label(fact_2394_sin__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3831 (all W_1 all Ma ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> hAPP(nat,int,semiring_1_of_nat(int),Ma) = ti(int,W_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> zero_zero(nat) = Ma) <-> Ma = hAPP(int,nat,nat_1,W_1))) # label(fact_1407_nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3832 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2039_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3833 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))))))) # label(fact_2574_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3834 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),M))) # label(fact_3214_gcd__dvd1__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3835 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)))))) # label(fact_1015_zdiv__mono1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3836 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))))) # label(fact_2646_log__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3837 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2076_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3838 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,abs_abs(real),X)) = hAPP(real,real,sgn_sgn(real),X)) # label(fact_2213_real__sgn__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3839 (all N (zero_zero(nat) != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_540_gr0I) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3840 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_1241_add__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3841 (all X_a (linordered_idom(X_a) -> one_one(X_a) = hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)))) # label(fact_1853_abs__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3842 (all X_a (ab_group_add(X_a) -> (all F all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))))) # label(fact_4618_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3843 (all P_1 all N_1 ((exists X_2 (hBOOL(hAPP(nat,bool,P_1,X_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) <-> (exists M_2 (hBOOL(hAPP(nat,bool,P_1,M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)))))) # label(fact_4193_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3844 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2388_sin__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3845 (all F all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),B_1),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_2))))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_1))))))) # label(fact_4924_LIM__less__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3846 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4))))) # label(fact_584_mult__le__mono1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3847 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_2706_real__root__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3848 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)),A_1)))) # label(fact_3376_powr__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3849 (all X_a all X_b (comm_semiring_1(X_b) -> (all D_1 all F all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(X_a,X_b,F,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4773_dvd__setsum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3850 (all X_a (ring_1(X_a) -> (all K_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,K_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),K_4))))))))) # label(fact_3559_of__int__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3851 (all A_1 zero_zero(complex) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,zero_zero(real)),A_1)) # label(fact_3168_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3852 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,B_1))))) # label(fact_4929_DERIV__isconst__end) # label(axiom) # label(non_clause). [assumption]. 7.81/7.79 3853 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))) # label(fact_1028_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3854 (all X_a (sgn_div_norm(X_a) -> norm_norm(X_a) = ti(fun(X_a,real),norm_norm(X_a)))) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3855 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),C),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),C),M))))) # label(fact_316_zcong__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3856 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)))))) # label(fact_3184_finite__Plus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3857 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))))))) # label(fact_1730_less__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3858 (all N all P_5 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M)))))) # label(fact_279_zprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3859 (all X_a all C_1 all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2194_Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3860 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1599_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3861 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3862 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),zero_zero(int)) = hAPP(int,int,abs_abs(int),X)) # label(fact_4388_gcd__0__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3863 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4149_setprod__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3864 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3020_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3865 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))) # label(fact_2207_sgn__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3866 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)))))) # label(fact_3984_suminf__divide) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3867 (all X all M all Y (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)))) # label(fact_959_Residues_Oaux) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3868 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))) -> (zero_zero(X_a) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))))))) # label(fact_2544_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3869 (all X_a (real_div_algebra(X_a) & divisi14063676e_zero(X_a) -> (all A_1 all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))) # label(fact_4684_inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3870 (all Z_1 all X all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D)))))) # label(fact_1987_incr__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3871 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)))) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3872 (all X_a (division_ring(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2582_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3873 (all N_1 all X_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1)))))))) # label(fact_4286_Maclaurin__all__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3874 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1) = zero_zero(nat))) # label(fact_684_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3875 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_679_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3876 (all X_1 all Y_1 all Z (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),Z) <-> X_1 = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z)))) # label(fact_1772_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3877 (all B all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A_1))),hAPP(complex,real,norm_norm(complex),B))),hAPP(complex,real,norm_norm(complex),A_1)))) # label(fact_1784_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3878 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_1865_abs__of__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3879 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_15_add__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3880 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_1612_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3881 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Y_1),X_1)))) # label(fact_3704_Sup__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3882 (all S ((exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_atMost(nat),K_1)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_4974_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3883 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)))) # label(fact_4001_summable__rabs__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3884 (all X_1 all Y_1 all Xa_2 (Xa_2 = X_1 & zero_zero(real) = Y_1 <-> hAPP(real,complex,of_real(complex),Xa_2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1))) # label(fact_2790_complex__eq__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3885 (all I all J (ti(int,J) = zero_zero(int) & ti(int,I) = zero_zero(int) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I),J))) # label(fact_3435_zgcd0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3886 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1701_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3887 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X)),one_one(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))),N))))) # label(fact_2370_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3888 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_2107_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3889 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2497_dvd__fact__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3890 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N)) -> I_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_1)))) # label(fact_672_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3891 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))) # label(fact_4682_complex__Re__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3892 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),Z_1),hAPP(real,complex,of_real(complex),hAPP(complex,real,norm_norm(complex),Z_1))) = hAPP(complex,complex,sgn_sgn(complex),Z_1)) # label(fact_2802_sgn__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3893 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),min_1)))) # label(fact_304_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3894 (all A_2 all B_1 all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_1),C_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_2),C_1) <-> A_2 = B_1))) # label(fact_708_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3895 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3))))) # label(fact_3667_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3896 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all A_2 all B_1 all W_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3897 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> zero_zero(nat) != hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3874_card__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3898 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_44_number__of__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3899 (all V_1 all V_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))))) # label(fact_79_less__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3900 (all X hAPP(real,real,sqrt,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))) # label(fact_2533_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3901 (all Z_1 all W ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))))) # label(fact_3902_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3902 (all Ma all K all N_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),N_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1)))))) # label(fact_4392_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3903 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),one_one(real)) = one_one(real))) # label(fact_2685_real__root__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3904 (all X_c all X_b all X_a (metric_space(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) -> ti(X_b,B_1) != hAPP(X_a,X_b,F,X_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4602_metric__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3905 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1756_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3906 (all K all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all D_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)))),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)),one_one(nat)))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4271_sumr__pos__lt__pair) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3907 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_2016_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3908 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X)))))) # label(fact_3612_floor__correct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3909 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_511_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3910 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) = X)) # label(fact_2461_even__nat__div__two__times__two) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3911 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2) = N_1))) # label(fact_2467_even__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3912 (all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I_1)) -> hAPP(list(int),nat,size_size(list(int)),hAPP(int,list(int),quickc666637781d_zero,I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,I_1))),one_one(nat)))) # label(fact_3203_length__around__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3913 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,one_one(real)),A_1) = hAPP(real,complex,cis,A_1)) # label(fact_3167_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3914 (all N all D all A_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)) = one_one(nat))) # label(fact_3277_coprime__exp__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3915 (all Y all X (X = hAPP(real,real,exp(real),Y) -> hAPP(real,real,ln,X) = Y)) # label(fact_2507_ln__unique) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3916 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y))) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_3010_complex__Im__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3917 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3918 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_3422_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3919 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))))))))) # label(fact_4024_powser__inside) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3920 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (ti(X_a,X_1) = ti(X_a,Y_1) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))))))) # label(fact_1595_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3921 (all K_4 ((zero_zero(code_code_numeral) = K_4 -> zero_zero(int) = hAPP(code_code_numeral,int,code_int_of,K_4)) & (zero_zero(code_code_numeral) != K_4 -> (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int))) & (zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1202_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3922 (all T_1 ord(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3923 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_995_div__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3924 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X)),Y)) # label(fact_4376_gcd__neg1__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3925 (all N_1 all X_1 (X_1 != one_one(real) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))) # label(fact_4206_sumr__geometric) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3926 (all A_2 all P_4 hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4) = hAPP(fun(int,bool),fun(fun(int,bool),bool),hAPP(fun(int,fun(int,bool)),fun(fun(int,bool),fun(fun(int,bool),bool)),image(int,fun(int,bool)),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4)),hAPP(int,fun(int,bool),sRStar,P_4))) # label(fact_3653_SetS__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3927 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),of_real(X_a)),hAPP(real,X_a,of_real(X_a),A_2)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4555_of__real_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3928 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N))) # label(fact_3439_zgcd__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3929 (all Ma all N_1 (ti(int,N_1) != zero_zero(int) | ti(int,Ma) != 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),gcd_gcd(int),Ma),N_1))))) # label(fact_4381_gcd__pos__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3930 (all X_a (group_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3931 (all V_1 all V_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2))))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2)))))))) # label(fact_3911_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3932 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2735_complex__norm) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3933 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2493_fact__ge__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3934 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)) # label(fact_3660_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3935 (all X_b all X_a all P_4 hAPP(product_prod(X_b,X_a),X_a,hAPP(fun(X_b,fun(X_a,X_a)),fun(product_prod(X_b,X_a),X_a),product_prod_case(X_b,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_b,fun(X_a,X_a)),combk(fun(X_a,X_a),X_b),combi(X_a))),P_4) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)) # label(fact_4003_snd__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3936 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (N_1 = Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma)))))) # label(fact_1332_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3937 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(real))))) # label(fact_1906_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3938 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_831_int__le__induct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3939 (all X_a all X_b all P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (all A_4 all B_4 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4)))))) # label(fact_3135_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3940 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> X_1 = Y_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_621_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3941 (all X_a (field(X_a) -> (all Z all N_1 all H (ti(X_a,H) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),H),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),N_1))),H)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))) # label(fact_4238_lemma__termdiff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3942 (all N_1 (one_one(nat) = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,N_1),N_1)))) # label(fact_2852_coprime__refl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3943 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> -(all K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)),one_one(int)) != ti(int,X_1)))) # label(fact_1072_zOddE) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3944 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3909_DERIV__sin__realpow2a) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3945 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ((ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = one_one(X_a)) & (zero_zero(X_a) = ti(X_a,A_1) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1)))))) # label(fact_1694_divide__self__if) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3946 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_1858_abs__minus__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3947 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1)),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),power_power(X_a)))),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))))))) # label(fact_4124_termdiffs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3948 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M)) -> zero_zero(int) = ti(int,X))))) # label(fact_451_Int2_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3949 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2))))) # label(fact_585_mult__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3950 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,sin,X))),hAPP(real,real,cos,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) # label(fact_2368_sin__double) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3951 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_1020_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3952 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_2108_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3953 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))),zero_zero(X_a))))) # label(fact_4078_sums__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3954 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4350_gcd__non__0__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3955 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3956 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2327_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3957 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) <-> hBOOL(hAPP(int,bool,nat_is_nat,X_1)))) # label(fact_4840_is__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3958 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) # label(fact_1302_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3959 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3960 (all F all J all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists B_6 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),J)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_6),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))) = hAPP(real,real,F,H)))) # label(fact_4272_Maclaurin__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3961 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all R_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_5),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_4),T_6))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)),S_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),T_5),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5))) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5)))) # label(fact_3083_xzgcda_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3962 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))))) # label(fact_2694_real__root__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3963 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> X = Y | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)))) # label(fact_628_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3964 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)))))) # label(fact_4949_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3965 (all X_a (field(X_a) -> (all N_1 all X_1 (ti(X_a,X_1) != one_one(X_a) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),one_one(X_a))))))) # label(fact_4179_geometric__sum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3966 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1)))) # label(fact_110_mult__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3967 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2129_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3968 (all M all N ((hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = one_one(nat)) & (zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),one_one(nat))))))) # label(fact_2482_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3969 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_377_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3970 (all M all K_4 (M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))))) # label(fact_1386_one__less__k) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3971 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) = one_one(int) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))))) # label(fact_3615_card__nor__eq__noX) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3972 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | N_1 = Ma)) # label(fact_564_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3973 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_1550_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3974 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1822_finite__subset) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3975 (all X_a (ring_11004092258visors(X_a) -> (all X_1 (ti(X_a,X_1) = one_one(X_a) | ti(X_a,X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1) = one_one(X_a))))) # label(fact_2072_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3976 (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_1569_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3977 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N)) # label(fact_1340_mult__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3978 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)))))) # label(fact_4598_setsum__head__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3979 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2472_lemma__not__even__div2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3980 (all Z all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1137_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3981 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_atMost(X_a)) = ord_atMost(X_a))) # label(tsy_c_SetInterval_Oord__class_OatMost_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3982 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1)))) # label(fact_2067_left__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3983 (all X_a (real_normed_algebra(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4679_mult__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3984 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4502_summable__Leibniz_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3985 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))) # label(fact_2515_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3986 (all X_1 (X_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_1641_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3987 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (X_1 = Y_1 <-> hAPP(real,real,ln,X_1) = hAPP(real,real,ln,Y_1))))) # label(fact_1934_ln__inj__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3988 (all X_a all F1 all F2 all Code_numeral hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral)) = hAPP(code_code_numeral,X_a,F2,Code_numeral)) # label(fact_3531_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3989 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2)) = N_1))) # label(fact_2469_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3990 (all X_a (ordere142940540dd_abs(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3991 (all Z1 all Z2 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W))) # label(fact_481_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3992 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> ti(int,N) = hAPP(real,int,archim2085082626_floor(real),X)))) # label(fact_3412_floor__eq2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3993 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_351_power__one__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3994 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_4942_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3995 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))))) # label(fact_125_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3996 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2833_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3997 (all V all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))) # label(fact_2169_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.80 3998 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1))))) # label(fact_1203_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 3999 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),X)))) # label(fact_2190_ln__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4000 (all X_a measure(X_a) = ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a))) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4001 (all X all Y all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M))),M)) # label(fact_957_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4002 (all X_a (real_normed_vector(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E_2))))))))))) # label(fact_3315_CauchyD) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4003 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) <-> zero_zero(real) = X_1))) # label(fact_2679_real__root__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4004 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),S_3) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),hAPP(real,real,uminus_uminus(real),S_3))) # label(fact_2091_real__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4005 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))))) # label(fact_4178_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4006 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) # label(fact_521_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4007 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real)))))) # label(fact_2695_real__root__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4008 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),L)) # label(fact_3465_zgcd__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4009 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int)))))) # label(fact_3782_Fract__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4010 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))) # label(fact_4969_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4011 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_170_number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4012 (all M all N hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) # label(fact_3094_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4013 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),W)))))) # label(fact_2185_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4014 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Z_2)),hAPP(real,real,F,X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)))))))) # label(fact_4932_lemma__isCont__inj2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4015 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(X_a,fun(nat,X_a))),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combs(X_a,X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),X_a),combc(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))),combi(X_a))))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(X_a)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4532_termdiffs__aux) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4016 (all X hAPP(int,nat,nat_1,hAPP(real,int,archimedean_ceiling(real),X)) = hAPP(real,nat,natceiling,X)) # label(fact_3284_natceiling__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4017 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1247_le__SucI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4018 (all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2473_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4019 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archimedean_ceiling(X_a)) = archimedean_ceiling(X_a))) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4020 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))),one_one(int)))) # label(fact_900_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4021 (all X_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_3244_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4022 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_981_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4023 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2832_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4024 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(real,real,exp(real),X_1) = hAPP(real,real,exp(real),Y_1))) # label(fact_2524_exp__inj__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4025 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3525_metric__CauchyI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4026 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3040_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4027 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_711_real__mult__order) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4028 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1601_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4029 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = ti(X_a,X_1) & ti(X_a,Y_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))))))) # label(fact_45_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4030 (all X_a (number_ring(X_a) -> (all V all C all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W)))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),hAPP(int,X_a,number_number_of(X_a),W)))))) # label(fact_2174_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4031 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_407_zero__less__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4032 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3586_le__of__int__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4033 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))) = hAPP(real,real,cos,X_1)) # label(fact_3972_cos__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4034 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4035 (all X_a (real_n2089651433ebra_1(X_a) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),one_one(X_a)))) # label(fact_2206_sgn__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4036 (all Y all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)))))))) # label(fact_847_MultInv__prop5) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4037 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B))))) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4038 (all F all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) = zero_zero(real)) # label(fact_4192_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4039 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_1420_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4040 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y))) # label(fact_2263_cos__arccos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4041 (all R_4 hAPP(real,real,norm_norm(real),R_4) = hAPP(real,real,abs_abs(real),R_4)) # label(fact_1857_real__norm__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4042 (all X_a (archim1804426504_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),X)))))))) # label(fact_2724_ex__less__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4043 (all X all Y hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),X),Y) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_3520_dist__complex__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4044 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))))))) # label(fact_3349_powr__less__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4045 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4733_scaleR__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4046 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1275_even__odd__disj) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4047 (all B_2 all K all Diff all H all N_1 ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (hAPP(nat,nat,suc,K) = N_1 -> (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(nat,fun(real,real),Diff,M_2))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),M_2))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),power_power(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2))))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),B_2)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))))))),T_4),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_2)))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),T_4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),T_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))))))))))))) # label(fact_4268_Maclaurin__lemma2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4048 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),A_2))))) # label(fact_4898_isCont__const) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4049 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_4)),K_4) = hAPP(int,int,bit1,K_4)) # label(fact_165_Bit1__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4050 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B))))) # label(fact_885_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4051 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1814_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4052 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,sin,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,cos,X))) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2322_sin__diff2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4053 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))))) # label(fact_839_wset__g__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4054 (all V_1 all N_1 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_3896_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4055 (all X_1 (zero_zero(real) = hAPP(int,real,real_1(int),X_1) <-> zero_zero(int) = ti(int,X_1))) # label(fact_3330_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4056 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_580_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4057 (all X_b (division_ring(X_b) & number(X_b) -> (all W hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),one_one(X_b)),hAPP(int,X_b,number_number_of(X_b),W)) = hAPP(X_b,X_b,inverse_inverse(X_b),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4058 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_143_power2__eq__square) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4059 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_1565_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4060 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))))) # label(fact_1078_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4061 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4025_complete__algebra__summable__geometric) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4062 (all X_a (real_algebra_1(X_a) -> (all X_1 all Y_1 (hAPP(real,X_a,of_real(X_a),X_1) = hAPP(real,X_a,of_real(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_2777_of__real__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4063 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))))) # label(fact_2125_arctan__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4064 (all X_a (real_normed_vector(X_a) -> (all K all Sa all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (ti(X_a,Sa) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))))) # label(fact_4168_suminf__minus__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4065 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) = hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))))))) # label(fact_3935_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4066 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))))) # label(fact_4945_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4067 (all X_1 all Y_1 all P_1 ((-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),X_1),Y_1)) = hAPP(nat,int,semiring_1_of_nat(int),Y_1)) & (hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))))) # label(fact_1484_int__if__cong) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4068 (all X_a (number_ring(X_a) & linord1117847801e_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1768_half) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4069 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)))) # label(fact_976_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4070 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4071 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))))) # label(fact_3243_gcd__greatest__iff__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4072 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2652_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4073 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,exp(X_a),X))))) # label(fact_2535_exp__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4074 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1140_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4075 (all X_a (comm_ring(X_a) & dvd(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))))))))) # label(fact_487_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4076 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2788_of__real__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4077 (all X_a (mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) & power(X_a) -> (all A_2 all W_1 (zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),W_1)) <-> ti(X_a,A_2) = zero_zero(X_a) & hAPP(int,nat,number_number_of(nat),W_1) != zero_zero(nat))))) # label(fact_256_power__eq__0__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4078 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_806_inv__not__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4079 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)))) # label(fact_1624_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4080 (all X_a (ordere1490568538miring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_371_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4081 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3400_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4082 (all D_1 (D_1 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),zero_zero(nat))))) # label(fact_2866_coprime__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4083 (all P_1 all A0 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),zero_zero(int))) -> (zero_zero(int) != ti(int,I_2) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) -> hBOOL(hAPP(int,bool,P_1,A0))))) # label(fact_3177_around__zero_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4084 (all N zero_zero(nat) = hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_2167_nat__zminus__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4085 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,L_2) = ti(X_b,M_1)))))) # label(fact_4546_LIM__unique) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4086 (all X_1 all Y_1 all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y_1),Z))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_3242_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4087 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1021_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4088 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4089 (all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),log,B_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,ln,B_1)),X_1)))))) # label(fact_3904_DERIV__log) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4090 (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2))))) # label(fact_239_add__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4091 (all X_a all Q_1 all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) -> (hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1))) -> (hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),Q_1) -> (exists A_4 (hBOOL(hAPP(X_a,bool,P_1,A_4)) & hBOOL(hAPP(X_a,bool,Q_1,A_4)))))))) # label(fact_4866_EulerFermat_Oaux) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4092 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1092_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4093 (all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))))) # label(fact_1394_nat__one__le__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4094 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_115_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4095 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4909_isCont__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4096 (all X_a all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_3636_image__Pow__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4097 (all X_a (linorder(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X) = ti(X_a,X)))) # label(fact_4802_Min_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4098 (all A_1 all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1))))) # label(fact_199_zprime__zdvd__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4099 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3))))))) # label(fact_3982_suminf__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4100 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_2862_coprime__Suc0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4101 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,int,uminus_uminus(int),A_1)) # label(fact_2172_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4102 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2736_ex__less__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4103 (all A_3 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(int,nat,nat_1,X_1)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))))))) # label(fact_4859_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4104 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,one_one(int)),hAPP(int,int,number_number_of(int),min_1)),M)))) # label(fact_466_one__not__neg__one__mod__m) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4105 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1)) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b)))) # label(fact_4782_Eps__split) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4106 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1303_int__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4107 (all A_1 hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1981_abs__power2__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4108 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2)) # label(fact_3442_zgcd__zminus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4109 (all X_a (linordered_semidom(X_a) -> (all N all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N)))))))) # label(fact_406_less__1__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4110 (all X_a (semiring_div(X_a) -> (all N all K_4 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N)))))))) # label(fact_949_dvd__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4111 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2490_fact__less__mono__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4112 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_865_d22set__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4113 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4114 (all N hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N)) = hAPP(int,nat,number_number_of(nat),N)) # label(fact_1889_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4115 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1)))) # label(fact_2070_diff__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4116 (all X_a all F all A_3 hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) # label(fact_3943_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4117 (all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),Y))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M)))) # label(fact_901_StandardRes__prop4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4118 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arctan,hAPP(real,real,tan,X)) = X))) # label(fact_2279_arctan__tan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4119 (all M hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),M)) # label(fact_1923_abs__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4120 (all X_a (real_normed_field(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_4707_divide_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4121 (all A_2 all P_4 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))) # label(fact_1669_wset__fin) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4122 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))))) # label(fact_3847_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4123 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3596_floor__add__of__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4124 (all N N = hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N))) # label(fact_2294_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4125 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4515_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.81 4126 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (zero_zero(real) != L -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (X_2 != C_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) -> hAPP(real,real,F,X_2) != zero_zero(real)))))))) # label(fact_4627_LIM__fun__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4127 (all Y all X (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X)) -> (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,Y)) -> hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_211_is__mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4128 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1682_divide__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4129 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1)))) # label(fact_1174_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4130 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4863_vanishes__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4131 (all X_a (field(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2578_inverse__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4132 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1016_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4133 (all A_1 all B all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3))) # label(fact_3735_quotient__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4134 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X_1)))))) # label(fact_1975_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4135 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1) = ti(int,Z_1)) # label(fact_66_zmult__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4136 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_3041_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4137 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) <-> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) & hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),A_3))) # label(fact_3627_is__RRset__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4138 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B))))) # label(fact_1040_div__mult__self2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4139 (all N_1 all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) -> (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4)))))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))))))) # label(fact_3144_not__P__Bolzano__bisect) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4140 (all R_4 all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3))) # label(fact_4404_normalize__coprime) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4141 (all X_1 (X_1 = 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),X_1),X_1))))) # label(fact_474_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4142 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1))))))) # label(fact_2432_zero__le__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4143 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> (exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1)) = N_1))) # label(fact_1327_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4144 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all G all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,G,X_2) = hAPP(int,X_a,F,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),G),B_2))))))) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4145 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X))))) # label(fact_3293_floor__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4146 (all K_4 all L_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4))) # label(fact_3776_Fract__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4147 (all X_a (comm_ring_1(X_a) -> (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N))))) # label(fact_2425_power__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4148 (all P_4 hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,P_4),hAPP(int,fun(int,bool),sRStar,P_4)))) # label(fact_2917_ResSet__SRStar__prop) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4149 (all X_a (number_ring(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_591_power2__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4150 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),zero_zero(nat))) <-> zero_zero(nat) = N_1)) # label(fact_548_le__0__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4151 (all X_a (semiring_div(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),A_1) = one_one(X_a))))) # label(fact_999_div__self) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4152 (all X_a (idom(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) | ti(X_a,C_1) = zero_zero(X_a))))) # label(fact_409_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4153 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_441_power__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4154 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2567_exp__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4155 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) != ti(fun(X_a,bool),A_3) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))) # label(fact_1999_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4156 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_1674_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4157 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1157_Int2_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4158 (all X_a (semiring_div(X_a) -> (all A_1 all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B)))) # label(fact_909_mod__div__trivial) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4159 (all X_a (ring_1(X_a) -> (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3604_of__nat__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4160 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_929_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4161 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2057_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4162 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),re),hAPP(complex,real,re,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4568_Re_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4163 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),exp(X_a)),X_1),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_2632_DERIV__exp) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4164 (all N hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))) # label(fact_2324_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4165 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K))))) # label(fact_3801_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4166 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2699_real__root__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4167 (all F all Y_1 all X_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Y_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1)))))) # label(fact_3687_DERIV__isconst3) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4168 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4720_scaleR__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4169 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1683_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4170 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1602_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4171 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),U))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)))) # label(fact_2087_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4172 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,cnj,X))) # label(fact_2929_complex__cnj__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4173 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_576_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4174 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_4829_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4175 (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y)))) -> X = zero_zero(real)))) # label(fact_1891_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4176 (all X_a (semiring_div(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_916_div__mod__equality2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4177 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))) # label(fact_1936_abs__div) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4178 (all N all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),hAPP(nat,nat,suc,N)) = A_1)))) # label(fact_1479_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4179 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1702_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4180 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(int,int,number_number_of(int),min_1)))) # label(fact_1063_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4181 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))))))) # label(fact_1998_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4182 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1264_Parity_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4183 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))) # label(fact_4966_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4184 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N) = X))) # label(fact_2711_real__root__pow__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4185 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_2080_abs__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4186 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),A_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),A_2))))) # label(fact_4432_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4187 (all X_1 (zero_zero(real) != hAPP(real,real,cos,X_1) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),tan),X_1)))) # label(fact_4885_isCont__tan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4188 (all X all Y all M (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),M) = one_one(int))) # label(fact_4349_invertible__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4189 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))))))) # label(fact_4080_sums__mult2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4190 (all X_a (linorder(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1)))) # label(fact_4972_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4191 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_2894_floor__le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4192 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,nat_1,X_1)))))) # label(fact_2462_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4193 (all X_1 all Y_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),zero_zero(real)))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_1),Y_1))))) # label(fact_1699_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4194 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1)) # label(fact_229_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4195 (all X_a (semiring_div(X_a) -> (all C_1 all B_1 all A_2 (zero_zero(X_a) != ti(X_a,A_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (ti(X_a,C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) <-> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2))))))) # label(fact_1044_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4196 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))))))) # label(fact_2865_floor__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4197 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),P_5)))))) # label(fact_848_Int2_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4198 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),zero_zero(nat))) # label(fact_4155_nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4199 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) # label(fact_179_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4200 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K_4))) # label(fact_1252_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4201 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> zero_zero(nat) = hAPP(real,nat,natfloor,X))) # label(fact_1895_natfloor__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4202 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),J_2))))) # label(fact_38_zadd__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4203 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1))))) # label(fact_738_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4204 (all X_a zero_frac(X_a) = ti(X_a,zero_frac(X_a))) # label(tsy_c_Nitpick_Ozero__frac_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4205 (all X_5 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X_5)))))) # label(fact_2704_real__root__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4206 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),N)) # label(fact_1440_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4207 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),M))) # label(fact_958_mod__mod__is__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4208 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)))))) # label(fact_4830_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4209 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1)))) # label(fact_4164_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4210 (all X_a (ring_1(X_a) -> ring_1_Ints(X_a) = ti(fun(X_a,bool),ring_1_Ints(X_a)))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4211 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_1560_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4212 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hAPP(fun(int,bool),nat,finite_card(int),X_2) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1539_SetS__elems__card) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4213 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,X))))) # label(fact_1629_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4214 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)))) # label(fact_2870_floor__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4215 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),L)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4091_sums__summable) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4216 (all N -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1501_not__neg__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4217 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (one_one(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) <-> one_one(real) = X_1))) # label(fact_2686_real__root__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4218 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))))) # label(fact_3461_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4219 (all X all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> X = one_one(nat))))) # label(fact_3264_coprime__common__divisor__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4220 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_398_not__square__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4221 (all X_1 all Y_1 (Y_1 = zero_zero(real) & X_1 = zero_zero(real) <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_615_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4222 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_1842_abs__le__D1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4223 (all A_1 one_one(real) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1)))) # label(fact_2749_cmod__unit__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4224 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),K_4)),L_4) != zero_zero(int) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))) # label(fact_2158_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4225 (all X_a (metric_space(X_a) -> (all X_3 hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(filter(nat),fun(X_a,bool),hAPP(fun(X_a,fun(filter(nat),bool)),fun(filter(nat),fun(X_a,bool)),combc(X_a,filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3)),sequentially)) = hAPP(fun(nat,X_a),X_a,lim(X_a),X_3)))) # label(fact_4495_lim__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4226 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),Ma))) # label(fact_3931_Bnor__prod__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4227 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_376_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4228 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2196_ComplD) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4229 (all X_a all F all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3) = hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3))) # label(fact_3940_real__of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4230 (all F all X_1 all F_2 all N_1 all Ma ((all R_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),R_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),F,R_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),F_2,R_2),X_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),X_1),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F_2),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))) # label(fact_4289_DERIV__sumr) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4231 (all Y hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,tan,Y))) # label(fact_2275_tan__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4232 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2131_arcsin__lbound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4233 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,A_2)),A_3)))) # label(fact_4508_Im_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4234 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_4810_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4235 (all X all Y all L_4 all M hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),L_4)),hAPP(real,real,uminus_uminus(real),M))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),L_4)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),M))))))) # label(fact_2112_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4236 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3509_dist__triangle__lt) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4237 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> N != zero_zero(nat))) # label(fact_539_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4238 (all X_a (semiring_div(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),zero_zero(X_a))))) # label(fact_925_mod__by__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4239 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_637_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4240 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2))))))))) # label(fact_1915_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4241 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_4811_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4242 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zOdd)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd))))) # label(fact_1046_power__preserves__odd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4243 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2696_real__root__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4244 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y_1)),hAPP(real,real,tan,X_1))))))))) # label(fact_2273_tan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4245 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_147_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4246 (all Diff all F all N_1 all H (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)))))) # label(fact_4279_Maclaurin__objl) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4247 (all X_a all X_b (field_inverse_zero(X_b) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),A_3))))) # label(fact_3957_setprod__dividef) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4248 (all X_a (ordered_ring_abs(X_a) -> (all B all A_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1))) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_1878_abs__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4249 (all X_a all X_b (linordered_semidom(X_b) -> (all G all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4150_setprod__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4250 (all X_a (number_ring(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2622_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4251 (all X_b all X_a all R_3 all K all Ta all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ta)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),Ta)) -> hAPP(X_b,nat,K,X_2) = hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Sa))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))))) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),K),Ta) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Ta)))),R_3)))),Sa))))) # label(fact_4303_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4252 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_1341_mult__Suc__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4253 (all M all N all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_4) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_561_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4254 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_383_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4255 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_689_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4256 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))))))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4257 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1)))))) # label(fact_3378_powr__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4258 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)))))))) # label(fact_4011_summable__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4259 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3860_Ints__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4260 (all X_a (ring_1(X_a) -> (all K ((ti(int,K) != zero_zero(int) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(product_prod(int,int),X_a,hAPP(fun(int,fun(int,X_a)),fun(product_prod(int,int),X_a),product_prod_case(int,int,X_a),hAPP(fun(int,X_a),fun(int,fun(int,X_a)),hAPP(fun(int,fun(X_a,fun(int,X_a))),fun(fun(int,X_a),fun(int,fun(int,X_a))),combs(int,X_a,fun(int,X_a)),hAPP(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a))),hAPP(fun(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a))),fun(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a)))),combb(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),int),combc(int,X_a,X_a)),hAPP(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a))),hAPP(fun(X_a,fun(int,fun(X_a,X_a))),fun(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a)))),combb(X_a,fun(int,fun(X_a,X_a)),int),hAPP(fun(int,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(int,fun(X_a,X_a))),combc(int,X_a,fun(X_a,X_a)),hAPP(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),int),if(X_a)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a))))),hAPP(X_a,fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),combc(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a)))),one_one(X_a)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),K))) = hAPP(int,X_a,ring_1_of_int(X_a),K))) & (ti(int,K) = zero_zero(int) -> zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),K)))))) # label(fact_3978_of__int__num) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4261 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> ti(X_a,A_2) = one_one(X_a) | hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = ti(X_a,A_2))))) # label(fact_2116_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4262 (all Y (Y != zero_zero(nat) -> -(all Nat_2 hAPP(nat,nat,suc,Nat_2) != Y))) # label(fact_1607_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4263 (all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,int,number_number_of(int),V) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1513_int__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4264 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,cos,X_1)))) # label(fact_4106_cos__paired) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4265 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) = one_one(nat) <-> (exists X_2 (hAPP(X_a,nat,F,X_2) = one_one(nat) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,X_2) != ti(X_a,Xa) -> hAPP(X_a,nat,F,Xa) = zero_zero(nat)))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))))))) # label(fact_4257_setsum__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.82 4266 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> (ti(X_a,B_1) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),sequentially)))))))) # label(fact_4451_LIMSEQ__divide) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4267 (all X_b all X_a (real_normed_field(X_a) -> (all G all A_3 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),G)),Y_1)),A_3)))) # label(fact_4184_divide_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4268 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2690_real__root__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4269 (all X_a (real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),combi(X_a)),X_1),one_one(X_a)))))) # label(fact_3839_DERIV__ident) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4270 (all X all Y (hAPP(complex,real,re,Y) = hAPP(complex,real,re,X) -> (hAPP(complex,real,im,X) = hAPP(complex,real,im,Y) -> Y = X))) # label(fact_2997_complex__eqI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4271 (all N all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)) = one_one(int))) # label(fact_4359_coprime__exp__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4272 (all X_b all X_a all P_1 all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1))),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1)))))) # label(fact_3123_exI__realizer) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4273 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1466_even__sum__div__2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4274 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))))))) # label(fact_2502_Ln_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4275 (all X_a (ordere779506340up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_781_add__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4276 (all X_a (number_ring(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X))))) # label(fact_2443_Parity_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4277 (all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))))),one_one(int)),P_5))))) # label(fact_1151_Little__Fermat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4278 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4279 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3110_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4280 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),hAPP(int,int,succ,L_4))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_1532_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4281 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X)),P_5)))) # label(fact_1010_StandardRes__ubound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4282 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J))) # label(fact_4223_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4283 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K_3 all F all L_2 all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (ti(X_b,K_3) = ti(X_b,L_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),K_3),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4545_LIM__cong__limit) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4284 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))))) # label(fact_1438_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4285 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_411_power__increasing) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4286 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))))) # label(fact_3416_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4287 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,ln,X)),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),A_1)),X)))))) # label(fact_3421_ln__powr__bound2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4288 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),G),S)),Ma)))) # label(fact_4419_setprod__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4289 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,A_2,zero_zero(nat))),zero_zero(real))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat))))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2))))))))))) # label(fact_4522_summable__Leibniz_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4290 (all P_5 all M ((M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M)) & (M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = one_one(nat)))) # label(fact_720_power__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4291 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2304_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4292 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_142_mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4293 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_1583_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4294 (all U_1 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U_1)))))) # label(fact_4163_finite__less__ub) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4295 (all X_a ti(fun(filter(X_a),bool),trivial_limit(X_a)) = trivial_limit(X_a)) # label(tsy_c_Limits_Otrivial__limit_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4296 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_1881_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4297 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (ti(int,B) != zero_zero(int) -> ti(int,Q_3) = ti(int,Q_5))))) # label(fact_1187_unique__quotient) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4298 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4140_mono__SucI2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4299 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)))) # label(fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4300 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A_1)) -> hAPP(int,int,abs_abs(int),A_1) = hAPP(int,int,abs_abs(int),B)))) # label(fact_1924_zdvd__antisym__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4301 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_1))))))) # label(fact_1913_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4302 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2136_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4303 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) <-> zero_zero(X_a) = ti(X_a,X_1) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4304 (all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) -> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2474_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4305 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,cos,X)))) # label(fact_2217_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4306 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1715_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4307 (all A_2 all B_1 (B_1 = A_2 <-> hAPP(rat,product_prod(int,int),quotient_of,A_2) = hAPP(rat,product_prod(int,int),quotient_of,B_1))) # label(fact_3721_quotient__of__inject__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4308 (all N_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1) = hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1)) # label(fact_4948_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4309 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X)))) # label(fact_2598_exp__ge__add__one__self) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4310 (all X all D (zero_zero(int) != ti(int,D) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),D))),hAPP(int,real,real_1(int),D))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),D)))) # label(fact_3411_real__of__int__div__aux) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4311 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),one_one(nat)),X) = one_one(nat)) # label(fact_3250_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4312 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all A_2 all B_1 all W_1 ((zero_zero(X_a) != hAPP(int,X_a,number_number_of(X_a),W_1) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))) & (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),W_1) -> ti(X_a,A_2) = zero_zero(X_a)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,A_2))))) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4313 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1)))))))))) # label(fact_3818_DERIV__mult_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4314 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archim2085082626_floor(X_a)) = archim2085082626_floor(X_a))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4315 (all X_a (semiring_1(X_a) -> (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))))))) # label(fact_1204_of__nat__double) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4316 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1))) # label(fact_40_eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4317 (all A_3 all B_2 all Ma (hBOOL(hAPP(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool,hAPP(product_prod(fun(int,bool),fun(int,bool)),fun(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool),member(product_prod(fun(int,bool),fun(int,bool))),hAPP(fun(int,bool),product_prod(fun(int,bool),fun(int,bool)),hAPP(fun(int,bool),fun(fun(int,bool),product_prod(fun(int,bool),fun(int,bool))),product_Pair(fun(int,bool),fun(int,bool)),A_3),B_2)),hAPP(fun(int,fun(int,bool)),fun(product_prod(fun(int,bool),fun(int,bool)),bool),bijR(int,int),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),A_3)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),B_2)),Ma)))) # label(fact_4874_bijzcong__zcong__prod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4318 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_385_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4319 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N)) # label(fact_1356_zpower__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4320 (all J_2 all I_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),I_1))) # label(fact_555_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4321 (all R_4 exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)))) # label(fact_3424_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4322 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U)))))))) # label(fact_1650_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4323 (all X_1 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),R_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),R_1)),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),R_1)))) # label(fact_2090_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4324 (all K_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3730_quotient__of__number_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4325 (all X_1 all Y_1 (Y_1 = zero_zero(nat) & X_1 = zero_zero(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = zero_zero(nat))) # label(fact_3256_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4326 (all A_1 all B all M hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),M)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),M)))) # label(fact_969_zcong__zmod__aux) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4327 (all K_4 hAPP(int,int,bit0,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),K_4)) # label(fact_133_Bit0__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4328 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4)) # label(fact_666_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4329 (all P_1 all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4536_all__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4330 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arctan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2654_DERIV__arctan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4331 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_802_mult__1__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4332 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)))) # label(fact_4861_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4333 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),min_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))))))) # label(fact_3309_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4334 (all X_a (ring_1(X_a) -> ti(fun(fun(nat,X_a),fun(nat,X_a)),diffs(X_a)) = diffs(X_a))) # label(tsy_c_Transcendental_Odiffs_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4335 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),A_1)) # label(fact_952_zmod__self) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4336 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),zero_zero(X_a))))) # label(fact_1657_divide__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4337 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),Ma)))) # label(fact_3391_int__less__real__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4338 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1370_odd__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4339 (all X_c all X_a all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4340 (all X_c all X_b all X_a all C_1 all X_1 all P_4 ((all A_4 all B_4 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),X_1)))) # label(fact_4060_splitI2_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4341 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),X),P_5)))))) # label(fact_849_Int2_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4342 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1946_ln__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4343 (all N one_one(real) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N))),pi))) # label(fact_2393_cos__2npi) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4344 (all X_b all X_a (semiring_0(X_a) -> (all R_1 all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))))) # label(fact_4211_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4345 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4165_setsum__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4346 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2061_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4347 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),A_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),A_1)))) # label(fact_2332_natceiling__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4348 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))) # label(fact_253_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4349 (all J_2 all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_830_MultInvPair__distinct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4350 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),Ma)),one_one(real)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_2342_nat__le__real__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4351 (all R_4 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),Y))) # label(fact_2809_complex__of__real__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4352 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_254_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4353 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all B_1 all W_1 all A_2 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)))))) # label(fact_1748_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4354 (all Ma all Ta all K (ti(int,K) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))))) # label(fact_601_zdvd__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4355 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_790_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4356 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (zero_zero(nat) != hAPP(int,nat,number_number_of(nat),W_1) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | ti(X_a,X_1) = zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))))))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4357 (all Diff all N_1 all X_1 (X_1 = zero_zero(real) -> (N_1 != zero_zero(nat) -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(nat,fun(real,real),Diff,zero_zero(nat)),zero_zero(real))))) # label(fact_4230_Maclaurin__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4358 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),hAPP(real,real,inverse_inverse(real),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) # label(fact_2563_divide__real__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4359 (all F all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),A_3)) -> (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,F,X_2)),hAPP(int,int,F,Xa)),Ma)) -> ti(int,X_2) = ti(int,Xa)))))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),F),A_3))))))) # label(fact_3644_ResSet__image) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4360 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)),Ma))))) # label(fact_3618_noX__is__RRset) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4361 (all M all K_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) != M -> (hAPP(nat,nat,suc,zero_zero(nat)) != M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))))) # label(fact_1387_one__less__m) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4362 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1593_leD) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4363 (all X_b all X_a all X_c (comm_monoid_add(X_c) -> (all F all R_3 all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3))))),T_3)))))) # label(fact_4188_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4364 (all X_a (metric_space(X_a) -> dist_dist(X_a) = ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)))) # label(tsy_c_RealVector_Odist__class_Odist_1_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4365 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_609_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4366 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,hAPP(int,int,succ,K_4))) # label(fact_1526_succ__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4367 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3226_gcd__assoc__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4368 (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_127_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4369 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2752_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4370 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),A_1)))))) # label(fact_3320_ln__powr__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4371 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)))) # label(fact_2075_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4372 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_1494_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4373 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) <-> hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1) = hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1))))) # label(fact_4316_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4374 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_1732_divide__Numeral0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4375 (all V_3 all K_4 all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_4))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)))) # label(fact_1512_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4376 (all X_a all X_b all X_c all X_d all F all G hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c),hAPP(fun(product_prod(X_a,X_b),fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),X_c)),combs(product_prod(X_a,X_b),X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(product_prod(X_a,X_b),X_d),fun(product_prod(X_a,X_b),fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),product_prod(X_a,X_b)),F),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d),hAPP(fun(X_a,X_d),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),X_d)),combb(X_a,X_d,product_prod(X_a,X_b)),G),product_fst(X_a,X_b)))),product_snd(X_a,X_b)) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,X_d),fun(X_a,fun(X_b,X_c)),hAPP(fun(X_d,fun(X_b,X_c)),fun(fun(X_a,X_d),fun(X_a,fun(X_b,X_c))),combb(X_d,fun(X_b,X_c),X_a),F),G))) # label(fact_4015_split__comp__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4377 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))) # label(fact_152_add__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4378 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> one_one(X_a) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)))) # label(fact_1885_abs__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4379 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4380 (all K_4 hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4)) # label(fact_22_number__of__is__id) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4381 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),one_one(X_a)))))))) # label(fact_1404_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4382 (all Y_3 all X_3 ((exists A_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A_4)) & (all N_2 hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),A_4))))) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),X_3)),Y_3)))))) # label(fact_4838_vanishes__mult__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4383 (all N all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_4846_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4384 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4040_splitI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4385 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B)) # label(fact_3326_powr__powr) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4386 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,sgn_sgn(X_a),Y)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_2204_sgn__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4387 (all X_b all X_c all X_a all P_1 all Z hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Z)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Z))) # label(fact_4016_split__beta) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4388 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_4391_coprime__dvd__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4389 (all X_b (number(X_b) & monoid_mult(X_b) -> (all V all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> one_one(X_b) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))))))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4390 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3))))) # label(fact_4207_setsum_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4391 (all W ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3890_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4392 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))))) # label(fact_840_wset__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4393 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)) = hAPP(real,nat,natceiling,X)))) # label(fact_2383_natceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4394 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5))))) # label(fact_844_MultInv__zcong__prop1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4395 (all M_5 all D_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M_5),D_4) = zero_zero(int) -> (exists Q_4 ti(int,M_5) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_4),Q_4)))) # label(fact_1171_zmod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4396 (all A_3 all B_2 (hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2) <-> A_3 = B_2)) # label(fact_3648_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4397 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_4847_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4398 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))))) # label(fact_1760_neg__one__special) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4399 (all X_a all N_1 all F all C_1 all H ((all N_2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2) = hAPP(nat,X_a,F,N_2)) -> hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),H,N_1),hAPP(nat,X_a,F,N_1)))) # label(fact_4330_def__nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4400 (all P_1 all A_2 all B_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all D_3 (A_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) -> hBOOL(hAPP(nat,bool,P_1,D_3)))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))))) # label(fact_700_nat__diff__split) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4401 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (C = B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_631_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4402 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)))) # label(fact_752_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4403 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))))) # label(fact_4092_summable__sums) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4404 (all Q_3 ((-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> Q_3 = hAPP(rat,rat,abs_abs(rat),Q_3)) & (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_3) = hAPP(rat,rat,uminus_uminus(rat),Q_3)))) # label(fact_3715_abs__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4405 (all X_a (number_ring(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),Y_1))))) <-> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1))))) # label(fact_2504_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4406 (all B all A_1 all X (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3229_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4407 (all J all K all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K))))) # label(fact_698_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 7.81/7.83 4408 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,re,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)))) # label(fact_4048_Re_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4409 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_27_le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4410 (all Z_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),N))))) # label(fact_210_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4411 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C))))) # label(fact_1003_div__mult__swap) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4412 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_800_mult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4413 (all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (exists K_1 (J_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)))))) # label(fact_860_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4414 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) != zero_zero(int))))) # label(fact_810_inv__not__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4415 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_494_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4416 (all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U_1)) = U_1) # label(fact_4315_card__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4417 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y))))))) # label(fact_2705_real__root__less__mono__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4418 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D)))))))) # label(fact_4976_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4419 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,zero_zero(nat)),D_1)) <-> D_1 = one_one(nat))) # label(fact_2867_coprime__0_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4420 (all X_a (real_n2089651433ebra_1(X_a) -> (all Z_1 hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),Z_1))))) # label(fact_3575_norm__of__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4421 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_721_diff__square) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4422 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,re,X))) # label(fact_4690_Re_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4423 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))))) # label(fact_805_inv__not__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4424 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_4))))) # label(fact_674_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4425 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,X)),N) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)))) # label(fact_1145_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4426 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_1778_norm__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4427 (all N_1 hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1)) = hAPP(nat,nat,fact_fact(nat),N_1)) # label(fact_4541_fact__altdef__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4428 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4554_LIM__minus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4429 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) & -hBOOL(hAPP(nat,bool,prime,N)) -> (exists M_2 exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_2),K_1) = N & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_1)))))) # label(fact_3091_not__prime__ex__mk) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4430 (all X hAPP(complex,real,re,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_3019_complex__Re__inverse) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4431 (all X_a all X_b (ordere216010020id_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all B_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,B_4))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4293_setsum__mono2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4432 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),one_one(int))))))) # label(fact_190_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4433 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),N)))) # label(fact_4366_dvd__gcd__D2__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4434 (all N all M hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),product_Pair(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M)) = hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),quickc495462417de_int,N),M)) # label(fact_3175_div__mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4435 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2958_compl__le__swap1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4436 (all Y exists X_2 (hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)))) # label(fact_2284_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4437 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),X)))) # label(fact_1933_ln__less__self) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4438 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all G all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_2))))))))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4439 (all X_1 all Y_1 (hAPP(int,real,real_1(int),Y_1) = hAPP(int,real,real_1(int),X_1) <-> ti(int,X_1) = ti(int,Y_1))) # label(fact_3328_real__of__int__inject) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4440 (all X_b all X_a (uminus(X_a) -> (all A_3 all X_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_3,X_1)) = hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_3),X_1)))) # label(fact_2928_uminus__apply) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4441 (all P_1 hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),P_1),semiring_1_of_nat(int)))) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))) # label(fact_3807_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4442 (all P_5 all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N)))))) # label(fact_454_zpower__zdvd__prop1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4443 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))))) # label(fact_486_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4444 (all Z_1 hAPP(complex,complex,cnj,Z_1) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,Z_1)))) # label(fact_3012_cnj__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4445 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4764_metric__LIM__I) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4446 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) & hBOOL(hAPP(nat,bool,P_1,K_1)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2))))))))) # label(fact_859_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4447 (all X hAPP(real,real,inverse_inverse(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,real,ratreal,hAPP(rat,rat,inverse_inverse(rat),X))) # label(fact_3772_real__inverse__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4448 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1956_in__mono) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4449 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),N_1)) <-> ti(int,Ma) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),Ma)))) # label(fact_3457_zdvd__iff__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4450 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B))) # label(fact_1358_zmod__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4451 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1706_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4452 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_4815_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4453 (all N all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) & (M = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_2481_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4454 (all X_1 all N_1 (one_one(nat) = X_1 | N_1 = zero_zero(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1) = one_one(nat))) # label(fact_730_exp__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4455 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))))) # label(fact_3377_ge__one__powr__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4456 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,inverse_inverse(X_a),B_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_2) <-> ti(X_a,B_1) = ti(X_a,A_2))))) # label(fact_2522_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4457 (all Ma all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))))) # label(fact_1423_nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4458 (all X_1 all Y_1 all F ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real)))) -> hAPP(real,real,F,Y_1) = hAPP(real,real,F,X_1))) # label(fact_2731_DERIV__isconst__all) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4459 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)))) # label(fact_3346_powr__ge__pzero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4460 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,abs_abs(X_a),Ma)),K)))))) # label(fact_1846_abs__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4461 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq)))) # label(fact_3489_pair__leqI1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4462 (all L all K ((zero_zero(int) != ti(int,K) -> (ti(int,L) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K)) & (zero_zero(int) != ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),L),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))))) & (ti(int,K) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)))) # label(fact_4063_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4463 (all W hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),W)) = hAPP(int,nat,number_number_of(nat),W)) # label(fact_1113_nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4464 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_1882_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4465 (all X_a all X_b product_snd(X_a,X_b) = ti(fun(product_prod(X_a,X_b),X_b),product_snd(X_a,X_b))) # label(tsy_c_Product__Type_Osnd_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4466 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,A_2)),A_3)))) # label(fact_4507_cnj_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4467 (all M all N hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),M),N),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N)) # label(fact_3084_xzgcd__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4468 (all K_4 all I_1 all J_2 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),K_4))))) # label(fact_3463_zrelprime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4469 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))))) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4470 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1)),L) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1))) # label(fact_4571_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4471 (all X_a (comple44059174attice(X_a) -> complete_Sup_Sup(X_a) = ti(fun(fun(X_a,bool),X_a),complete_Sup_Sup(X_a)))) # label(tsy_c_Complete__Lattice_OSup__class_OSup_1_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4472 (all X_b all X_a all B_1 all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (ti(X_b,B_1) = hAPP(X_a,X_b,F,X_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)))))) # label(fact_3639_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4473 (all N all F_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)))))) # label(fact_961_zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4474 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4475 (all Ma all N_1 (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(nat,int,semiring_1_of_nat(int),N_1) <-> Ma = N_1)) # label(fact_1486_int__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4476 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))) # label(fact_4233_setsum__diff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4477 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1))))))) # label(fact_4082_mult__left_Osums) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4478 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_812_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4479 (all K_4 all L_4 hAPP(int,int,bit1,L_4) != hAPP(int,int,bit0,K_4)) # label(fact_119_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4480 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_4967_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4481 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1))))) # label(fact_3590_of__int__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4482 (all X_a (real_normed_field(X_a) -> (all G all E_2 all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_2)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_2),hAPP(X_a,X_a,F,X_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))))) # label(fact_3899_DERIV__quotient) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4483 (all P_1 ((all X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))))) # label(fact_1106_all__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4484 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1681_divide__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4485 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4794_dvd_OmonoI) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4486 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1909_real__sqrt__ge__abs2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4487 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int))) = hAPP(int,rat,number_number_of(rat),K_4)) # label(fact_3707_Frct__code__post_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4488 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_1301_zle__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4489 (all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))))) # label(fact_1024_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4490 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K))))) # label(fact_3802_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4491 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C))) # label(fact_919_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4492 (all X_a (abs_if(X_a) -> abs_abs(X_a) = ti(fun(X_a,X_a),abs_abs(X_a)))) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4493 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4494 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int)) = ti(int,Z_1)) # label(fact_134_zadd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4495 (all A_1 hAPP(complex,real,im,hAPP(real,complex,cis,A_1)) = hAPP(real,real,sin,A_1)) # label(fact_3027_Im__cis) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4496 (all Y all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N) = X -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X) = Y))) # label(fact_2674_odd__real__root__unique) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4497 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_820_add__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4498 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),A_2)))))) # label(fact_4906_isCont__rabs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4499 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2401_sin__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4500 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1060_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4501 (all X_b all X_c all X_a all F all A_2 all B_1 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,A_2),B_1)) # label(fact_3993_split__conv) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4502 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_4)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_4),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1757_half__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4503 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_70_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4504 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))))) # label(fact_1168_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4505 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4506 (all X_a (semiring_div(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),C_1),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C_1)))))))) # label(fact_967_div__dvd__div) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4507 (all Z all Y_1 all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3))))))) # label(fact_3714_SupInf_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4508 (all P_1 all P_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2845_plusinfinity) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4509 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4582_LIM__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4510 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1659_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4511 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5))))) # label(fact_880_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4512 (all X all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),M) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,phi,M))),one_one(int)),M))))) # label(fact_3427_Euler__Fermat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4513 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1742_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4514 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E all F_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)))) # label(fact_3150_prod__induct6) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4515 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a)) = dvd_dvd(X_a))) # label(tsy_c_Rings_Odvd__class_Odvd_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4516 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1910_arctan__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4517 (all Ma all X_3 ((all Y1 all Y2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y1),X_3)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y2),X_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y1),Y2),Ma)) -> ti(int,Y1) = ti(int,Y2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)))) # label(fact_2916_ResSet__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4518 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A0),A1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_2),Y_2))) -> ((zero_zero(nat) != Y_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Y_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_2),Y_2)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,X_2),Y_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,A0),A1))))) # label(fact_3672_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4519 (all A_1 all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))))) # label(fact_1194_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4520 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))))) # label(fact_680_diff__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4521 (all X_a (linordered_ring(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))))) # label(fact_46_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4522 (all X_b all X_a (topological_space(X_b) & metric_space(X_a) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4652_metric__LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4523 (all X_a size_size(list(X_a)) = ti(fun(list(X_a),nat),size_size(list(X_a)))) # label(tsy_c_Nat_Osize__class_Osize_0_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4524 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2959_compl__le__swap2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4525 (all X_a (real_algebra_1(X_a) -> (all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,ring_1_of_int(real),Z_1))))) # label(fact_3573_of__real__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4526 (all X_b all X_a ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a)) = image(X_b,X_a)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4527 (all U all M all N all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N)))) # label(fact_753_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4528 (all N_1 all Ma hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_max(nat),N_1))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),Ma)) # label(fact_4954_max__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4529 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_2))) <-> zero_zero(X_a) != ti(X_a,A_2))))) # label(fact_1864_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4530 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,one_one(nat)),A_1))) # label(fact_2854_coprime__1_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4531 (all X_a (semiring_0(X_a) & power(X_a) -> (all N ((N != zero_zero(nat) -> zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N)) & (N = zero_zero(nat) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N)))))) # label(fact_446_power__0__left) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4532 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_445_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4533 (all X all Y ((zero_zero(nat) = Y -> hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int))) & (Y != zero_zero(nat) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),Y))))) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y)))) # label(fact_3113_bezw_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4534 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_493_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4535 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4536 (all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) <-> A_2 = zero_zero(nat))) # label(fact_891_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4537 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int)))))) # label(fact_982_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4538 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Y_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),Y_1)),A_3) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Y_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)))))) # label(fact_3959_setprod__constant) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4539 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)) -> X = one_one(real)))) # label(fact_1938_ln__eq__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4540 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4641_aset_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4541 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_2028_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4542 (all V_3 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V_3)))) # label(fact_87_add__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4543 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) # label(fact_3754_divide__rat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4544 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2)))))) # label(fact_3917_DERIV__sin__circle__all) # label(axiom) # label(non_clause). [assumption]. 7.81/7.84 4545 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (zero_zero(X_a) != ti(X_a,C_1) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1678_divide__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4546 (all M all X hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)) # label(fact_911_StandardRes__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4547 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1918_DiffE) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4548 (all X_a (real_normed_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_879_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4549 (all X_a all R_1 all A_2 ((exists X_2 ((all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Xa),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Xa)))) & ti(X_a,A_2) = ti(X_a,X_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2)))) # label(fact_2918_accp_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4550 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all A_2 all L_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4581_LIM__offset__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4551 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_1572_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4552 (all X_1 ((exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X_1)) | (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X_1)) <-> zero_zero(real) = hAPP(real,real,sin,X_1))) # label(fact_2411_sin__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4553 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))) # label(fact_3209_Bnor__mem__zg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4554 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M))))))) # label(fact_417_zcong__not) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4555 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_1662_add__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4556 (all X_a (real_field(X_a) -> (all A_1 all B all C all D all H_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)),H_2))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C)),H_2)),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))),H_2)))) # label(fact_1801_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4557 (all X_a (dist_norm(X_a) -> ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)) = dist_dist(X_a))) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4558 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)) = N))) # label(fact_1491_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4559 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1368_even__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4560 (all X_b all X_c all X_a (semiring_0(X_a) -> (all F all A_3 all G all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B_2)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B_2)),A_3)))) # label(fact_4209_setsum__product) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4561 (all X_a (zero(X_a) -> (all Diff all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,zero_zero(nat)),zero_zero(X_a)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(X_a,fun(nat,real),hAPP(fun(nat,fun(X_a,real)),fun(X_a,fun(nat,real)),combc(nat,X_a,real),Diff),zero_zero(X_a)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,N_1),zero_zero(X_a))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))))))) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4562 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_391_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4563 (all K all L (K = L <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,K) = hAPP(quickcheck_code_int,int,quickcheck_int_of,L))) # label(fact_3162_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4564 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4565 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_3297_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4566 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))))))) # label(fact_176_less__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4567 (all M all N hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_2308_real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4568 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),B_1)),sequentially))))))) # label(fact_4739_scaleR_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4569 (all X_a (real_algebra_1(X_a) -> (all F all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),F)),X_2) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),F),X_2))))) # label(fact_4111_diffs__of__real) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4570 (all P_1 all I hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),P_1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3869_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4571 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_2988_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4572 (all B_1 all Q_2 all R_1 hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),R_1)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) # label(fact_3798_adjust__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4573 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> one_one(int) = ti(int,A_1) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)) = ti(int,A_1)))))) # label(fact_534_zcong__square__zless) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4574 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)) # label(fact_541_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4575 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(real)) # label(fact_2387_sin__cos__squared__add2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4576 (all M all N all K_4 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),K_4))),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) # label(fact_3447_zgcd__zadd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4577 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,complex,cnj,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)))) # label(fact_4041_cnj_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4578 (all X all Y all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y)))))) # label(fact_712_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4579 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Q_3),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,uminus_uminus(int),P_5)),hAPP(int,int,uminus_uminus(int),Q_3))) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)))) # label(fact_3718_normalize__negative) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4580 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1916_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4581 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_945_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4582 (all X_a (linordered_idom(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),X)) = ti(X_a,X)))) # label(fact_2215_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4583 (all Z_1 hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1) # label(fact_2994_Re__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4584 (all X_a (ring_1(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),ring_1_Ints(X_a)))))) # label(fact_3804_Ints__of__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4585 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3076_prime__dvd__square) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4586 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = one_one(nat) <-> one_one(nat) = N_1 & one_one(nat) = Ma)) # label(fact_590_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4587 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1)))))))) # label(fact_443_power__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4588 (all X_a (real_normed_field(X_a) -> (all H_2 all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),H_2))),hAPP(X_a,X_a,inverse_inverse(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))),H_2)))))) # label(fact_2620_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4589 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))))))) # label(fact_4129_summable__le) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4590 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_785_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4591 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),L) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1))) # label(fact_4202_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4592 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U))))) # label(fact_1839_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4593 (all X_b all X_c all X_a product_prod_rec(X_b,X_c,X_a) = ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a))) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4594 (all X_a (linordered_idom(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),B_1)))))) # label(fact_2083_abs__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4595 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_1444_le__div__geq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4596 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M)) # label(fact_3533_mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4597 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> -(all N_2 hAPP(nat,int,semiring_1_of_nat(int),N_2) != ti(int,K_4)))) # label(fact_1489_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4598 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> Z_2 = hAPP(real,real,G,hAPP(real,real,F,Z_2)))) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1)))),E)) -> Y_2 = hAPP(real,real,F,hAPP(real,real,G,Y_2)))))))))) # label(fact_4931_isCont__inv__fun__inv) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4599 (all A_2 all D_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),A_2)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)))) # label(fact_4311_arith__series__int) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4600 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1)),hAPP(X_a,X_a,sgn_sgn(X_a),B)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2205_sgn__times) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4601 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_826_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4602 (all C_2 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C_2)))) # label(fact_3663_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4603 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3824_Ints__add) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4604 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1177_transfer__morphism__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4605 (all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) -> hAPP(nat,nat,suc,zero_zero(nat)) = X | X = zero_zero(nat))) # label(fact_1319_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4606 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4607 (all A_1 all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),A_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) # label(fact_3220_gcd__commute__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4608 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = zero_zero(X_a) & ti(X_a,X_1) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) = zero_zero(X_a))))) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4609 (all X_a (real_vector(X_a) -> (all X all Y all A_1 (A_1 != zero_zero(real) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) -> ti(X_a,Y) = ti(X_a,X)))))) # label(fact_4701_scaleR__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4610 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_1856_abs__add__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4611 (all A_3 all B_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))))) # label(fact_3647_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4612 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)))))))) # label(fact_1672_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4613 (all T_1 preorder(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4614 (all P_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),P_4)) & (all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_2),P_4)) -> M_2 = one_one(nat) | P_4 = M_2)) <-> hBOOL(hAPP(nat,bool,prime,P_4)))) # label(fact_3067_prime__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4615 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1))))))) # label(fact_797_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4616 (all X_a (linordered_idom(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_2426_power__even__abs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4617 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real)))))) # label(fact_2692_real__root__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4618 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2127_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4619 (all K_4 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),M)))))) # label(fact_1117_div__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4620 (all A_1 hAPP(real,complex,cis,A_1) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) # label(fact_3032_cis__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4621 (all X_a all A_1 all B hAPP(int,X_a,hAPP(int,fun(int,X_a),frac(X_a),A_1),B) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) # label(fact_4420_Nitpick_Ofrac__def) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4622 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_2878_floor__minus__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4623 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4462_LIMSEQ__Suc) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4624 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3155_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4625 (all X all Y all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),R_4)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),R_4))) # label(fact_2808_Complex__mult__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4626 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_2768_i__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4627 (all X hAPP(real,real,uminus_uminus(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,real,ratreal,hAPP(rat,rat,uminus_uminus(rat),X))) # label(fact_3769_real__uminus__code) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4628 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X -> Y = zero_zero(real))) # label(fact_1647_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption]. 7.81/7.85 4629 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),sequentially)))))) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4630 (all X_a (ordered_semiring(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_367_mult__mono) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4631 (all X_a (linordered_ring(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))))) # label(fact_381_zero__le__square) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4632 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) <-> -hBOOL(hAPP(int,bool,nat_neg,X_1)))) # label(fact_1503_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4633 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2262_arccos__lbound) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4634 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))))) # label(fact_4940_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4635 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,pred,K_4)),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_2909_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4636 (all R1 all A_1 all R2 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3171_rcis__mult) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4637 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a))),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) -> ti(int,Z_1) = hAPP(X_a,int,archimedean_ceiling(X_a),X)))))) # label(fact_3606_ceiling__unique) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4638 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B_1) <-> hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,B_1))))) # label(fact_2042_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4639 (all X_a (ord(X_a) -> min(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4640 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4592_LIM__rabs__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4641 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1972_psubsetD) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4642 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,norm_norm(complex),X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2094_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4643 (all X_b all X_a (ord(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2834_xt6) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4644 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4445_LIMSEQ__add__const) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4645 (all X_a (semiring_div(X_a) -> (all C all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_931_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4646 (all R1 all A_1 all R2 all B hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B))) # label(fact_3172_rcis__divide) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4647 (all X_a (real_normed_vector(X_a) -> (all K all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))))))))) # label(fact_4167_sums__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4648 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))) # label(fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4649 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4021_summable__sin) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4650 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> one_one(nat) = hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) = hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1537_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4651 (all X_a (real_normed_field(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))))) # label(fact_4231_sums__group) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4652 (all X_1 all N_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1)))))))) # label(fact_4278_Maclaurin__bi__le) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4653 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_2530_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4654 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),K_4))))) # label(fact_1087_div__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4655 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D))))) # label(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4656 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))))))) # label(fact_3316_Cauchy__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4657 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2484_fact__mono__nat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4658 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1))))))) # label(fact_4666_scaleR__left_Osums) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4659 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),A_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))) # label(fact_138_power3__eq__cube) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4660 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),Y_1),X_1)))) # label(fact_4244_Sup__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4661 (all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_1295_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4662 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))),U_1)) # label(fact_4261_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4663 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2830_minf_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4664 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = one_one(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = ti(X_a,B))))) # label(fact_2552_inverse__unique) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4665 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),Y_1) = hAPP(int,X_a,number_number_of(X_a),X_1) <-> ti(int,Y_1) = ti(int,X_1))))) # label(fact_89_eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4666 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),one_one(int)),P_4)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),P_4)))) # label(fact_513_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4667 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_2),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_4))))) # label(fact_29_zle__trans) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4668 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2224_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4669 (all I_1 all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)))) # label(fact_562_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4670 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2353_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4671 (all X all Y hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) # label(fact_3016_complex__mult__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4672 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),X)))) # label(fact_3392_lemma__floor2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4673 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N) # label(fact_589_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4674 (all X all K_4 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4) = hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4))) # label(fact_1618_real__sqrt__power) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4675 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) # label(fact_2981_Im_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4676 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))))) # label(fact_594_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4677 (all X_a all P ti(X_a,P) = hAPP(X_a,X_a,combi(X_a),P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4678 (all X_a complex_case(X_a) = ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_case(X_a))) # label(tsy_c_Complex_Ocomplex_Ocomplex__case_res) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4679 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_1155_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4680 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))),one_one(real)))) # label(fact_2359_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4681 (all X_b all X_a (real_n1866405975lgebra(X_b) & topological_space(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (zero_zero(X_b) != ti(X_b,L_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4588_LIM__inverse) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4682 (all Nat_1 hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2920_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4683 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1869_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4684 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2026_le__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4685 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X))))) # label(fact_2595_exp__gt__one) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4686 (all X_b all X_a (ord(X_a) & real_normed_vector(X_b) -> (all X_3 all M_1 ((all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,X_3,M_1)),hAPP(X_a,X_b,X_3,N_2)))),one_one(real))))) -> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,M_1))))))))))) # label(fact_1838_lemmaCauchy) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4687 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))))) # label(fact_442_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4688 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> ti(X_a,A_2) = ti(X_a,B_1))))) # label(fact_2044_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4689 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_3258_gcd__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4690 (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_1581_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4691 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_1414_Suc__diff__1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4692 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> (exists Y_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2) = ti(int,X_1)))) # label(fact_1447_even__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4693 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_1750_Union__upper) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4694 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3300_one__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4695 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1)))))) # label(fact_2182_neg__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4696 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,B) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Q_3),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)))))))) # label(fact_1185_zmult2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4697 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,exp(real),X)) = hAPP(X_a,X_a,exp(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2799_exp__of__real) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4698 (all X_a (linordered_idom(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))) # label(fact_7_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4699 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),K)))))) # label(fact_4988_atMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4700 (all N -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2176_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption]. 7.90/7.85 4701 (all X_b all X_a (semiring_1(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3))))) # label(fact_3928_of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4702 (all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool,hAPP(product_prod(product_prod(int,int),product_prod(int,int)),fun(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool),member(product_prod(product_prod(int,int),product_prod(int,int))),hAPP(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int)),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int))),product_Pair(product_prod(int,int),product_prod(int,int)),X_1),Y_1)),ratrel)) <-> zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),Y_1) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) & hAPP(product_prod(int,int),int,product_snd(int,int),X_1) != zero_zero(int))) # label(fact_3732_ratrel__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4703 (all X_a all One all Times all A_2 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),hAPP(nat,nat,suc,N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),Times,A_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),N_1))) # label(fact_2841_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4704 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_485_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4705 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4706 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4757_scaleR__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4707 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (ti(X_a,Y) != zero_zero(X_a) -> (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1))))))) # label(fact_1722_add__frac__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4708 (all X_a all X_b all P_4 hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4) = hAPP(product_prod(X_a,X_b),X_a,hAPP(fun(X_a,fun(X_b,X_a)),fun(product_prod(X_a,X_b),X_a),product_prod_case(X_a,X_b,X_a),combk(X_a,X_b)),P_4)) # label(fact_4004_fst__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4709 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))))) # label(fact_3386_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4710 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_2967_cnj_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4711 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4712 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2289_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4713 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3698_Rats__minus) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4714 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_387_mult__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4715 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Y_1)))))) # label(fact_60_le__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4716 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))) # label(fact_2514_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4717 (all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) # label(fact_3432_zgcd__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4718 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),min_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2102_mult__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4719 (all N all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),A_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),B)))))) # label(fact_3077_prime__divprod__pow) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4720 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2339_cos__diff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4721 (all X_1 all W_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),W_1) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(int,nat,number_number_of(nat),W_1)))))) # label(fact_228_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4722 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_3212_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4723 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_517_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4724 (all K all Ma all N_1 (N_1 = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) # label(fact_524_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4725 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> zero_zero(X_b) = hAPP(X_a,X_b,G,X_2))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)))))) # label(fact_4307_setsum_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4726 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4727 (all U all X (hAPP(real,real,exp(real),U) = X -> U = hAPP(real,real,ln,X))) # label(fact_2508_exp__ln__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4728 (all X_1 all Y_1 ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven)))) # label(fact_1272_even__diff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4729 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),one_one(int))),K_4))))))) # label(fact_3200_fact__less__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4730 (all F all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),K) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))))) # label(fact_2667_DERIV__const__ratio__const) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4731 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc))))),R_1),sequentially))) # label(fact_4492_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4732 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = one_one(X_b))))) # label(fact_3951_setprod__infinite) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4733 (all E_1 all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),E_1)))))) # label(fact_2856_coprime__divisors) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4734 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))))) # label(fact_1125_zless__nat__conj) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4735 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_1399_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4736 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,uminus_uminus(int),X_1))))) # label(fact_2152_even__neg) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4737 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))) # label(fact_522_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4738 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1058_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4739 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_1 = zero_zero(nat))) # label(fact_1321_less__Suc0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4740 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))) # label(fact_4970_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4741 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1234_less__SucI) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4742 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_2701_real__root__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4743 (all A_2 all B_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zEven))))) # label(fact_1366_even__plus__odd__prop1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4744 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1827_card__psubset) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4745 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1))))) # label(fact_311_dvd__refl) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4746 (all Code_numeral_3 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_3) != zero_zero(code_code_numeral)) # label(fact_2947_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4747 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(int,int,number_number_of(int),V) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V))))) # label(fact_3283_ceiling__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4748 (all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,real_1(int),A_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)))) # label(fact_3367_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4749 (all X_a (linorder(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X))))))) # label(fact_4977_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4750 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all K hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4182_sumr__offset3) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4751 (all A_1 all M all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),M))) # label(fact_355_zcong__zmult__self) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4752 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,Y)),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),X)))))) # label(fact_2619_ln__x__over__x__mono) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4753 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_3332_real__of__int__diff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4754 (all X_a (ord(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)) = ord_max(X_a))) # label(fact_4947_max__ord__max) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4755 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))))))) # label(fact_1017_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4756 (all X_a (real_field(X_a) -> (all X all Y (zero_zero(real) != Y -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)))))) # label(fact_2805_nonzero__of__real__divide) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4757 (all X_a (real_vector(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),one_one(real)),X)))) # label(fact_4706_real__vector_Oscale__one) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4758 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_4877_fin__bijRr) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4759 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_1422_tsub__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4760 (all X (zero_zero(real) != X -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),X)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,arctan,X)))) # label(fact_2187_arctan__inverse) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4761 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,X))) = one_one(real)) # label(fact_2336_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4762 (all X_a (real_normed_algebra(X_a) -> (all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B) = zero_zero(X_a)))) # label(fact_876_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4763 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4793_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4764 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),E_3)))))))) # label(fact_3823_DERIV__add) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4765 (all I all J all F ((all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J)))))) # label(fact_1205_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4766 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_3)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3))))))) # label(fact_3497_BseqI) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4767 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_3288_divides__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4768 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))))) # label(fact_2360_natfloor__add) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4769 (all A_1 (one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> one_one(int) = hAPP(int,int,abs_abs(int),A_1))) # label(fact_1985_power2__eq1__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4770 (all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),A_1)))) # label(fact_2642_log__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4771 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),A_2)),A_3)))))) # label(fact_4459_tendsto__norm) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4772 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) # label(fact_2395_cos__double) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4773 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_573_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4774 (all X_a ti(fun(product_prod(int,int),X_a),abs_Frac(X_a)) = abs_Frac(X_a)) # label(tsy_c_Nitpick_OAbs__Frac_res) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4775 (all X_b (ord(X_b) & number(X_b) -> (all U all V ((-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)))))) # label(fact_4831_min__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4776 (all B_5 all A_6 all A_1 all B (zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_6),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = A_1 -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = B -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_6),B_5) = one_one(nat))))) # label(fact_3286_gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4777 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))) # label(fact_3756_mult__rat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4778 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> one_one(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_3))))))) # label(fact_3960_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4779 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_4010_summable__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4780 (all X all Y all Xa_1 all Ya hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1606_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4781 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_971_odd__mult__odd__prop) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4782 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)))) # label(fact_306_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4783 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),ring_1_Ints(real)))) # label(fact_3852_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4784 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2779_Pow__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4785 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1))))) # label(fact_793_right__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4786 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_3)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3)))))) # label(fact_3796_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4787 (all M all N all K_4 ((zero_zero(nat) = K_4 -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = zero_zero(nat)) & (K_4 != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))))) # label(fact_1099_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4788 (all Z all Z_3 ((hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3)) = hAPP(int,nat,nat_1,Z)) & (-hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3))))) # label(fact_3835_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4789 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> Y != X)) # label(fact_638_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4790 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_514_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4791 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,inverse_inverse(real),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),hAPP(real,real,inverse_inverse(real),X1_1)))))))) # label(fact_2591_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4792 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2225_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4793 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1))))))) # label(fact_4319_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4794 (all X_a (number_semiring(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_1212_number__of__int) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4795 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_1774_norm__minus__commute) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4796 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),zero_zero(X_a)),A_1)))) # label(fact_965_div__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4797 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_985_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4798 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int)) = hAPP(nat,rat,semiring_1_of_nat(rat),K_4)) # label(fact_3743_Fract__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4799 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2541_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4800 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V)) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_2888_floor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4801 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),im),A_2))) # label(fact_4893_Im_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4802 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(real) = hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,real,number_number_of(real),V)))) # label(fact_2358_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4803 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_2606_inverse__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4804 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> X != Y)) # label(fact_643_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4805 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))))) # label(fact_694_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4806 (all Diff all F all N_1 all H ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4)) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),zero_zero(real))))))) # label(fact_4283_Maclaurin__minus__objl) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4807 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1))))) # label(fact_4959_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4808 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)))))) # label(fact_1609_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4809 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1))))) # label(fact_88_le__imp__0__less) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4810 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)))) # label(fact_298_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4811 (all A_2 all B_1 all C_1 all D_1 all X_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_1),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)),C_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) = one_one(int) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),C_1) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_1),A_2) -> (exists K_1 exists L_3 exists M_2 (ti(int,B_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),hAPP(int,nat,nat_1,X_1)) & ti(int,C_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),hAPP(int,nat,nat_1,X_1)) & ti(int,A_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1))))))))))) # label(fact_3481_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4812 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (zero_zero(real) != hAPP(real,real,cos,Y) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))))) # label(fact_2371_add__tan__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4813 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1334_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4814 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2))))) # label(fact_4115_Im_Osums) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4815 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_1)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C)))) # label(fact_326_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4816 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))) # label(fact_1071_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4817 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C))))) # label(fact_948_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4818 (all X_b all X_a (semiring_1(X_a) -> (all Y_1 all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),Y_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),Y_1)))) # label(fact_4228_setsum__constant) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4819 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_172_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4820 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5)))))) # label(fact_1164_Euler__part2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4821 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4919_isCont__root__pos) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4822 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4823_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4823 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2817_of__real_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4824 (all X_a (comm_monoid_add(X_a) -> (all F all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4173_sumr__group) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4825 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))))) # label(fact_72_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4826 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),min_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_2105_divide__minus1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4827 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4131_monoI1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4828 (all J_2 all A_1 all P_5 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)))) # label(fact_835_aux______1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4829 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_392_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4830 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4427_setprod__dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4831 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> (exists X_2 exists Y_2 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),Y_2)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),Y_2)) = one_one(nat))))) # label(fact_2896_coprime__bezout) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4832 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4723_scaleR__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4833 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X))),one_one(real)))) # label(fact_2218_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4834 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4835 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) != zero_zero(X_a) | ti(X_a,X_1) != zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4836 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_4849_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4837 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all G all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),G),B_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))))) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4838 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) != ti(X_a,X_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))))))) # label(fact_3513_zero__less__dist__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4839 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))))) # label(fact_864_d22set__le__swap) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4840 (all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)))) # label(fact_1110_mod__if) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4841 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_2106_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4842 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_574_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4843 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),L_4)))))) # label(fact_586_mult__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.90/7.86 4844 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))))))) # label(fact_4531_summable) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4845 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X)))) # label(fact_2683_real__root__mult__exp) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4846 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_124_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4847 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B))))))) # label(fact_2081_abs__leI) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4848 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5))))))) # label(fact_1022_zdiv__mono2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4849 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_1297_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4850 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2018_minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4851 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2886_number__of__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4852 (all X_a (real_normed_field(X_a) -> deriv(X_a) = ti(fun(fun(X_a,X_a),fun(X_a,fun(X_a,bool))),deriv(X_a)))) # label(tsy_c_Deriv_Oderiv_res) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4853 (all X_a (real_algebra_1(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),R_4)),X)))) # label(fact_4680_scaleR__conv__of__real) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4854 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4745_scaleR_OLIM__prod__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4855 (all X_a (linordered_idom(X_a) -> (all K_4 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_4),hAPP(X_a,X_a,sgn_sgn(X_a),K_4)) = hAPP(X_a,X_a,abs_abs(X_a),K_4)))) # label(fact_2214_abs__sgn) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4856 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B))))) # label(fact_3354_powr__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4857 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all W_1 all B_1 all C_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1753_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4858 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B))))) # label(fact_4712_scaleR_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4859 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(nat,nat,suc,hAPP(int,nat,nat_1,Z_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)))) # label(fact_1435_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4860 (all X_a (real_algebra_1(X_a) -> (all X_1 (hAPP(real,X_a,of_real(X_a),X_1) = zero_zero(X_a) <-> X_1 = zero_zero(real))))) # label(fact_2781_of__real__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4861 (all X_c all X_b all X_a (topological_space(X_c) & topological_space(X_b) & metric_space(X_a) -> (all G all L all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4923_metric__isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4862 (all X_a (number_ring(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(int,X_a,number_number_of(X_a),min_1)))) # label(fact_1474_power__m1__odd) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4863 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1703_frac__less2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4864 (all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5) = one_one(int)))) # label(fact_3466_zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4865 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4596_Re_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4866 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,K))))) # label(fact_55_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4867 (all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))))) # label(fact_837_wset__mem__mem) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4868 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a))) # label(fact_1281_of__nat__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4869 (all X_a (topological_space(X_a) -> (all K hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),K),sequentially))))) # label(fact_4464_LIMSEQ__const) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4870 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)))))) # label(fact_3592_floor__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4871 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3598_floor__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4872 (all X_a (real_n2089651433ebra_1(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)))) = hAPP(nat,X_a,F,zero_zero(nat))))) # label(fact_3973_powser__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4873 (all X_a all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_1826_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4874 (all N -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),zero_zero(real)))) # label(fact_2303_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4875 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1579_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4876 (all R_4 all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(rat,product_prod(int,int),quotient_of,R_4) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3724_quotient__of__denom__pos) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4877 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2389_cos__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4878 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))))))) # label(fact_3659_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4879 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> -(all K_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1) != ti(int,X_1)))) # label(fact_1477_zEvenE) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4880 (all X hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))) # label(fact_3004_Re_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4881 (all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) = hAPP(complex,complex,uminus_uminus(complex),X)) # label(fact_3015_complex__minus__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4882 (all Nat_4 hAPP(nat,nat,suc,Nat_4) != zero_zero(nat)) # label(fact_1224_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4883 (all X all Y all Z_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z_1)) # label(fact_203_zpower__zpower) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4884 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat))) # label(fact_4960_max__0R) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4885 (all X_1 all P_4 (hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) != zero_zero(int) <-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_1012_StandardRes__prop3) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4886 (all K_4 all L_4 hAPP(int,int,bit1,K_4) != hAPP(int,int,bit0,L_4)) # label(fact_118_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4887 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1))))) # label(fact_1947_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4888 (all B all A_1 all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4)) # label(fact_920_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4889 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (N != M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_566_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4890 (all Ma all X_2 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_2),Xa),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma),X_2),Xa)))) # label(fact_4872_zcongm__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4891 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) & power(X_b) -> (all N_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),A_2)))))) # label(fact_4902_isCont__power) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4892 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),D)),D))) # label(fact_1925_zdvd__self__abs2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4893 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_3800_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4894 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),cnj),hAPP(complex,complex,cnj,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4570_cnj_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4895 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4824_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4896 (all Ma all X_1 hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),norRRset,Ma)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) # label(fact_3878_noXRRset__def) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4897 (all X_a (semiring_1(X_a) -> (all N_1 hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),one_one(X_a))),N_1),zero_zero(X_a)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_4158_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4898 (all X_a (real_normed_vector(X_a) -> (all X_1 (hAPP(X_a,X_a,sgn_sgn(X_a),X_1) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_2200_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4899 (all X_a (ring_char_0(X_a) -> (all Z (hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a) <-> ti(int,Z) = zero_zero(int))))) # label(fact_3578_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4900 (all X_a (divisi14063676e_zero(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)))) # label(fact_2526_inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4901 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_937_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4902 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),A_1))))) # label(fact_1002_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4903 (all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)))) # label(fact_476_dvd__reduce) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4904 (all A_1 all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_184_zadd__power2) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4905 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_496_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4906 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))))) # label(fact_675_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4907 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),zero_zero(real)))))) # label(fact_1950_ln__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4908 (all X_2 hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,X_2)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),X_2)) # label(fact_4122_cos__fdiffs) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4909 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),M)))) # label(fact_4367_dvd__gcd__D1__int) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4910 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1))))) # label(fact_1729_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4911 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> hAPP(int,nat,nat_1,Z_1) = zero_zero(nat))) # label(fact_1123_nat__le__0) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4912 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)))) # label(fact_3061_prime__coprime__strong) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4913 (all X_1 all Y_1 all Z (Y_1 = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z) <-> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z) = X_1)) # label(fact_1178_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4914 (all X_b all X_a (comm_monoid_add(X_b) & ord(X_a) -> (all F all G all B_1 all D_1 all A_2 all C_1 (ti(X_a,A_2) = ti(X_a,C_1) -> (ti(X_a,D_1) = ti(X_a,B_1) -> ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),D_1)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)))))))) # label(fact_4302_setsum__ivl__cong) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4915 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_1 all A_2 all B_1 (ti(X_a,B_1) != ti(X_a,A_2) & ti(X_a,D_1) != ti(X_a,C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D_1)))))) # label(fact_241_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4916 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)))) # label(fact_3363_real__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4917 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_432_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4918 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),Q_3) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3))))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4919 (all X all K_4 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (N != zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) -> (exists I_2 X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2)))))) # label(fact_3087_prime__power__exp) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4920 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N) != zero_zero(X_a))))) # label(fact_328_field__power__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4921 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1868_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4922 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> X != Y)) # label(fact_642_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4923 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))) # label(fact_1088_div__le__dividend) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4924 (all X_a (semiring_div(X_a) -> (all Y all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Z_1)))))) # label(fact_1005_div__add) # label(axiom) # label(non_clause). [assumption]. 7.90/7.87 4925 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1673_divide__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.99/7.99 4926 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),field_char_0_Rats(real)))) # label(fact_3682_Rats__real__nat) # label(axiom) # label(non_clause). [assumption]. 7.99/7.99 4927 (all X_a ti(fun(fun(X_a,bool),nat),finite_card(X_a)) = finite_card(X_a)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption]. 7.99/7.99 4928 (all X_a (semiri456707255roduct(X_a) -> (all W_1 all Y_1 all X_1 all Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z)) <-> ti(X_a,Z) = ti(X_a,Y_1) | ti(X_a,W_1) = ti(X_a,X_1))))) # label(fact_244_crossproduct__eq) # label(axiom) # label(non_clause). [assumption]. 7.99/7.99 7.99/7.99 ============================== end of process non-clausal formulas === 7.99/7.99 7.99/7.99 ============================== PROCESS INITIAL CLAUSES =============== 7.99/7.99 7.99/7.99 ============================== PREDICATE ELIMINATION ================= 7.99/7.99 4929 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_461_one__less__power) # label(axiom). [clausify(40)]. 7.99/7.99 4930 linordered_semidom(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semidom) # label(axiom). [assumption]. 7.99/7.99 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(4929,a,4930,a)]. 7.99/7.99 4931 -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_1278_zero__le__imp__of__nat) # label(axiom). [clausify(41)]. 7.99/7.99 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))). [resolve(4931,a,4930,a)]. 7.99/7.99 4932 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2494_of__nat__fact__ge__zero) # label(axiom). [clausify(149)]. 7.99/7.99 4933 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom). [assumption]. 7.99/7.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(4933,a,4929,a)]. 7.99/7.99 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(4933,a,4931,a)]. 7.99/7.99 4934 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_448_power__less__imp__less__exp) # label(axiom). [clausify(248)]. 8.06/8.01 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4934,a,4930,a)]. 8.06/8.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4934,a,4933,a)]. 8.06/8.01 4935 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_404_power__mono) # label(axiom). [clausify(389)]. 8.06/8.01 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(4935,a,4930,a)]. 8.06/8.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(4935,a,4933,a)]. 8.06/8.01 4936 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_459_power__strict__decreasing) # label(axiom). [clausify(424)]. 8.06/8.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A))). [resolve(4936,a,4930,a)]. 8.06/8.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(4936,a,4933,a)]. 8.06/8.04 4937 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_408_less__add__one) # label(axiom). [clausify(497)]. 8.06/8.04 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int)))). [resolve(4937,a,4930,a)]. 8.06/8.04 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real)))). [resolve(4937,a,4933,a)]. 8.06/8.04 4938 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_449_power__strict__increasing__iff) # label(axiom). [clausify(549)]. 8.06/8.04 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(4938,a,4930,a)]. 8.06/8.04 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),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(4938,a,4933,a)]. 8.06/8.04 4939 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_449_power__strict__increasing__iff) # label(axiom). [clausify(549)]. 8.06/8.04 4940 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)))) # label(fact_1375_power__gt1) # label(axiom). [clausify(589)]. 8.06/8.04 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)))). [resolve(4940,a,4930,a)]. 8.06/8.04 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)))). [resolve(4940,a,4933,a)]. 8.06/8.04 4941 -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_1280_of__nat__less__0__iff) # label(axiom). [clausify(617)]. 8.11/8.10 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))). [resolve(4941,a,4930,a)]. 8.11/8.10 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(4941,a,4933,a)]. 8.11/8.10 4942 -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_1397_of__nat__0__less__iff) # label(axiom). [clausify(785)]. 8.11/8.10 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))). [resolve(4942,a,4930,a)]. 8.11/8.10 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(4942,a,4933,a)]. 8.11/8.10 4943 -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_1397_of__nat__0__less__iff) # label(axiom). [clausify(785)]. 8.11/8.10 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))). [resolve(4943,a,4930,a)]. 8.11/8.10 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(4943,a,4933,a)]. 8.11/8.10 4944 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_399_pos__add__strict) # label(axiom). [clausify(885)]. 8.11/8.10 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(4944,a,4930,a)]. 8.11/8.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(4944,a,4933,a)]. 8.11/8.10 4945 -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_1279_of__nat__0__le__iff) # label(axiom). [clausify(899)]. 8.11/8.10 4946 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_403_not__one__less__zero) # label(axiom). [clausify(941)]. 8.11/8.10 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),zero_zero(quickcheck_code_int))). [resolve(4946,a,4930,a)]. 8.20/8.18 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))). [resolve(4946,a,4933,a)]. 8.20/8.18 4947 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_460_power__eq__imp__eq__base) # label(axiom). [clausify(999)]. 8.20/8.18 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(4947,a,4930,a)]. 8.20/8.18 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(real,A) = ti(real,C). [resolve(4947,a,4933,a)]. 8.20/8.18 4948 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_447_power__strict__increasing) # label(axiom). [clausify(1149)]. 8.20/8.18 4949 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_440_power__less__imp__less__base) # label(axiom). [clausify(1210)]. 8.20/8.18 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(4949,a,4930,a)]. 8.20/8.18 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(4949,a,4933,a)]. 8.20/8.18 4950 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_439_zero__less__two) # label(axiom). [clausify(1273)]. 8.20/8.18 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int)))). [resolve(4950,a,4930,a)]. 8.54/8.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))). [resolve(4950,a,4933,a)]. 8.54/8.51 4951 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_105_power2__less__imp__less) # label(axiom). [clausify(1432)]. 8.54/8.51 4952 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_405_zero__le__power) # label(axiom). [clausify(1515)]. 8.54/8.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(4952,a,4930,a)]. 8.54/8.51 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,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(4952,a,4933,a)]. 8.54/8.51 4953 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_402_zero__less__one) # label(axiom). [clausify(1915)]. 8.54/8.51 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),one_one(quickcheck_code_int))). [resolve(4953,a,4930,a)]. 8.54/8.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))). [resolve(4953,a,4933,a)]. 8.54/8.51 4954 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f393(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(2178)]. 8.54/8.51 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(4954,a,4930,a)]. 8.54/8.51 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(4954,a,4933,a)]. 8.54/8.51 4955 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f393(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(2178)]. 8.54/8.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f393(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(4955,a,4930,a)]. 8.57/8.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f393(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(4955,a,4933,a)]. 8.57/8.55 4956 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 8.57/8.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(4956,a,4929,a)]. 8.57/8.55 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(4956,a,4931,a)]. 8.57/8.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4956,a,4934,a)]. 8.57/8.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(4956,a,4935,a)]. 8.57/8.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A))). [resolve(4956,a,4936,a)]. 8.57/8.55 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(4956,a,4937,a)]. 8.57/8.55 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),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(4956,a,4938,a)]. 8.57/8.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)))). [resolve(4956,a,4940,a)]. 8.57/8.55 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(4956,a,4942,a)]. 8.57/8.55 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(4956,a,4943,a)]. 8.57/8.55 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C). [resolve(4956,a,4947,a)]. 8.73/8.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(4956,a,4949,a)]. 8.73/8.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))). [resolve(4956,a,4950,a)]. 8.73/8.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(4956,a,4952,a)]. 8.73/8.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(4956,a,4953,a)]. 8.73/8.71 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(4956,a,4954,a)]. 8.73/8.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f393(A,nat,B,C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(4956,a,4955,a)]. 8.73/8.71 4957 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(A,B,C,D,E)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),B)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(2396)]. 8.73/8.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(quickcheck_code_int,A,B,C,D)),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),D)),C))). [resolve(4957,a,4930,a)]. 8.73/8.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(real,A,B,C,D)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),C))). [resolve(4957,a,4933,a)]. 8.73/8.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(nat,A,B,C,D)),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),D)),C))). [resolve(4957,a,4956,a)]. 8.73/8.73 4958 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,B,f431(A,C,B,D,E))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),C)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(2396)]. 8.73/8.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,A,f431(quickcheck_code_int,B,A,C,D))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),D)),C))). [resolve(4958,a,4930,a)]. 8.73/8.73 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A,f431(real,B,A,C,D))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),C))). [resolve(4958,a,4933,a)]. 8.73/8.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,A,f431(nat,B,A,C,D))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),D)),C))). [resolve(4958,a,4956,a)]. 8.73/8.73 4959 -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_1282_of__nat__less__imp__less) # label(axiom). [clausify(2432)]. 8.73/8.73 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4959,a,4930,a)]. 8.84/8.80 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(4959,a,4933,a)]. 8.84/8.80 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(4959,a,4956,a)]. 8.84/8.80 4960 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_444_power__less__power__Suc) # label(axiom). [clausify(2536)]. 8.84/8.80 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)))). [resolve(4960,a,4930,a)]. 8.84/8.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)))). [resolve(4960,a,4933,a)]. 8.84/8.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(4960,a,4956,a)]. 8.84/8.80 4961 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_1285_of__nat__le__iff) # label(axiom). [clausify(2555)]. 8.84/8.80 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4961,a,4930,a)]. 8.84/8.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4961,a,4933,a)]. 8.84/8.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4961,a,4956,a)]. 8.84/8.80 4962 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_1285_of__nat__le__iff) # label(axiom). [clausify(2555)]. 8.84/8.80 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4962,a,4930,a)]. 8.89/8.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4962,a,4933,a)]. 8.89/8.91 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4962,a,4956,a)]. 8.89/8.91 4963 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_412_one__le__power) # label(axiom). [clausify(2584)]. 8.89/8.91 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(4963,a,4930,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(4963,a,4933,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(4963,a,4956,a)]. 8.89/8.91 4964 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_401_not__one__le__zero) # label(axiom). [clausify(2644)]. 8.89/8.91 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),zero_zero(quickcheck_code_int))). [resolve(4964,a,4930,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))). [resolve(4964,a,4933,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(4964,a,4956,a)]. 8.89/8.91 4965 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),B)) # label(fact_1403_realpow__Suc__le__self) # label(axiom). [clausify(2720)]. 8.89/8.91 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),A)). [resolve(4965,a,4930,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),A)). [resolve(4965,a,4933,a)]. 8.89/8.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B))),A)). [resolve(4965,a,4956,a)]. 9.17/9.15 4966 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(4966,a,4929,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4966,a,4934,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(4966,a,4935,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(4966,a,4936,a)]. 9.17/9.15 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))). [resolve(4966,a,4937,a)]. 9.17/9.15 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),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(4966,a,4938,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)))). [resolve(4966,a,4940,a)]. 9.17/9.15 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(4966,a,4941,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(4966,a,4944,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(4966,a,4946,a)]. 9.17/9.15 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C). [resolve(4966,a,4947,a)]. 9.17/9.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(4966,a,4949,a)]. 9.17/9.15 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))). [resolve(4966,a,4950,a)]. 9.27/9.25 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,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(4966,a,4952,a)]. 9.27/9.25 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(4966,a,4953,a)]. 9.27/9.25 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(4966,a,4954,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f393(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(4966,a,4955,a)]. 9.27/9.25 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(int,A,B,C,D)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),D)),C))). [resolve(4966,a,4957,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,A,f431(int,B,A,C,D))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),D)),C))). [resolve(4966,a,4958,a)]. 9.27/9.25 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(4966,a,4959,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(4966,a,4960,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(4966,a,4963,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(4966,a,4964,a)]. 9.27/9.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),A)). [resolve(4966,a,4965,a)]. 9.27/9.25 4967 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_1374_power__le__imp__le__base) # label(axiom). [clausify(3037)]. 9.27/9.25 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(4967,a,4930,a)]. 9.27/9.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(4967,a,4933,a)]. 9.27/9.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(4967,a,4966,a)]. 9.27/9.27 4968 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_276_power__strict__mono) # label(axiom). [clausify(3053)]. 9.27/9.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(4968,a,4930,a)]. 9.27/9.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(4968,a,4933,a)]. 9.27/9.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(4968,a,4956,a)]. 9.27/9.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(4968,a,4966,a)]. 9.42/9.39 4969 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = ti(A,D) # label(fact_1373_power__inject__base) # label(axiom). [clausify(3127)]. 9.42/9.39 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(4969,a,4930,a)]. 9.42/9.39 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = ti(real,C). [resolve(4969,a,4933,a)]. 9.42/9.39 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | ti(nat,A) = ti(nat,C). [resolve(4969,a,4956,a)]. 9.42/9.39 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | ti(int,A) = ti(int,C). [resolve(4969,a,4966,a)]. 9.42/9.39 4970 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = ti(A,C) # label(fact_102_power2__eq__imp__eq) # label(axiom). [clausify(3161)]. 9.42/9.39 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B). [resolve(4970,a,4930,a)]. 9.42/9.39 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = ti(real,B). [resolve(4970,a,4933,a)]. 9.49/9.45 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | ti(nat,A) = ti(nat,B). [resolve(4970,a,4956,a)]. 9.49/9.45 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | ti(int,A) = ti(int,B). [resolve(4970,a,4966,a)]. 9.49/9.45 4971 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_103_power2__le__imp__le) # label(axiom). [clausify(3207)]. 9.49/9.45 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(4971,a,4930,a)]. 9.49/9.45 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(4971,a,4933,a)]. 9.49/9.45 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4971,a,4956,a)]. 9.49/9.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(4971,a,4966,a)]. 9.49/9.45 4972 -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_1283_less__imp__of__nat__less) # label(axiom). [clausify(3211)]. 9.75/9.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))). [resolve(4972,a,4930,a)]. 9.75/9.71 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(4972,a,4933,a)]. 9.75/9.71 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(4972,a,4956,a)]. 9.75/9.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))). [resolve(4972,a,4966,a)]. 9.75/9.71 4973 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2495_of__nat__fact__gt__zero) # label(axiom). [clausify(3511)]. 9.75/9.71 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4973,a,4930,a)]. 9.75/9.71 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4973,a,4933,a)]. 9.75/9.71 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4973,a,4956,a)]. 9.75/9.71 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4973,a,4966,a)]. 9.75/9.71 4974 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C != D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_413_power__inject__exp) # label(axiom). [clausify(3532)]. 9.75/9.71 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | B != C | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C). [resolve(4974,a,4930,a)]. 9.75/9.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B != C | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C). [resolve(4974,a,4933,a)]. 9.75/9.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B != C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(4974,a,4956,a)]. 9.75/9.71 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B != C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(4974,a,4966,a)]. 9.75/9.71 4975 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C = D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_413_power__inject__exp) # label(axiom). [clausify(3532)]. 9.90/9.88 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | B = C | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C). [resolve(4975,a,4930,a)]. 9.90/9.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B = C | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C). [resolve(4975,a,4933,a)]. 9.90/9.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B = C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(4975,a,4956,a)]. 9.90/9.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B = C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(4975,a,4966,a)]. 9.90/9.88 4976 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_400_zero__le__one) # label(axiom). [clausify(3608)]. 9.90/9.88 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),one_one(quickcheck_code_int))). [resolve(4976,a,4930,a)]. 9.90/9.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))). [resolve(4976,a,4933,a)]. 9.90/9.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(4976,a,4956,a)]. 9.90/9.88 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(4976,a,4966,a)]. 9.90/9.88 4977 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_458_power__Suc__less) # label(axiom). [clausify(3724)]. 9.90/9.88 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(4977,a,4930,a)]. 9.90/9.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(4977,a,4933,a)]. 9.90/9.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(4977,a,4956,a)]. 10.07/10.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(4977,a,4966,a)]. 10.07/10.03 4978 -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_1284_of__nat__less__iff) # label(axiom). [clausify(3731)]. 10.07/10.03 4979 -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_1284_of__nat__less__iff) # label(axiom). [clausify(3731)]. 10.07/10.03 4980 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f681(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(3863)]. 10.07/10.03 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(4980,a,4930,a)]. 10.07/10.03 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(4980,a,4933,a)]. 10.07/10.03 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(4980,a,4956,a)]. 10.07/10.03 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(4980,a,4966,a)]. 10.07/10.03 4981 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(B,A,C,f681(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(3863)]. 10.07/10.03 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f681(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C))). [resolve(4981,a,4930,a)]. 10.07/10.03 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(A,real,B,f681(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(4981,a,4933,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(A,nat,B,f681(A,nat,B,C)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C))). [resolve(4981,a,4956,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,B,f681(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(4981,a,4966,a)]. 10.31/10.27 4982 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_407_zero__less__power) # label(axiom). [clausify(4031)]. 10.31/10.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(4982,a,4930,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(4982,a,4933,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(4982,a,4956,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(4982,a,4966,a)]. 10.31/10.27 4983 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_406_less__1__mult) # label(axiom). [clausify(4109)]. 10.31/10.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(4983,a,4930,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4983,a,4933,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(4983,a,4956,a)]. 10.31/10.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4983,a,4966,a)]. 10.37/10.34 4984 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_441_power__decreasing) # label(axiom). [clausify(4153)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A))). [resolve(4984,a,4930,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(4984,a,4933,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A))). [resolve(4984,a,4956,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(4984,a,4966,a)]. 10.37/10.34 4985 linordered_semidom(rat) # label(arity_Rat_Orat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(4985,a,4929,a)]. 10.37/10.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))). [resolve(4985,a,4931,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4985,a,4934,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(4985,a,4935,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(4985,a,4936,a)]. 10.37/10.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat)))). [resolve(4985,a,4937,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(4985,a,4938,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)))). [resolve(4985,a,4940,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),zero_zero(rat))). [resolve(4985,a,4941,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))). [resolve(4985,a,4942,a)]. 10.37/10.34 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),A))). [resolve(4985,a,4943,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(4985,a,4944,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),zero_zero(rat))). [resolve(4985,a,4946,a)]. 10.37/10.34 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(rat,A) = ti(rat,C). [resolve(4985,a,4947,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(4985,a,4949,a)]. 10.37/10.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)))). [resolve(4985,a,4950,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(4985,a,4952,a)]. 10.37/10.34 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),one_one(rat))). [resolve(4985,a,4953,a)]. 10.37/10.34 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(4985,a,4954,a)]. 10.37/10.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f393(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(4985,a,4955,a)]. 10.37/10.35 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(rat,A,B,C,D)),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),D)),C))). [resolve(4985,a,4957,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,A,f431(rat,B,A,C,D))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),D)),C))). [resolve(4985,a,4958,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4985,a,4959,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)))). [resolve(4985,a,4960,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4985,a,4961,a)]. 10.37/10.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4985,a,4962,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(4985,a,4963,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),zero_zero(rat))). [resolve(4985,a,4964,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),A)). [resolve(4985,a,4965,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(4985,a,4967,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(4985,a,4968,a)]. 10.37/10.35 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | ti(rat,A) = ti(rat,C). [resolve(4985,a,4969,a)]. 10.37/10.35 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | ti(rat,A) = ti(rat,B). [resolve(4985,a,4970,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(4985,a,4971,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))). [resolve(4985,a,4972,a)]. 10.37/10.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4985,a,4973,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | B != C | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C). [resolve(4985,a,4974,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | B = C | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C). [resolve(4985,a,4975,a)]. 10.37/10.35 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),one_one(rat))). [resolve(4985,a,4976,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(4985,a,4977,a)]. 10.37/10.35 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(4985,a,4980,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(A,rat,B,f681(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(4985,a,4981,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(4985,a,4982,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4985,a,4983,a)]. 10.37/10.35 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(4985,a,4984,a)]. 10.42/10.43 4986 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f733(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E))) # label(fact_4150_setprod__mono) # label(axiom). [clausify(4249)]. 10.42/10.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D))). [resolve(4986,a,4930,a)]. 10.42/10.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D))). [resolve(4986,a,4933,a)]. 10.42/10.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D))). [resolve(4986,a,4956,a)]. 10.42/10.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D))). [resolve(4986,a,4966,a)]. 10.42/10.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D))). [resolve(4986,a,4985,a)]. 10.42/10.43 4987 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f733(B,A,D,C,E))),hAPP(B,A,D,f733(B,A,D,C,E)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f733(B,A,D,C,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4150_setprod__mono) # label(axiom). [clausify(4249)]. 10.42/10.43 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f733(A,quickcheck_code_int,C,B,D))),hAPP(A,quickcheck_code_int,C,f733(A,quickcheck_code_int,C,B,D)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f733(A,quickcheck_code_int,C,B,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))). [resolve(4987,a,4930,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f733(A,real,C,B,D))),hAPP(A,real,C,f733(A,real,C,B,D)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f733(A,real,C,B,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))). [resolve(4987,a,4933,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f733(A,nat,C,B,D))),hAPP(A,nat,C,f733(A,nat,C,B,D)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f733(A,nat,C,B,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D))). [resolve(4987,a,4956,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f733(A,int,C,B,D))),hAPP(A,int,C,f733(A,int,C,B,D)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f733(A,int,C,B,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D))). [resolve(4987,a,4966,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f733(A,rat,C,B,D))),hAPP(A,rat,C,f733(A,rat,C,B,D)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f733(A,rat,C,B,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))). [resolve(4987,a,4985,a)]. 10.50/10.48 4988 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_411_power__increasing) # label(axiom). [clausify(4285)]. 10.50/10.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),one_one(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))). [resolve(4988,a,4930,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(4988,a,4933,a)]. 10.50/10.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(4988,a,4956,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(4988,a,4966,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))). [resolve(4988,a,4985,a)]. 10.72/10.67 4989 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),one_one(A))) # label(fact_1404_power__Suc__less__one) # label(axiom). [clausify(4381)]. 10.72/10.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),one_one(quickcheck_code_int))). [resolve(4989,a,4930,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),one_one(real))). [resolve(4989,a,4933,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B))),one_one(nat))). [resolve(4989,a,4956,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),one_one(int))). [resolve(4989,a,4966,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),one_one(rat))). [resolve(4989,a,4985,a)]. 10.72/10.67 4990 linordered_semidom(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semidom) # label(axiom). [assumption]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(4990,a,4929,a)]. 10.72/10.67 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))). [resolve(4990,a,4931,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(4990,a,4934,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(4990,a,4935,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A))). [resolve(4990,a,4936,a)]. 10.72/10.67 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral)))). [resolve(4990,a,4937,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(4990,a,4938,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)))). [resolve(4990,a,4940,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),zero_zero(code_code_numeral))). [resolve(4990,a,4941,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))). [resolve(4990,a,4942,a)]. 10.72/10.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))). [resolve(4990,a,4943,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(4990,a,4944,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),zero_zero(code_code_numeral))). [resolve(4990,a,4946,a)]. 10.72/10.67 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(4990,a,4947,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(4990,a,4949,a)]. 10.72/10.67 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral)))). [resolve(4990,a,4950,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(4990,a,4952,a)]. 10.72/10.67 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),one_one(code_code_numeral))). [resolve(4990,a,4953,a)]. 10.72/10.67 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f393(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(4990,a,4954,a)]. 10.72/10.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f393(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(4990,a,4955,a)]. 10.72/10.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f431(code_code_numeral,A,B,C,D)),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),A)))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),D)),C))). [resolve(4990,a,4957,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,A,f431(code_code_numeral,B,A,C,D))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),B)))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),D)),C))). [resolve(4990,a,4958,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4990,a,4959,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)))). [resolve(4990,a,4960,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4990,a,4961,a)]. 10.72/10.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4990,a,4962,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(4990,a,4963,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),zero_zero(code_code_numeral))). [resolve(4990,a,4964,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),A)). [resolve(4990,a,4965,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(4990,a,4967,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(4990,a,4968,a)]. 10.72/10.68 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(4990,a,4969,a)]. 10.72/10.68 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = ti(code_code_numeral,B). [resolve(4990,a,4970,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(4990,a,4971,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))). [resolve(4990,a,4972,a)]. 10.72/10.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(4990,a,4973,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | B != C | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C). [resolve(4990,a,4974,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | B = C | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C). [resolve(4990,a,4975,a)]. 10.72/10.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),one_one(code_code_numeral))). [resolve(4990,a,4976,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(4990,a,4977,a)]. 10.72/10.68 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f681(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(4990,a,4980,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f681(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C))). [resolve(4990,a,4981,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(4990,a,4982,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(4990,a,4983,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A))). [resolve(4990,a,4984,a)]. 10.72/10.68 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f733(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D))). [resolve(4990,a,4986,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f733(A,code_code_numeral,C,B,D))),hAPP(A,code_code_numeral,C,f733(A,code_code_numeral,C,B,D)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f733(A,code_code_numeral,C,B,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))). [resolve(4990,a,4987,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))). [resolve(4990,a,4988,a)]. 10.72/10.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),one_one(code_code_numeral))). [resolve(4990,a,4989,a)]. 10.82/10.81 4991 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_445_power__gt1__lemma) # label(axiom). [clausify(4532)]. 10.82/10.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)))). [resolve(4991,a,4930,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)))). [resolve(4991,a,4933,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(4991,a,4956,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(4991,a,4966,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)))). [resolve(4991,a,4985,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)))). [resolve(4991,a,4990,a)]. 10.82/10.82 4992 -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_eq(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_443_power__increasing__iff) # label(axiom). [clausify(4587)]. 10.82/10.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(4992,a,4930,a)]. 10.82/10.82 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_eq(nat),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(4992,a,4933,a)]. 10.82/10.82 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),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(4992,a,4956,a)]. 10.82/10.82 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_eq(nat),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(4992,a,4966,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(4992,a,4985,a)]. 10.82/10.82 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(4992,a,4990,a)]. 10.82/10.82 4993 -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_eq(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_443_power__increasing__iff) # label(axiom). [clausify(4587)]. 10.82/10.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(4993,a,4930,a)]. 10.82/10.82 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_eq(nat),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(4993,a,4933,a)]. 10.82/10.82 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),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(4993,a,4956,a)]. 10.82/10.82 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_eq(nat),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(4993,a,4966,a)]. 15.43/15.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(4993,a,4985,a)]. 15.43/15.39 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(4993,a,4990,a)]. 15.43/15.39 4994 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_442_power__le__imp__le__exp) # label(axiom). [clausify(4687)]. 15.43/15.39 4995 one(rat) # label(arity_Rat_Orat___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 4996 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(15)]. 15.43/15.39 Derived: one_one(rat) = ti(rat,one_one(rat)). [resolve(4995,a,4996,a)]. 15.43/15.39 4997 one(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(code_code_numeral) = ti(code_code_numeral,one_one(code_code_numeral)). [resolve(4997,a,4996,a)]. 15.43/15.39 4998 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(int) = ti(int,one_one(int)). [resolve(4998,a,4996,a)]. 15.43/15.39 4999 one(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(quickcheck_code_int) = ti(quickcheck_code_int,one_one(quickcheck_code_int)). [resolve(4999,a,4996,a)]. 15.43/15.39 5000 one(complex) # label(arity_Complex_Ocomplex___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(complex) = ti(complex,one_one(complex)). [resolve(5000,a,4996,a)]. 15.43/15.39 5001 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(5001,a,4996,a)]. 15.43/15.39 5002 one(real) # label(arity_RealDef_Oreal___Groups_Oone) # label(axiom). [assumption]. 15.43/15.39 Derived: one_one(real) = ti(real,one_one(real)). [resolve(5002,a,4996,a)]. 15.43/15.39 5003 comm_monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 15.43/15.39 5004 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f4(C,A,D,E,F,B)),f6(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f8(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.43/15.39 5005 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f4(C,A,D,E,F,B)),f6(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f8(C,A,D,E,F,B))),hAPP(C,A,E,f8(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.45/15.39 5006 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f5(C,A,D,E,F,B)),f7(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f8(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.45/15.39 5007 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f5(C,A,D,E,F,B)),f7(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f8(C,A,D,E,F,B))),hAPP(C,A,E,f8(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.45/15.39 5008 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f4(C,A,D,E,F,B)),f5(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f6(C,A,D,E,F,B)),f7(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f8(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.45/15.39 5009 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f4(C,A,D,E,F,B)),f5(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f6(C,A,D,E,F,B)),f7(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f8(C,A,D,E,F,B))),hAPP(C,A,E,f8(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(22)]. 15.45/15.39 5010 -comm_monoid_mult(A) | -comm_monoid_add(A) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),B),C) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom). [clausify(68)]. 15.45/15.39 5011 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_3952_setprod_Oinfinite) # label(axiom). [clausify(516)]. 15.45/15.39 5012 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_3955_setprod__delta_H) # label(axiom). [clausify(712)]. 15.45/15.39 5013 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) # label(fact_3955_setprod__delta_H) # label(axiom). [clausify(712)]. 15.45/15.39 5014 -comm_monoid_mult(A) | -dvd(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom). [clausify(1025)]. 15.45/15.39 5015 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(B,bool),nat,finite_card(B),C)),one_one(nat)))) # label(fact_3936_setprod__gen__delta) # label(axiom). [clausify(1085)]. 15.45/15.39 5016 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_3936_setprod__gen__delta) # label(axiom). [clausify(1085)]. 15.45/15.39 5017 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) # label(fact_3956_setprod__delta) # label(axiom). [clausify(1250)]. 15.45/15.39 5018 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_3956_setprod__delta) # label(axiom). [clausify(1250)]. 15.45/15.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f4(B,quickcheck_code_int,C,D,E,A)),f6(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5004,a)]. 15.45/15.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f4(B,quickcheck_code_int,C,D,E,A)),f6(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f8(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f8(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5005,a)]. 15.45/15.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f5(B,quickcheck_code_int,C,D,E,A)),f7(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5006,a)]. 15.45/15.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,f5(B,quickcheck_code_int,C,D,E,A)),f7(B,quickcheck_code_int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f8(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f8(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5007,a)]. 15.45/15.40 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),f4(B,quickcheck_code_int,C,D,E,A)),f5(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),f6(B,quickcheck_code_int,C,D,E,A)),f7(B,quickcheck_code_int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,quickcheck_code_int,C,D,E,A)),E)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5008,a)]. 15.45/15.40 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,one_one(quickcheck_code_int)),one_one(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),f4(B,quickcheck_code_int,C,D,E,A)),f5(B,quickcheck_code_int,C,D,E,A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),f6(B,quickcheck_code_int,C,D,E,A)),f7(B,quickcheck_code_int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(B,quickcheck_code_int,C,f8(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f8(B,quickcheck_code_int,C,D,E,A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),A,hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),C),E)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co302546470etprod(B,quickcheck_code_int),D),E))). [resolve(5003,a,5009,a)]. 15.45/15.40 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),A),B). [resolve(5003,a,5010,a)]. 15.45/15.40 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B). [resolve(5003,a,5011,a)]. 15.45/15.40 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C). [resolve(5003,a,5012,a)]. 15.45/15.40 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(quickcheck_code_int))),B). [resolve(5003,a,5013,a)]. 15.45/15.40 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B))). [resolve(5003,a,5014,a)]. 15.45/15.40 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5003,a,5015,a)]. 15.45/15.41 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5003,a,5016,a)]. 15.45/15.41 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(quickcheck_code_int))),B). [resolve(5003,a,5017,a)]. 15.58/15.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combs(A,quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),hAPP(fun(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int))),fun(fun(A,bool),fun(A,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)))),combb(bool,fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),A),if(quickcheck_code_int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(quickcheck_code_int))),B) = hAPP(A,quickcheck_code_int,D,C). [resolve(5003,a,5018,a)]. 15.58/15.54 5019 -comm_monoid_add(A) | -comm_monoid_mult(A) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),C) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom). [clausify(1548)]. 15.58/15.54 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),B). [resolve(5019,b,5003,a)]. 15.58/15.54 5020 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f320(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4769_setprod_Ocong) # label(axiom). [clausify(1737)]. 15.58/15.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,quickcheck_code_int,C,D,B)),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B). [resolve(5020,a,5003,a)]. 15.58/15.54 5021 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f320(B,A,E,D,C)) != hAPP(B,A,E,f320(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_4769_setprod_Ocong) # label(axiom). [clausify(1737)]. 15.58/15.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f320(A,quickcheck_code_int,D,C,B)) != hAPP(A,quickcheck_code_int,D,f320(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B). [resolve(5021,a,5003,a)]. 15.58/15.59 5022 -comm_monoid_mult(A) | -ring_1(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,int),fun(B,A),hAPP(fun(int,A),fun(fun(B,int),fun(B,A)),combb(int,A,B),ring_1_of_int(A)),C)),D) = hAPP(int,A,ring_1_of_int(A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),D)) # label(fact_3929_of__int__setprod) # label(axiom). [clausify(1833)]. 15.58/15.59 Derived: -ring_1(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(fun(A,int),fun(A,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(A,int),fun(A,quickcheck_code_int)),combb(int,quickcheck_code_int,A),ring_1_of_int(quickcheck_code_int)),B)),C) = hAPP(int,quickcheck_code_int,ring_1_of_int(quickcheck_code_int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5022,a,5003,a)]. 15.58/15.59 5023 comm_monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 15.58/15.59 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f4(B,complex,C,D,E,A)),f6(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5004,a)]. 15.58/15.59 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f4(B,complex,C,D,E,A)),f6(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f8(B,complex,C,D,E,A))),hAPP(B,complex,D,f8(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5005,a)]. 15.58/15.59 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f5(B,complex,C,D,E,A)),f7(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5006,a)]. 15.58/15.59 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f5(B,complex,C,D,E,A)),f7(B,complex,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f8(B,complex,C,D,E,A))),hAPP(B,complex,D,f8(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5007,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f4(B,complex,C,D,E,A)),f5(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f6(B,complex,C,D,E,A)),f7(B,complex,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,complex,C,D,E,A)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5008,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f4(B,complex,C,D,E,A)),f5(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f6(B,complex,C,D,E,A)),f7(B,complex,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(B,complex,C,f8(B,complex,C,D,E,A))),hAPP(B,complex,D,f8(B,complex,C,D,E,A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),C),E)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co302546470etprod(B,complex),D),E))). [resolve(5023,a,5009,a)]. 15.65/15.60 Derived: -comm_monoid_add(complex) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),A),B). [resolve(5023,a,5010,a)]. 15.65/15.60 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B). [resolve(5023,a,5011,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(complex))),B) = hAPP(A,complex,D,C). [resolve(5023,a,5012,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(complex))),B). [resolve(5023,a,5013,a)]. 15.65/15.60 Derived: -dvd(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B))). [resolve(5023,a,5014,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(A,complex,D,C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5023,a,5015,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5023,a,5016,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(complex))),B). [resolve(5023,a,5017,a)]. 15.65/15.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(complex))),B) = hAPP(A,complex,D,C). [resolve(5023,a,5018,a)]. 16.10/16.04 Derived: -comm_monoid_add(complex) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),B). [resolve(5023,a,5019,b)]. 16.10/16.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,complex,C,D,B)),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B). [resolve(5023,a,5020,a)]. 16.10/16.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f320(A,complex,D,C,B)) != hAPP(A,complex,D,f320(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B). [resolve(5023,a,5021,a)]. 16.10/16.04 Derived: -ring_1(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,int),fun(A,complex),hAPP(fun(int,complex),fun(fun(A,int),fun(A,complex)),combb(int,complex,A),ring_1_of_int(complex)),B)),C) = hAPP(int,complex,ring_1_of_int(complex),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5023,a,5022,a)]. 16.10/16.04 5024 -comm_monoid_mult(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),C),B) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom). [clausify(2525)]. 16.10/16.04 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),B),A) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5024,a,5003,a)]. 16.10/16.04 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),B),A) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5024,a,5023,a)]. 16.10/16.11 5025 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_3954_setprod_Odistrib) # label(axiom). [clausify(2594)]. 16.10/16.11 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combs(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),C)),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B)). [resolve(5025,a,5003,a)]. 16.10/16.11 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),C)),D)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B)). [resolve(5025,a,5023,a)]. 16.10/16.11 5026 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),one_one(A))),C) # label(fact_3947_setprod__1) # label(axiom). [clausify(2630)]. 16.10/16.11 Derived: one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),one_one(quickcheck_code_int))),B). [resolve(5026,a,5003,a)]. 16.10/16.11 Derived: one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),one_one(complex))),B). [resolve(5026,a,5023,a)]. 16.10/16.13 5027 comm_monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f4(B,real,C,D,E,A)),f6(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5004,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f4(B,real,C,D,E,A)),f6(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f8(B,real,C,D,E,A))),hAPP(B,real,D,f8(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5005,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f5(B,real,C,D,E,A)),f7(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5006,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,f5(B,real,C,D,E,A)),f7(B,real,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f8(B,real,C,D,E,A))),hAPP(B,real,D,f8(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5007,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f4(B,real,C,D,E,A)),f5(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f6(B,real,C,D,E,A)),f7(B,real,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,real,C,D,E,A)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5008,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,one_one(real)),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f4(B,real,C,D,E,A)),f5(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f6(B,real,C,D,E,A)),f7(B,real,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(B,real,C,f8(B,real,C,D,E,A))),hAPP(B,real,D,f8(B,real,C,D,E,A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),A,hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),C),E)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co302546470etprod(B,real),D),E))). [resolve(5027,a,5009,a)]. 16.10/16.13 Derived: -comm_monoid_add(real) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),A),B). [resolve(5027,a,5010,a)]. 16.10/16.13 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B). [resolve(5027,a,5011,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(real))),B) = hAPP(A,real,D,C). [resolve(5027,a,5012,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(real))),B). [resolve(5027,a,5013,a)]. 16.10/16.13 Derived: -dvd(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B))). [resolve(5027,a,5014,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,D,C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5027,a,5015,a)]. 16.10/16.13 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5027,a,5016,a)]. 16.20/16.14 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(real))),B). [resolve(5027,a,5017,a)]. 16.20/16.14 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(A,fun(real,fun(real,real))),fun(fun(A,real),fun(A,fun(real,real))),combs(A,real,fun(real,real)),hAPP(fun(A,bool),fun(A,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(A,bool),fun(A,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),A),if(real)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(real))),B) = hAPP(A,real,D,C). [resolve(5027,a,5018,a)]. 16.20/16.14 Derived: -comm_monoid_add(real) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),B). [resolve(5027,a,5019,b)]. 16.20/16.14 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B). [resolve(5027,a,5020,a)]. 16.20/16.14 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f320(A,real,D,C,B)) != hAPP(A,real,D,f320(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B). [resolve(5027,a,5021,a)]. 16.20/16.14 Derived: -ring_1(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,int),fun(A,real),hAPP(fun(int,real),fun(fun(A,int),fun(A,real)),combb(int,real,A),ring_1_of_int(real)),B)),C) = hAPP(int,real,ring_1_of_int(real),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5027,a,5022,a)]. 16.20/16.14 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),B),A) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5027,a,5024,a)]. 16.25/16.21 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),C)),D)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B)). [resolve(5027,a,5025,a)]. 16.25/16.21 Derived: one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),combk(real,A),one_one(real))),B). [resolve(5027,a,5026,a)]. 16.25/16.21 5028 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_801_mult__1) # label(axiom). [clausify(2675)]. 16.25/16.21 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),one_one(quickcheck_code_int)),A). [resolve(5028,a,5003,a)]. 16.25/16.21 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),one_one(complex)),A). [resolve(5028,a,5023,a)]. 16.25/16.21 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A). [resolve(5028,a,5027,a)]. 16.25/16.21 5029 -comm_monoid_mult(A) | big_co302546470etprod(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co302546470etprod(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom). [clausify(2733)]. 16.25/16.21 Derived: big_co302546470etprod(A,quickcheck_code_int) = ti(fun(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int)),big_co302546470etprod(A,quickcheck_code_int)). [resolve(5029,a,5003,a)]. 16.25/16.21 Derived: big_co302546470etprod(A,complex) = ti(fun(fun(A,complex),fun(fun(A,bool),complex)),big_co302546470etprod(A,complex)). [resolve(5029,a,5023,a)]. 16.25/16.21 Derived: big_co302546470etprod(A,real) = ti(fun(fun(A,real),fun(fun(A,bool),real)),big_co302546470etprod(A,real)). [resolve(5029,a,5027,a)]. 16.25/16.21 5030 -comm_monoid_add(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),C),B) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom). [clausify(2766)]. 16.25/16.21 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),B),A) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5030,b,5003,a)]. 16.25/16.21 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),B),A) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5030,b,5023,a)]. 16.50/16.45 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),B),A) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5030,b,5027,a)]. 16.50/16.45 5031 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f521(B,A,D,C)),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4148_setprod_Oneutral) # label(axiom). [clausify(2913)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,quickcheck_code_int,C,B)),B)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B). [resolve(5031,a,5003,a)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,complex,C,B)),B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B). [resolve(5031,a,5023,a)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,real,C,B)),B)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B). [resolve(5031,a,5027,a)]. 16.50/16.45 5032 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) != hAPP(B,A,D,f521(B,A,D,C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4148_setprod_Oneutral) # label(axiom). [clausify(2913)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f521(A,quickcheck_code_int,C,B)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B). [resolve(5032,a,5003,a)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(complex) != hAPP(A,complex,C,f521(A,complex,C,B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B). [resolve(5032,a,5023,a)]. 16.50/16.45 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(real) != hAPP(A,real,C,f521(A,real,C,B)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B). [resolve(5032,a,5027,a)]. 16.50/16.45 5033 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f524(B,A,C,D)),D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_4772_setprod__1_H) # label(axiom). [clausify(2921)]. 16.50/16.45 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,quickcheck_code_int,B,C)),C)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C). [resolve(5033,a,5003,a)]. 16.80/16.78 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,complex,B,C)),C)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),C). [resolve(5033,a,5023,a)]. 16.80/16.78 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,real,B,C)),C)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C). [resolve(5033,a,5027,a)]. 16.80/16.78 5034 -comm_monoid_mult(A) | one_one(A) != hAPP(B,A,C,f524(B,A,C,D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_4772_setprod__1_H) # label(axiom). [clausify(2921)]. 16.80/16.78 Derived: one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,B,f524(A,quickcheck_code_int,B,C)) | one_one(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),C). [resolve(5034,a,5003,a)]. 16.80/16.78 Derived: one_one(complex) != hAPP(A,complex,B,f524(A,complex,B,C)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),C). [resolve(5034,a,5023,a)]. 16.80/16.78 Derived: one_one(real) != hAPP(A,real,B,f524(A,real,B,C)) | one_one(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C). [resolve(5034,a,5027,a)]. 16.80/16.78 5035 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_799_mult_Ocomm__neutral) # label(axiom). [clausify(3153)]. 16.80/16.78 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),one_one(quickcheck_code_int)). [resolve(5035,a,5003,a)]. 16.80/16.78 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),one_one(complex)). [resolve(5035,a,5023,a)]. 16.80/16.78 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)). [resolve(5035,a,5027,a)]. 16.80/16.78 5036 comm_monoid_mult(rat) # label(arity_Rat_Orat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 16.80/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f4(B,rat,C,D,E,A)),f6(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5004,a)]. 16.80/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f4(B,rat,C,D,E,A)),f6(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f8(B,rat,C,D,E,A))),hAPP(B,rat,D,f8(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5005,a)]. 16.80/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f5(B,rat,C,D,E,A)),f7(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5006,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,f5(B,rat,C,D,E,A)),f7(B,rat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f8(B,rat,C,D,E,A))),hAPP(B,rat,D,f8(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5007,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f4(B,rat,C,D,E,A)),f5(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f6(B,rat,C,D,E,A)),f7(B,rat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,rat,C,D,E,A)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5008,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,one_one(rat)),one_one(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f4(B,rat,C,D,E,A)),f5(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f6(B,rat,C,D,E,A)),f7(B,rat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(B,rat,C,f8(B,rat,C,D,E,A))),hAPP(B,rat,D,f8(B,rat,C,D,E,A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),A,hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),C),E)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co302546470etprod(B,rat),D),E))). [resolve(5036,a,5009,a)]. 16.84/16.78 Derived: -comm_monoid_add(rat) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),A),B). [resolve(5036,a,5010,a)]. 16.84/16.78 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B). [resolve(5036,a,5011,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(rat))),B) = hAPP(A,rat,D,C). [resolve(5036,a,5012,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(rat))),B). [resolve(5036,a,5013,a)]. 16.84/16.78 Derived: -dvd(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B))). [resolve(5036,a,5014,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(A,rat,D,C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5036,a,5015,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5036,a,5016,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(rat))),B). [resolve(5036,a,5017,a)]. 16.84/16.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(rat))),B) = hAPP(A,rat,D,C). [resolve(5036,a,5018,a)]. 16.84/16.78 Derived: -comm_monoid_add(rat) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),B). [resolve(5036,a,5019,b)]. 16.84/16.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B). [resolve(5036,a,5020,a)]. 16.84/16.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f320(A,rat,D,C,B)) != hAPP(A,rat,D,f320(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B). [resolve(5036,a,5021,a)]. 16.84/16.79 Derived: -ring_1(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,int),fun(A,rat),hAPP(fun(int,rat),fun(fun(A,int),fun(A,rat)),combb(int,rat,A),ring_1_of_int(rat)),B)),C) = hAPP(int,rat,ring_1_of_int(rat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5036,a,5022,a)]. 16.84/16.79 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),B),A) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5036,a,5024,a)]. 16.84/16.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),C)),D)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B)). [resolve(5036,a,5025,a)]. 16.84/16.79 Derived: one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),one_one(rat))),B). [resolve(5036,a,5026,a)]. 16.84/16.79 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),one_one(rat)),A). [resolve(5036,a,5028,a)]. 16.84/16.79 Derived: big_co302546470etprod(A,rat) = ti(fun(fun(A,rat),fun(fun(A,bool),rat)),big_co302546470etprod(A,rat)). [resolve(5036,a,5029,a)]. 16.84/16.79 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),B),A) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5036,a,5030,b)]. 16.84/16.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,rat,C,B)),B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B). [resolve(5036,a,5031,a)]. 16.84/16.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(rat) != hAPP(A,rat,C,f521(A,rat,C,B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B). [resolve(5036,a,5032,a)]. 17.24/17.17 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,rat,B,C)),C)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C). [resolve(5036,a,5033,a)]. 17.24/17.17 Derived: one_one(rat) != hAPP(A,rat,B,f524(A,rat,B,C)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C). [resolve(5036,a,5034,a)]. 17.24/17.17 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),one_one(rat)). [resolve(5036,a,5035,a)]. 17.24/17.17 5037 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f650(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3961_setprod__mono__one__right) # label(axiom). [clausify(3725)]. 17.24/17.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C). [resolve(5037,a,5003,a)]. 17.24/17.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,complex,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C). [resolve(5037,a,5023,a)]. 17.24/17.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C). [resolve(5037,a,5027,a)]. 17.24/17.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C). [resolve(5037,a,5036,a)]. 17.24/17.17 5038 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f650(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3961_setprod__mono__one__right) # label(axiom). [clausify(3725)]. 17.24/17.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f650(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C). [resolve(5038,a,5003,a)]. 17.24/17.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(complex) != hAPP(A,complex,D,f650(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C). [resolve(5038,a,5023,a)]. 17.24/17.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(real) != hAPP(A,real,D,f650(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C). [resolve(5038,a,5027,a)]. 17.24/17.18 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(rat) != hAPP(A,rat,D,f650(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C). [resolve(5038,a,5036,a)]. 17.24/17.18 5039 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_330_power__mult__distrib) # label(axiom). [clausify(3736)]. 17.24/17.18 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5039,a,5003,a)]. 17.24/17.18 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),B). [resolve(5039,a,5023,a)]. 17.24/17.18 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B). [resolve(5039,a,5027,a)]. 17.24/17.18 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B). [resolve(5039,a,5036,a)]. 17.30/17.25 5040 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f4(B,int,C,D,E,A)),f6(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5004,a)]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f4(B,int,C,D,E,A)),f6(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f8(B,int,C,D,E,A))),hAPP(B,int,D,f8(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5005,a)]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f5(B,int,C,D,E,A)),f7(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5006,a)]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f5(B,int,C,D,E,A)),f7(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f8(B,int,C,D,E,A))),hAPP(B,int,D,f8(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5007,a)]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f4(B,int,C,D,E,A)),f5(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f6(B,int,C,D,E,A)),f7(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5008,a)]. 17.30/17.25 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f4(B,int,C,D,E,A)),f5(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f6(B,int,C,D,E,A)),f7(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f8(B,int,C,D,E,A))),hAPP(B,int,D,f8(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(5040,a,5009,a)]. 17.30/17.25 Derived: -comm_monoid_add(int) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),A),B). [resolve(5040,a,5010,a)]. 17.32/17.25 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(5040,a,5011,a)]. 17.32/17.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(5040,a,5012,a)]. 17.32/17.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B). [resolve(5040,a,5013,a)]. 17.32/17.25 Derived: -dvd(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B))). [resolve(5040,a,5014,a)]. 17.32/17.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5040,a,5015,a)]. 17.32/17.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5040,a,5016,a)]. 17.32/17.26 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B). [resolve(5040,a,5017,a)]. 17.32/17.26 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(5040,a,5018,a)]. 17.32/17.26 Derived: -comm_monoid_add(int) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),B). [resolve(5040,a,5019,b)]. 17.32/17.26 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(5040,a,5020,a)]. 17.32/17.26 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f320(A,int,D,C,B)) != hAPP(A,int,D,f320(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B). [resolve(5040,a,5021,a)]. 17.32/17.26 Derived: -ring_1(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),ring_1_of_int(int)),B)),C) = hAPP(int,int,ring_1_of_int(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5040,a,5022,a)]. 17.32/17.26 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),B),A) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5040,a,5024,a)]. 17.32/17.26 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C)),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B)). [resolve(5040,a,5025,a)]. 17.32/17.27 Derived: one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),one_one(int))),B). [resolve(5040,a,5026,a)]. 17.32/17.27 Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)). [resolve(5040,a,5029,a)]. 17.32/17.27 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),B),A) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5040,a,5030,b)]. 17.32/17.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,int,C,B)),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(5040,a,5031,a)]. 17.32/17.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) != hAPP(A,int,C,f521(A,int,C,B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(5040,a,5032,a)]. 17.32/17.27 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,int,B,C)),C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C). [resolve(5040,a,5033,a)]. 17.32/17.27 Derived: one_one(int) != hAPP(A,int,B,f524(A,int,B,C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C). [resolve(5040,a,5034,a)]. 17.32/17.27 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)). [resolve(5040,a,5035,a)]. 17.32/17.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(5040,a,5037,a)]. 17.32/17.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f650(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(5040,a,5038,a)]. 17.32/17.27 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5040,a,5039,a)]. 17.32/17.27 5041 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)) # label(fact_3946_setprod__timesf) # label(axiom). [clausify(3801)]. 17.32/17.27 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combs(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D)). [resolve(5041,a,5003,a)]. 17.32/17.27 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)). [resolve(5041,a,5023,a)]. 17.32/17.27 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)). [resolve(5041,a,5027,a)]. 17.32/17.27 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D)). [resolve(5041,a,5036,a)]. 17.32/17.27 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)). [resolve(5041,a,5040,a)]. 17.54/17.50 5042 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f4(B,nat,C,D,E,A)),f6(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5004,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f4(B,nat,C,D,E,A)),f6(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f8(B,nat,C,D,E,A))),hAPP(B,nat,D,f8(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5005,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f5(B,nat,C,D,E,A)),f7(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5006,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f5(B,nat,C,D,E,A)),f7(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f8(B,nat,C,D,E,A))),hAPP(B,nat,D,f8(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5007,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f4(B,nat,C,D,E,A)),f5(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f6(B,nat,C,D,E,A)),f7(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5008,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f4(B,nat,C,D,E,A)),f5(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f6(B,nat,C,D,E,A)),f7(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f8(B,nat,C,D,E,A))),hAPP(B,nat,D,f8(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(5042,a,5009,a)]. 17.54/17.50 Derived: -comm_monoid_add(nat) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),A),B). [resolve(5042,a,5010,a)]. 17.54/17.50 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(5042,a,5011,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(5042,a,5012,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B). [resolve(5042,a,5013,a)]. 17.54/17.50 Derived: -dvd(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B))). [resolve(5042,a,5014,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5042,a,5015,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5042,a,5016,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B). [resolve(5042,a,5017,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(5042,a,5018,a)]. 17.54/17.50 Derived: -comm_monoid_add(nat) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),B). [resolve(5042,a,5019,b)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(5042,a,5020,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f320(A,nat,D,C,B)) != hAPP(A,nat,D,f320(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B). [resolve(5042,a,5021,a)]. 17.54/17.50 Derived: -ring_1(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,int),fun(A,nat),hAPP(fun(int,nat),fun(fun(A,int),fun(A,nat)),combb(int,nat,A),ring_1_of_int(nat)),B)),C) = hAPP(int,nat,ring_1_of_int(nat),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5042,a,5022,a)]. 17.54/17.50 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),B),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5042,a,5024,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C)),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B)). [resolve(5042,a,5025,a)]. 17.54/17.50 Derived: one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),one_one(nat))),B). [resolve(5042,a,5026,a)]. 17.54/17.50 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A). [resolve(5042,a,5028,a)]. 17.54/17.50 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(5042,a,5029,a)]. 17.54/17.50 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),B),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5042,a,5030,b)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,nat,C,B)),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(5042,a,5031,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) != hAPP(A,nat,C,f521(A,nat,C,B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(5042,a,5032,a)]. 17.54/17.50 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,nat,B,C)),C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C). [resolve(5042,a,5033,a)]. 17.54/17.50 Derived: one_one(nat) != hAPP(A,nat,B,f524(A,nat,B,C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C). [resolve(5042,a,5034,a)]. 17.54/17.50 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)). [resolve(5042,a,5035,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(5042,a,5037,a)]. 17.54/17.50 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f650(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(5042,a,5038,a)]. 17.54/17.50 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5042,a,5039,a)]. 17.54/17.50 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D)). [resolve(5042,a,5041,a)]. 17.62/17.62 5043 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(4144)]. 17.62/17.62 Derived: -comm_monoid_add(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),A). [resolve(5043,b,5003,a)]. 17.62/17.62 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),A). [resolve(5043,b,5023,a)]. 17.62/17.62 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),A). [resolve(5043,b,5027,a)]. 17.62/17.62 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),A). [resolve(5043,b,5036,a)]. 17.62/17.62 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),A). [resolve(5043,b,5040,a)]. 17.62/17.62 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),A). [resolve(5043,b,5042,a)]. 17.62/17.62 5044 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f724(A,D,E,C,B)) != hAPP(int,A,E,f724(A,D,E,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(4144)]. 18.05/18.04 Derived: -comm_monoid_add(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f724(quickcheck_code_int,C,D,B,A)) != hAPP(int,quickcheck_code_int,D,f724(quickcheck_code_int,C,D,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),A). [resolve(5044,b,5003,a)]. 18.05/18.04 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f724(complex,C,D,B,A)) != hAPP(int,complex,D,f724(complex,C,D,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),A). [resolve(5044,b,5023,a)]. 18.05/18.04 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f724(real,C,D,B,A)) != hAPP(int,real,D,f724(real,C,D,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),A). [resolve(5044,b,5027,a)]. 18.05/18.04 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f724(rat,C,D,B,A)) != hAPP(int,rat,D,f724(rat,C,D,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),A). [resolve(5044,b,5036,a)]. 18.05/18.04 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f724(int,C,D,B,A)) != hAPP(int,int,D,f724(int,C,D,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),A). [resolve(5044,b,5040,a)]. 18.05/18.04 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f724(nat,C,D,B,A)) != hAPP(int,nat,D,f724(nat,C,D,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),A). [resolve(5044,b,5042,a)]. 18.05/18.04 5045 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),D)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_3959_setprod__constant) # label(axiom). [clausify(4538)]. 18.05/18.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),C)),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5003,a)]. 18.05/18.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),C)),B) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5023,a)]. 18.05/18.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(real,fun(A,real),combk(real,A),C)),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5027,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),C)),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5036,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),C)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5040,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5045,a,5042,a)]. 18.22/18.15 5046 comm_monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f4(B,code_code_numeral,C,D,E,A)),f6(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5004,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f4(B,code_code_numeral,C,D,E,A)),f6(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f8(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f8(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5005,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f5(B,code_code_numeral,C,D,E,A)),f7(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5006,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,f5(B,code_code_numeral,C,D,E,A)),f7(B,code_code_numeral,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f8(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f8(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5007,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),f4(B,code_code_numeral,C,D,E,A)),f5(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),f6(B,code_code_numeral,C,D,E,A)),f7(B,code_code_numeral,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f8(B,code_code_numeral,C,D,E,A)),E)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5008,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,one_one(code_code_numeral)),one_one(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),f4(B,code_code_numeral,C,D,E,A)),f5(B,code_code_numeral,C,D,E,A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),f6(B,code_code_numeral,C,D,E,A)),f7(B,code_code_numeral,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(B,code_code_numeral,C,f8(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f8(B,code_code_numeral,C,D,E,A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),A,hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),C),E)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co302546470etprod(B,code_code_numeral),D),E))). [resolve(5046,a,5009,a)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),A),B). [resolve(5046,a,5010,a)]. 18.22/18.15 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B). [resolve(5046,a,5011,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C). [resolve(5046,a,5012,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(code_code_numeral))),B). [resolve(5046,a,5013,a)]. 18.22/18.15 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B))). [resolve(5046,a,5014,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(A,code_code_numeral,D,C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(5046,a,5015,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5046,a,5016,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(code_code_numeral))),B). [resolve(5046,a,5017,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combs(A,code_code_numeral,fun(code_code_numeral,code_code_numeral)),hAPP(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),hAPP(fun(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral))),fun(fun(A,bool),fun(A,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)))),combb(bool,fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),A),if(code_code_numeral)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(code_code_numeral))),B) = hAPP(A,code_code_numeral,D,C). [resolve(5046,a,5018,a)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),B). [resolve(5046,a,5019,b)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f320(A,code_code_numeral,C,D,B)),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B). [resolve(5046,a,5020,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f320(A,code_code_numeral,D,C,B)) != hAPP(A,code_code_numeral,D,f320(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B). [resolve(5046,a,5021,a)]. 18.22/18.15 Derived: -ring_1(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(fun(A,int),fun(A,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(A,int),fun(A,code_code_numeral)),combb(int,code_code_numeral,A),ring_1_of_int(code_code_numeral)),B)),C) = hAPP(int,code_code_numeral,ring_1_of_int(code_code_numeral),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C)). [resolve(5046,a,5022,a)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),B),A) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5046,a,5024,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combs(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),C)),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B)). [resolve(5046,a,5025,a)]. 18.22/18.15 Derived: one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),one_one(code_code_numeral))),B). [resolve(5046,a,5026,a)]. 18.22/18.15 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),one_one(code_code_numeral)),A). [resolve(5046,a,5028,a)]. 18.22/18.15 Derived: big_co302546470etprod(A,code_code_numeral) = ti(fun(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral)),big_co302546470etprod(A,code_code_numeral)). [resolve(5046,a,5029,a)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),B),A) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5046,a,5030,b)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f521(A,code_code_numeral,C,B)),B)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B). [resolve(5046,a,5031,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,C,f521(A,code_code_numeral,C,B)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B). [resolve(5046,a,5032,a)]. 18.22/18.15 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f524(A,code_code_numeral,B,C)),C)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C). [resolve(5046,a,5033,a)]. 18.22/18.15 Derived: one_one(code_code_numeral) != hAPP(A,code_code_numeral,B,f524(A,code_code_numeral,B,C)) | one_one(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),C). [resolve(5046,a,5034,a)]. 18.22/18.15 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),one_one(code_code_numeral)). [resolve(5046,a,5035,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f650(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C). [resolve(5046,a,5037,a)]. 18.22/18.15 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,D,f650(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C). [resolve(5046,a,5038,a)]. 18.22/18.15 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5046,a,5039,a)]. 18.22/18.15 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combs(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D)). [resolve(5046,a,5041,a)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f724(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),A). [resolve(5046,a,5043,b)]. 18.22/18.15 Derived: -comm_monoid_add(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f724(code_code_numeral,C,D,B,A)) != hAPP(int,code_code_numeral,D,f724(code_code_numeral,C,D,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),A). [resolve(5046,a,5044,b)]. 18.22/18.22 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),C)),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(5046,a,5045,a)]. 18.22/18.22 5047 -semiring_1(A) | -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,nat),fun(B,A),hAPP(fun(nat,A),fun(fun(B,nat),fun(B,A)),combb(nat,A,B),semiring_1_of_nat(A)),C)),D) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),D)) # label(fact_3928_of__nat__setprod) # label(axiom). [clausify(4701)]. 18.22/18.22 Derived: -semiring_1(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),hAPP(fun(A,nat),fun(A,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(A,nat),fun(A,quickcheck_code_int)),combb(nat,quickcheck_code_int,A),semiring_1_of_nat(quickcheck_code_int)),B)),C) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5003,a)]. 18.22/18.22 Derived: -semiring_1(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(fun(A,nat),fun(A,complex),hAPP(fun(nat,complex),fun(fun(A,nat),fun(A,complex)),combb(nat,complex,A),semiring_1_of_nat(complex)),B)),C) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5023,a)]. 18.22/18.22 Derived: -semiring_1(real) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,nat),fun(A,real),hAPP(fun(nat,real),fun(fun(A,nat),fun(A,real)),combb(nat,real,A),semiring_1_of_nat(real)),B)),C) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5027,a)]. 18.22/18.22 Derived: -semiring_1(rat) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,nat),fun(A,rat),hAPP(fun(nat,rat),fun(fun(A,nat),fun(A,rat)),combb(nat,rat,A),semiring_1_of_nat(rat)),B)),C) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5036,a)]. 18.22/18.22 Derived: -semiring_1(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,nat),fun(A,int),hAPP(fun(nat,int),fun(fun(A,nat),fun(A,int)),combb(nat,int,A),semiring_1_of_nat(int)),B)),C) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5040,a)]. 18.22/18.22 Derived: -semiring_1(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),semiring_1_of_nat(nat)),B)),C) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5042,a)]. 18.22/18.22 Derived: -semiring_1(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),hAPP(fun(A,nat),fun(A,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(A,nat),fun(A,code_code_numeral)),combb(nat,code_code_numeral,A),semiring_1_of_nat(code_code_numeral)),B)),C) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(5047,b,5046,a)]. 18.36/18.30 5048 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_3951_setprod__infinite) # label(axiom). [clausify(4732)]. 18.36/18.30 5049 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f819(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3960_setprod__mono__one__left) # label(axiom). [clausify(4778)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C). [resolve(5049,a,5003,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,complex,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C). [resolve(5049,a,5023,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C). [resolve(5049,a,5027,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C). [resolve(5049,a,5036,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(5049,a,5040,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(5049,a,5042,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f819(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C). [resolve(5049,a,5046,a)]. 18.36/18.30 5050 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f819(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3960_setprod__mono__one__left) # label(axiom). [clausify(4778)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f819(A,quickcheck_code_int,D,C,B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C). [resolve(5050,a,5003,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(complex) != hAPP(A,complex,D,f819(A,complex,D,C,B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C). [resolve(5050,a,5023,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(real) != hAPP(A,real,D,f819(A,real,D,C,B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C). [resolve(5050,a,5027,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(rat) != hAPP(A,rat,D,f819(A,rat,D,C,B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C). [resolve(5050,a,5036,a)]. 18.36/18.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f819(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(5050,a,5040,a)]. 18.36/18.37 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f819(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(5050,a,5042,a)]. 18.36/18.37 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,D,f819(A,code_code_numeral,D,C,B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C). [resolve(5050,a,5046,a)]. 18.36/18.37 5051 -comm_monoid_mult(A) | -dvd(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f829(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom). [clausify(4830)]. 18.36/18.37 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))). [resolve(5051,a,5003,a)]. 18.36/18.37 Derived: -dvd(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D))). [resolve(5051,a,5023,a)]. 18.36/18.37 Derived: -dvd(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))). [resolve(5051,a,5027,a)]. 18.36/18.37 Derived: -dvd(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))). [resolve(5051,a,5036,a)]. 18.36/18.37 Derived: -dvd(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D))). [resolve(5051,a,5040,a)]. 18.36/18.37 Derived: -dvd(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D))). [resolve(5051,a,5042,a)]. 18.45/18.37 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f829(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))). [resolve(5051,a,5046,a)]. 18.45/18.37 5052 -comm_monoid_mult(A) | -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,C,f829(B,A,C,D,E))),hAPP(B,A,D,f829(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom). [clausify(4830)]. 18.45/18.37 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f829(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f829(A,quickcheck_code_int,B,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),D))). [resolve(5052,a,5003,a)]. 18.45/18.37 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,B,f829(A,complex,B,C,D))),hAPP(A,complex,C,f829(A,complex,B,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D))). [resolve(5052,a,5023,a)]. 18.45/18.37 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,B,f829(A,real,B,C,D))),hAPP(A,real,C,f829(A,real,B,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))). [resolve(5052,a,5027,a)]. 18.45/18.37 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,B,f829(A,rat,B,C,D))),hAPP(A,rat,C,f829(A,rat,B,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D))). [resolve(5052,a,5036,a)]. 18.45/18.37 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,B,f829(A,int,B,C,D))),hAPP(A,int,C,f829(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D))). [resolve(5052,a,5040,a)]. 18.45/18.37 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,B,f829(A,nat,B,C,D))),hAPP(A,nat,C,f829(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D))). [resolve(5052,a,5042,a)]. 18.45/18.37 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,B,f829(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f829(A,code_code_numeral,B,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),D))). [resolve(5052,a,5046,a)]. 18.45/18.38 5053 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4837)]. 18.45/18.38 Derived: -comm_monoid_add(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),A). [resolve(5053,b,5003,a)]. 18.45/18.38 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),A). [resolve(5053,b,5023,a)]. 18.45/18.38 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),A). [resolve(5053,b,5027,a)]. 18.45/18.38 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),A). [resolve(5053,b,5036,a)]. 18.45/18.38 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),A). [resolve(5053,b,5040,a)]. 18.45/18.38 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),A). [resolve(5053,b,5042,a)]. 18.45/18.38 Derived: -comm_monoid_add(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f833(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),A). [resolve(5053,b,5046,a)]. 19.35/19.30 5054 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f833(A,D,E,C,B)) != hAPP(int,A,E,f833(A,D,E,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4837)]. 19.35/19.30 Derived: -comm_monoid_add(quickcheck_code_int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,quickcheck_code_int,C,f833(quickcheck_code_int,C,D,B,A)) != hAPP(int,quickcheck_code_int,D,f833(quickcheck_code_int,C,D,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),A). [resolve(5054,b,5003,a)]. 19.35/19.30 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f833(complex,C,D,B,A)) != hAPP(int,complex,D,f833(complex,C,D,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),A). [resolve(5054,b,5023,a)]. 19.35/19.30 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f833(real,C,D,B,A)) != hAPP(int,real,D,f833(real,C,D,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),A). [resolve(5054,b,5027,a)]. 19.35/19.30 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f833(rat,C,D,B,A)) != hAPP(int,rat,D,f833(rat,C,D,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),A). [resolve(5054,b,5036,a)]. 19.35/19.30 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f833(int,C,D,B,A)) != hAPP(int,int,D,f833(int,C,D,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),A). [resolve(5054,b,5040,a)]. 19.35/19.30 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f833(nat,C,D,B,A)) != hAPP(int,nat,D,f833(nat,C,D,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),A). [resolve(5054,b,5042,a)]. 19.35/19.30 Derived: -comm_monoid_add(code_code_numeral) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,code_code_numeral,C,f833(code_code_numeral,C,D,B,A)) != hAPP(int,code_code_numeral,D,f833(code_code_numeral,C,D,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),A). [resolve(5054,b,5046,a)]. 19.35/19.30 5055 ordered_semiring(rat) # label(arity_Rat_Orat___Rings_Oordered__semiring) # label(axiom). [assumption]. 19.72/19.67 5056 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_372_mult__left__mono) # label(axiom). [clausify(24)]. 19.72/19.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(5055,a,5056,a)]. 19.72/19.67 5057 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_368_mult__mono_H) # label(axiom). [clausify(1453)]. 19.72/19.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5057,a,5055,a)]. 19.72/19.67 5058 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_373_mult__right__mono) # label(axiom). [clausify(1753)]. 19.72/19.68 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(5058,a,5055,a)]. 19.72/19.68 5059 ordered_semiring(int) # label(arity_Int_Oint___Rings_Oordered__semiring) # label(axiom). [assumption]. 19.72/19.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(5059,a,5056,a)]. 19.72/19.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5059,a,5057,a)]. 19.72/19.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(5059,a,5058,a)]. 19.72/19.68 5060 ordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Oordered__semiring) # label(axiom). [assumption]. 20.82/20.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5060,a,5056,a)]. 20.82/20.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5060,a,5057,a)]. 20.82/20.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5060,a,5058,a)]. 20.82/20.74 5061 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption]. 20.82/20.74 5062 ordered_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__semiring) # label(axiom). [assumption]. 20.82/20.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(5062,a,5056,a)]. 20.82/20.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(5062,a,5057,a)]. 20.82/20.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(5062,a,5058,a)]. 21.60/21.57 5063 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_367_mult__mono) # label(axiom). [clausify(4630)]. 21.60/21.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5063,a,5055,a)]. 21.60/21.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5063,a,5059,a)]. 21.60/21.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5063,a,5060,a)]. 21.60/21.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(5063,a,5062,a)]. 21.60/21.57 5064 ordered_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__semiring) # label(axiom). [assumption]. 21.60/21.57 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(5064,a,5056,a)]. 22.72/22.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(5064,a,5057,a)]. 22.72/22.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(5064,a,5058,a)]. 22.72/22.69 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(5064,a,5063,a)]. 22.72/22.69 5065 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,B)))) # label(fact_2602_iszero__number__of__Bit1) # label(axiom). [clausify(47)]. 22.72/22.69 5066 number_ring(rat) # label(arity_Rat_Orat___Int_Onumber__ring) # label(axiom). [assumption]. 22.72/22.69 Derived: -ring_char_0(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,A)))). [resolve(5065,a,5066,a)]. 22.72/22.69 5067 -number_ring(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) # label(fact_111_mult__numeral__1__right) # label(axiom). [clausify(55)]. 22.72/22.69 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))). [resolve(5067,a,5066,a)]. 22.72/22.69 5068 -number_ring(A) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(int,A,number_number_of(A),B) # label(fact_3581_number__of__eq) # label(axiom). [clausify(101)]. 22.72/22.69 Derived: hAPP(int,rat,ring_1_of_int(rat),A) = hAPP(int,rat,number_number_of(rat),A). [resolve(5068,a,5066,a)]. 22.72/22.69 5069 -number_ring(A) | -field_inverse_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2114_minus1__divide) # label(axiom). [clausify(190)]. 22.72/22.72 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),min_1)),A). [resolve(5069,a,5066,a)]. 22.72/22.72 5070 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_47_le__special_I3_J) # label(axiom). [clausify(215)]. 22.72/22.72 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5070,b,5066,a)]. 22.72/22.72 5071 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_47_le__special_I3_J) # label(axiom). [clausify(215)]. 22.72/22.72 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5071,b,5066,a)]. 22.72/22.72 5072 -number_ring(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2101_mult__minus1) # label(axiom). [clausify(263)]. 22.72/22.72 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),min_1)),A). [resolve(5072,a,5066,a)]. 22.72/22.72 5073 -number_ring(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_364_power__m1__even) # label(axiom). [clausify(266)]. 22.72/22.72 Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5073,a,5066,a)]. 22.72/22.72 5074 -linordered_idom(A) | -number_ring(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_1896_abs__power__minus__one) # label(axiom). [clausify(344)]. 22.72/22.72 Derived: -linordered_idom(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(5074,b,5066,a)]. 22.72/22.72 5075 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,bit1,pls))) # label(fact_16_add__special_I3_J) # label(axiom). [clausify(355)]. 22.72/22.72 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,bit1,pls))). [resolve(5075,a,5066,a)]. 22.72/22.72 5076 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom). [clausify(472)]. 22.72/22.72 Derived: -ring_char_0(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(5076,a,5066,a)]. 22.72/22.72 5077 -number_ring(A) | -ring_char_0(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom). [clausify(472)]. 22.82/22.78 Derived: -ring_char_0(rat) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(5077,a,5066,a)]. 22.82/22.78 5078 -number_ring(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)))) # label(fact_2621_not__iszero__Numeral1) # label(axiom). [clausify(500)]. 22.82/22.78 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)))). [resolve(5078,a,5066,a)]. 22.82/22.78 5079 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),D)) # label(fact_507_add__number__of__diff1) # label(axiom). [clausify(501)]. 22.82/22.78 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),C)). [resolve(5079,a,5066,a)]. 22.82/22.78 5080 -real_n2089651433ebra_1(A) | -number_ring(A) | hAPP(A,real,norm_norm(A),hAPP(int,A,number_number_of(A),B)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),B)) # label(fact_1892_norm__number__of) # label(axiom). [clausify(642)]. 22.82/22.78 Derived: -real_n2089651433ebra_1(rat) | hAPP(rat,real,norm_norm(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(5080,b,5066,a)]. 22.82/22.78 5081 -number_ring(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,A,number_number_of(A),B) = zero_zero(A) # label(fact_2625_eq__special_I3_J) # label(axiom). [clausify(881)]. 22.82/22.78 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,rat,number_number_of(rat),A) = zero_zero(rat). [resolve(5081,a,5066,a)]. 22.82/22.78 5082 -number_ring(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,A,number_number_of(A),B) != zero_zero(A) # label(fact_2625_eq__special_I3_J) # label(axiom). [clausify(881)]. 22.82/22.78 Derived: hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,rat,number_number_of(rat),A) != zero_zero(rat). [resolve(5082,a,5066,a)]. 22.82/22.78 5083 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) # label(fact_153_number__of__add) # label(axiom). [clausify(922)]. 22.82/22.78 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(5083,a,5066,a)]. 22.82/22.78 5084 -number_ring(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(int,A,number_number_of(A),min_1) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2458_neg__one__even__odd__power) # label(axiom). [clausify(930)]. 22.82/22.78 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,rat,number_number_of(rat),min_1) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),A). [resolve(5084,a,5066,a)]. 22.82/22.78 5085 -number_ring(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2458_neg__one__even__odd__power) # label(axiom). [clausify(930)]. 22.87/22.81 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),A). [resolve(5085,a,5066,a)]. 22.87/22.81 5086 number_ring(complex) # label(arity_Complex_Ocomplex___Int_Onumber__ring) # label(axiom). [assumption]. 22.87/22.81 Derived: -ring_char_0(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,A)))). [resolve(5086,a,5065,a)]. 22.87/22.81 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))). [resolve(5086,a,5067,a)]. 22.87/22.81 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(int,complex,number_number_of(complex),min_1)),A). [resolve(5086,a,5069,a)]. 22.87/22.81 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5086,a,5070,b)]. 22.87/22.81 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5086,a,5071,b)]. 22.87/22.81 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),min_1)),A). [resolve(5086,a,5072,a)]. 22.87/22.81 Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5086,a,5073,a)]. 22.87/22.81 Derived: -linordered_idom(complex) | one_one(complex) = hAPP(complex,complex,abs_abs(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),min_1)),A)). [resolve(5086,a,5074,b)]. 22.87/22.81 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,bit1,pls))). [resolve(5086,a,5075,a)]. 22.87/22.81 Derived: -ring_char_0(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(5086,a,5076,a)]. 22.87/22.81 Derived: -ring_char_0(complex) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(5086,a,5077,a)]. 22.87/22.81 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)))). [resolve(5086,a,5078,a)]. 22.87/22.81 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,number_number_of(complex),B)),C)). [resolve(5086,a,5079,a)]. 22.87/22.81 Derived: -real_n2089651433ebra_1(complex) | hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(5086,a,5080,b)]. 22.87/22.83 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,complex,number_number_of(complex),A) = zero_zero(complex). [resolve(5086,a,5081,a)]. 22.87/22.83 Derived: hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,complex,number_number_of(complex),A) != zero_zero(complex). [resolve(5086,a,5082,a)]. 22.87/22.83 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(5086,a,5083,a)]. 22.87/22.83 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,complex,number_number_of(complex),min_1) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),min_1)),A). [resolve(5086,a,5084,a)]. 22.87/22.83 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),min_1)),A). [resolve(5086,a,5085,a)]. 22.87/22.83 5087 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom). [assumption]. 22.87/22.83 Derived: -ring_char_0(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,A)))). [resolve(5087,a,5065,a)]. 22.87/22.83 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))). [resolve(5087,a,5067,a)]. 22.87/22.83 Derived: -field_inverse_zero(int) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),one_one(int)),A)) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),hAPP(int,int,number_number_of(int),min_1)),A). [resolve(5087,a,5069,a)]. 22.87/22.83 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5087,a,5070,b)]. 22.87/22.83 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5087,a,5071,b)]. 22.87/22.83 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),min_1)),A). [resolve(5087,a,5072,a)]. 22.87/22.83 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5087,a,5073,a)]. 22.87/22.83 Derived: -linordered_idom(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),A)). [resolve(5087,a,5074,b)]. 22.87/22.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),one_one(int)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,bit1,pls))). [resolve(5087,a,5075,a)]. 22.87/22.83 Derived: -ring_char_0(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(5087,a,5076,a)]. 22.87/22.83 Derived: -ring_char_0(int) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(5087,a,5077,a)]. 22.87/22.83 Derived: -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)))). [resolve(5087,a,5078,a)]. 22.87/22.83 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),B)),C)). [resolve(5087,a,5079,a)]. 22.87/22.85 Derived: -real_n2089651433ebra_1(int) | hAPP(int,real,norm_norm(int),hAPP(int,int,number_number_of(int),A)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(5087,a,5080,b)]. 22.87/22.85 Derived: -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,int,number_number_of(int),A) = zero_zero(int). [resolve(5087,a,5081,a)]. 22.87/22.85 Derived: hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,int,number_number_of(int),A) != zero_zero(int). [resolve(5087,a,5082,a)]. 22.87/22.85 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(5087,a,5083,a)]. 22.87/22.85 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,int,number_number_of(int),min_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),A). [resolve(5087,a,5084,a)]. 22.87/22.85 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),A). [resolve(5087,a,5085,a)]. 22.87/22.85 5088 -number_ring(A) | hAPP(int,A,number_number_of(A),B) != zero_zero(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2624_eq__special_I1_J) # label(axiom). [clausify(1000)]. 22.87/22.85 Derived: hAPP(int,rat,number_number_of(rat),A) != zero_zero(rat) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5088,a,5066,a)]. 22.87/22.85 Derived: hAPP(int,complex,number_number_of(complex),A) != zero_zero(complex) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5088,a,5086,a)]. 22.87/22.85 Derived: hAPP(int,int,number_number_of(int),A) != zero_zero(int) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5088,a,5087,a)]. 22.87/22.85 5089 -number_ring(A) | hAPP(int,A,number_number_of(A),B) = zero_zero(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2624_eq__special_I1_J) # label(axiom). [clausify(1000)]. 22.87/22.85 Derived: hAPP(int,rat,number_number_of(rat),A) = zero_zero(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5089,a,5066,a)]. 22.87/22.85 Derived: hAPP(int,complex,number_number_of(complex),A) = zero_zero(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5089,a,5086,a)]. 22.87/22.85 Derived: hAPP(int,int,number_number_of(int),A) = zero_zero(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5089,a,5087,a)]. 22.87/22.85 5090 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_180_less__special_I4_J) # label(axiom). [clausify(1005)]. 22.98/22.91 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5090,a,5066,a)]. 22.98/22.91 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5090,a,5086,a)]. 22.98/22.91 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5090,a,5087,a)]. 22.98/22.91 5091 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_180_less__special_I4_J) # label(axiom). [clausify(1005)]. 22.98/22.91 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5091,a,5066,a)]. 22.98/22.91 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5091,a,5086,a)]. 22.98/22.91 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5091,a,5087,a)]. 22.98/22.91 5092 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) # label(fact_1531_number__of__succ) # label(axiom). [clausify(1136)]. 22.98/22.91 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,succ,A)). [resolve(5092,a,5066,a)]. 22.98/22.91 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,succ,A)). [resolve(5092,a,5086,a)]. 22.98/22.91 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)). [resolve(5092,a,5087,a)]. 22.98/22.91 5093 -number_ring(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),pls))) # label(fact_2603_iszero__Numeral0) # label(axiom). [clausify(1168)]. 22.98/22.91 Derived: hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),pls))). [resolve(5093,a,5066,a)]. 22.98/22.91 Derived: hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),pls))). [resolve(5093,a,5086,a)]. 22.98/22.91 Derived: hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),pls))). [resolve(5093,a,5087,a)]. 22.98/22.91 5094 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom). [clausify(1195)]. 22.98/22.91 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5094,b,5066,a)]. 22.98/22.91 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5094,b,5086,a)]. 23.02/22.99 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5094,b,5087,a)]. 23.02/22.99 5095 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom). [clausify(1195)]. 23.02/22.99 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5095,b,5066,a)]. 23.02/22.99 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5095,b,5086,a)]. 23.02/22.99 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5095,b,5087,a)]. 23.02/22.99 5096 -number_ring(A) | one_one(A) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) # label(fact_173_numeral__1__eq__1) # label(axiom). [clausify(1330)]. 23.02/22.99 Derived: one_one(rat) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)). [resolve(5096,a,5066,a)]. 23.02/22.99 Derived: one_one(complex) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)). [resolve(5096,a,5086,a)]. 23.02/22.99 5097 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)) # label(fact_42_mult__number__of__left) # label(axiom). [clausify(1447)]. 23.02/22.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)). [resolve(5097,a,5066,a)]. 23.02/22.99 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C)). [resolve(5097,a,5086,a)]. 23.02/22.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C)). [resolve(5097,a,5087,a)]. 23.02/22.99 5098 -number_ring(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(A) = hAPP(int,A,number_number_of(A),B) # label(fact_2503_eq__special_I4_J) # label(axiom). [clausify(1459)]. 23.02/22.99 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(rat) = hAPP(int,rat,number_number_of(rat),A). [resolve(5098,a,5066,a)]. 23.02/23.00 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(complex) = hAPP(int,complex,number_number_of(complex),A). [resolve(5098,a,5086,a)]. 23.02/23.00 Derived: -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(int) = hAPP(int,int,number_number_of(int),A). [resolve(5098,a,5087,a)]. 23.02/23.00 5099 -number_ring(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(A) != hAPP(int,A,number_number_of(A),B) # label(fact_2503_eq__special_I4_J) # label(axiom). [clausify(1459)]. 23.02/23.00 Derived: hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(rat) != hAPP(int,rat,number_number_of(rat),A). [resolve(5099,a,5066,a)]. 23.02/23.00 Derived: hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(complex) != hAPP(int,complex,number_number_of(complex),A). [resolve(5099,a,5086,a)]. 23.02/23.00 Derived: hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(int) != hAPP(int,int,number_number_of(int),A). [resolve(5099,a,5087,a)]. 23.02/23.00 5100 number_ring(real) # label(arity_RealDef_Oreal___Int_Onumber__ring) # label(axiom). [assumption]. 23.02/23.00 Derived: -ring_char_0(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,A)))). [resolve(5100,a,5065,a)]. 23.02/23.00 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))). [resolve(5100,a,5067,a)]. 23.02/23.00 Derived: hAPP(int,real,ring_1_of_int(real),A) = hAPP(int,real,number_number_of(real),A). [resolve(5100,a,5068,a)]. 23.02/23.00 Derived: -field_inverse_zero(real) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5100,a,5069,a)]. 23.02/23.00 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5100,a,5070,b)]. 23.02/23.00 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(5100,a,5071,b)]. 23.02/23.00 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5100,a,5072,a)]. 23.02/23.00 Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5100,a,5073,a)]. 23.02/23.00 Derived: -linordered_idom(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(5100,a,5074,b)]. 23.02/23.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,bit1,pls))). [resolve(5100,a,5075,a)]. 23.02/23.02 Derived: -ring_char_0(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(5100,a,5076,a)]. 23.02/23.02 Derived: -ring_char_0(real) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(5100,a,5077,a)]. 23.02/23.02 Derived: -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)))). [resolve(5100,a,5078,a)]. 23.02/23.02 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),C)). [resolve(5100,a,5079,a)]. 23.02/23.02 Derived: -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,real,number_number_of(real),A) = zero_zero(real). [resolve(5100,a,5081,a)]. 23.02/23.02 Derived: hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),pls))))) | hAPP(int,real,number_number_of(real),A) != zero_zero(real). [resolve(5100,a,5082,a)]. 23.02/23.02 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(5100,a,5083,a)]. 23.02/23.02 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,real,number_number_of(real),min_1) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5100,a,5084,a)]. 23.02/23.02 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5100,a,5085,a)]. 23.02/23.02 Derived: hAPP(int,real,number_number_of(real),A) != zero_zero(real) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5100,a,5088,a)]. 23.02/23.02 Derived: hAPP(int,real,number_number_of(real),A) = zero_zero(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5100,a,5089,a)]. 23.02/23.02 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5100,a,5090,a)]. 23.02/23.02 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5100,a,5091,a)]. 23.02/23.02 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)). [resolve(5100,a,5092,a)]. 23.02/23.02 Derived: hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),pls))). [resolve(5100,a,5093,a)]. 23.02/23.02 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5100,a,5094,b)]. 23.02/23.02 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5100,a,5095,b)]. 23.17/23.14 Derived: one_one(real) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)). [resolve(5100,a,5096,a)]. 23.17/23.14 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)). [resolve(5100,a,5097,a)]. 23.17/23.14 Derived: -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(real) = hAPP(int,real,number_number_of(real),A). [resolve(5100,a,5098,a)]. 23.17/23.14 Derived: hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))) | one_one(real) != hAPP(int,real,number_number_of(real),A). [resolve(5100,a,5099,a)]. 23.17/23.14 5101 -number_ring(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,A,number_number_of(A),min_1) # label(fact_3591_of__int__m1) # label(axiom). [clausify(1640)]. 23.17/23.14 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,rat,number_number_of(rat),min_1). [resolve(5101,a,5066,a)]. 23.17/23.14 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,complex,number_number_of(complex),min_1). [resolve(5101,a,5086,a)]. 23.17/23.14 Derived: hAPP(int,int,ring_1_of_int(int),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,int,number_number_of(int),min_1). [resolve(5101,a,5087,a)]. 23.17/23.14 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,real,number_number_of(real),min_1). [resolve(5101,a,5100,a)]. 23.17/23.14 5102 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B) # label(fact_140_mult__2) # label(axiom). [clausify(1752)]. 23.17/23.14 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(5102,a,5066,a)]. 23.17/23.14 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(5102,a,5086,a)]. 23.17/23.14 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(5102,a,5087,a)]. 23.17/23.14 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(5102,a,5100,a)]. 23.17/23.14 5103 -field_char_0(A) | -number_ring(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),field_char_0_Rats(A))) # label(fact_3694_Rats__number__of) # label(axiom). [clausify(1788)]. 23.17/23.14 Derived: -field_char_0(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,number_number_of(rat),A)),field_char_0_Rats(rat))). [resolve(5103,b,5066,a)]. 23.17/23.14 Derived: -field_char_0(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,number_number_of(complex),A)),field_char_0_Rats(complex))). [resolve(5103,b,5086,a)]. 23.17/23.14 Derived: -field_char_0(int) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,number_number_of(int),A)),field_char_0_Rats(int))). [resolve(5103,b,5087,a)]. 23.29/23.22 Derived: -field_char_0(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),field_char_0_Rats(real))). [resolve(5103,b,5100,a)]. 23.29/23.22 5104 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),one_one(A))),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,pred,B)) # label(fact_2910_number__of__pred) # label(axiom). [clausify(1810)]. 23.29/23.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,pred,A)). [resolve(5104,a,5066,a)]. 23.29/23.22 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,pred,A)). [resolve(5104,a,5086,a)]. 23.29/23.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,pred,A)). [resolve(5104,a,5087,a)]. 23.29/23.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),one_one(real))),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,pred,A)). [resolve(5104,a,5100,a)]. 23.29/23.22 5105 -number_ring(A) | -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_1514_of__nat__number__of__eq) # label(axiom). [clausify(1886)]. 23.29/23.22 Derived: -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(5105,a,5066,a)]. 23.29/23.22 Derived: -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(5105,a,5086,a)]. 23.29/23.22 Derived: -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(5105,a,5100,a)]. 23.29/23.22 5106 -number_ring(A) | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),B))) | hAPP(int,A,number_number_of(A),B) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) # label(fact_1514_of__nat__number__of__eq) # label(axiom). [clausify(1886)]. 23.29/23.22 Derived: hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(int,rat,number_number_of(rat),A) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,number_number_of(nat),A)). [resolve(5106,a,5066,a)]. 23.29/23.22 Derived: hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(int,complex,number_number_of(complex),A) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,number_number_of(nat),A)). [resolve(5106,a,5086,a)]. 23.29/23.22 Derived: hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(int,real,number_number_of(real),A) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)). [resolve(5106,a,5100,a)]. 23.29/23.22 5107 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_1445_of__nat__less__two__power) # label(axiom). [clausify(1992)]. 23.29/23.22 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5107,a,5066,a)]. 23.29/23.22 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5107,a,5086,a)]. 23.33/23.32 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,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5107,a,5087,a)]. 23.33/23.32 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,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5107,a,5100,a)]. 23.33/23.32 5108 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2113_abs__number__of) # label(axiom). [clausify(2006)]. 23.33/23.32 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(complex,complex,abs_abs(complex),hAPP(int,complex,number_number_of(complex),A)). [resolve(5108,a,5086,a)]. 23.33/23.32 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)). [resolve(5108,a,5087,a)]. 23.33/23.32 5109 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_2113_abs__number__of) # label(axiom). [clausify(2006)]. 23.33/23.32 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hAPP(complex,complex,abs_abs(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),A). [resolve(5109,a,5086,a)]. 23.33/23.32 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5109,a,5087,a)]. 23.33/23.32 5110 -real_algebra_1(A) | -number_ring(A) | hAPP(int,A,number_number_of(A),B) = hAPP(real,A,of_real(A),hAPP(int,real,number_number_of(real),B)) # label(fact_2785_of__real__number__of__eq) # label(axiom). [clausify(2029)]. 23.33/23.32 Derived: -real_algebra_1(rat) | hAPP(int,rat,number_number_of(rat),A) = hAPP(real,rat,of_real(rat),hAPP(int,real,number_number_of(real),A)). [resolve(5110,b,5066,a)]. 23.33/23.32 Derived: -real_algebra_1(complex) | hAPP(int,complex,number_number_of(complex),A) = hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),A)). [resolve(5110,b,5086,a)]. 23.33/23.32 Derived: -real_algebra_1(int) | hAPP(int,int,number_number_of(int),A) = hAPP(real,int,of_real(int),hAPP(int,real,number_number_of(real),A)). [resolve(5110,b,5087,a)]. 23.33/23.32 Derived: -real_algebra_1(real) | hAPP(int,real,number_number_of(real),A) = hAPP(real,real,of_real(real),hAPP(int,real,number_number_of(real),A)). [resolve(5110,b,5100,a)]. 23.33/23.32 5111 -number_ring(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2457_Parity_Oneg__one__even__power) # label(axiom). [clausify(2111)]. 23.33/23.32 5112 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),C))) # label(fact_2163_diff__number__of__eq) # label(axiom). [clausify(2214)]. 23.42/23.37 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B))). [resolve(5112,a,5066,a)]. 23.42/23.37 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B))). [resolve(5112,a,5086,a)]. 23.42/23.37 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B))). [resolve(5112,a,5087,a)]. 23.42/23.37 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B))). [resolve(5112,a,5100,a)]. 23.42/23.37 5113 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B))),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,uminus_uminus(int),B))),C) # label(fact_2045_minus__number__of__mult) # label(axiom). [clausify(2271)]. 23.42/23.37 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,number_number_of(rat),A))),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,uminus_uminus(int),A))),B). [resolve(5113,a,5066,a)]. 23.42/23.37 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),A))),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),A))),B). [resolve(5113,a,5086,a)]. 23.42/23.37 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),A))),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),A))),B). [resolve(5113,a,5087,a)]. 23.42/23.37 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),A))),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),A))),B). [resolve(5113,a,5100,a)]. 23.42/23.37 5114 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_150_less__number__of) # label(axiom). [clausify(2326)]. 23.42/23.37 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5114,b,5066,a)]. 23.42/23.37 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5114,b,5086,a)]. 23.42/23.37 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5114,b,5087,a)]. 23.53/23.48 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5114,b,5100,a)]. 23.53/23.48 5115 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_150_less__number__of) # label(axiom). [clausify(2326)]. 23.53/23.48 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5115,b,5066,a)]. 23.53/23.48 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5115,b,5086,a)]. 23.53/23.48 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5115,b,5087,a)]. 23.53/23.48 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5115,b,5100,a)]. 23.53/23.48 5116 -number_ring(A) | -linordered_idom(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)),hAPP(int,A,number_number_of(A),B))) # label(fact_181_less__special_I2_J) # label(axiom). [clausify(2345)]. 23.53/23.48 Derived: -linordered_idom(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5116,a,5066,a)]. 23.53/23.48 Derived: -linordered_idom(complex) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A))). [resolve(5116,a,5086,a)]. 23.53/23.48 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)),hAPP(int,int,number_number_of(int),A))). [resolve(5116,a,5087,a)]. 23.53/23.48 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)),hAPP(int,real,number_number_of(real),A))). [resolve(5116,a,5100,a)]. 23.53/23.48 5117 -number_ring(A) | -linordered_idom(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)),hAPP(int,A,number_number_of(A),B))) # label(fact_181_less__special_I2_J) # label(axiom). [clausify(2345)]. 23.53/23.48 Derived: -linordered_idom(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5117,a,5066,a)]. 23.53/23.48 Derived: -linordered_idom(complex) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A))). [resolve(5117,a,5086,a)]. 23.53/23.48 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)),hAPP(int,int,number_number_of(int),A))). [resolve(5117,a,5087,a)]. 23.59/23.52 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)),hAPP(int,real,number_number_of(real),A))). [resolve(5117,a,5100,a)]. 23.59/23.52 5118 -number_ring(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(int,A,number_number_of(A),min_1) # label(fact_2104_number__of__Min) # label(axiom). [clausify(2363)]. 23.59/23.52 Derived: hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(int,rat,number_number_of(rat),min_1). [resolve(5118,a,5066,a)]. 23.59/23.52 Derived: hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) = hAPP(int,complex,number_number_of(complex),min_1). [resolve(5118,a,5086,a)]. 23.59/23.52 Derived: hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(int,int,number_number_of(int),min_1). [resolve(5118,a,5087,a)]. 23.59/23.52 Derived: hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(int,real,number_number_of(real),min_1). [resolve(5118,a,5100,a)]. 23.59/23.52 5119 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) # label(fact_475_number__of__diff) # label(axiom). [clausify(2389)]. 23.59/23.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)). [resolve(5119,a,5066,a)]. 23.59/23.52 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)). [resolve(5119,a,5086,a)]. 23.59/23.52 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)). [resolve(5119,a,5087,a)]. 23.59/23.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)). [resolve(5119,a,5100,a)]. 23.59/23.52 5120 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_48_le__special_I1_J) # label(axiom). [clausify(2402)]. 23.59/23.52 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5120,a,5066,a)]. 23.59/23.52 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5120,a,5086,a)]. 23.59/23.52 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5120,a,5087,a)]. 23.59/23.52 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5120,a,5100,a)]. 23.59/23.52 5121 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_48_le__special_I1_J) # label(axiom). [clausify(2402)]. 23.64/23.60 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5121,a,5066,a)]. 23.64/23.60 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5121,a,5086,a)]. 23.64/23.60 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5121,a,5087,a)]. 23.64/23.60 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(5121,a,5100,a)]. 23.64/23.60 5122 -number_ring(A) | -field(A) | hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) # label(fact_2587_inverse__numeral__1) # label(axiom). [clausify(2441)]. 23.64/23.60 Derived: -field(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)). [resolve(5122,a,5066,a)]. 23.64/23.60 Derived: -field(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)). [resolve(5122,a,5086,a)]. 23.64/23.60 Derived: -field(int) | hAPP(int,int,inverse_inverse(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)). [resolve(5122,a,5087,a)]. 23.64/23.60 Derived: -field(real) | hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)). [resolve(5122,a,5100,a)]. 23.64/23.60 5123 -number_ring(A) | -field(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) # label(fact_1733_divide__numeral__1) # label(axiom). [clausify(2498)]. 23.64/23.60 Derived: -field(rat) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))). [resolve(5123,a,5066,a)]. 23.64/23.60 Derived: -field(complex) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))). [resolve(5123,a,5086,a)]. 23.64/23.60 Derived: -field(int) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))). [resolve(5123,a,5087,a)]. 23.64/23.60 Derived: -field(real) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))). [resolve(5123,a,5100,a)]. 23.64/23.60 5124 -number_ring(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),pls)) # label(fact_149_add__numeral__0__right) # label(axiom). [clausify(2524)]. 23.64/23.60 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),pls)). [resolve(5124,a,5066,a)]. 23.64/23.60 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(int,complex,number_number_of(complex),pls)). [resolve(5124,a,5086,a)]. 23.64/23.60 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,number_number_of(int),pls)). [resolve(5124,a,5087,a)]. 23.64/23.60 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),pls)). [resolve(5124,a,5100,a)]. 23.64/23.60 5125 -number_ring(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),pls)),B) # label(fact_148_add__numeral__0) # label(axiom). [clausify(2552)]. 23.73/23.67 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),pls)),A). [resolve(5125,a,5066,a)]. 23.73/23.67 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),pls)),A). [resolve(5125,a,5086,a)]. 23.73/23.67 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),pls)),A). [resolve(5125,a,5087,a)]. 23.73/23.67 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),pls)),A). [resolve(5125,a,5100,a)]. 23.73/23.67 5126 -number_ring(A) | hAPP(int,A,ring_1_of_int(A),hAPP(int,int,number_number_of(int),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_3565_of__int__number__of__eq) # label(axiom). [clausify(2574)]. 23.73/23.67 Derived: hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,number_number_of(int),A)) = hAPP(int,rat,number_number_of(rat),A). [resolve(5126,a,5066,a)]. 23.73/23.67 Derived: hAPP(int,complex,ring_1_of_int(complex),hAPP(int,int,number_number_of(int),A)) = hAPP(int,complex,number_number_of(complex),A). [resolve(5126,a,5086,a)]. 23.73/23.67 Derived: hAPP(int,int,ring_1_of_int(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5126,a,5087,a)]. 23.73/23.67 Derived: hAPP(int,real,ring_1_of_int(real),hAPP(int,int,number_number_of(int),A)) = hAPP(int,real,number_number_of(real),A). [resolve(5126,a,5100,a)]. 23.73/23.67 5127 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B))),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,B)) # label(fact_171_number__of__Bit1) # label(axiom). [clausify(2634)]. 23.73/23.67 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,A)). [resolve(5127,a,5066,a)]. 23.73/23.67 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A))),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,A)). [resolve(5127,a,5086,a)]. 23.73/23.67 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A))),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,A)). [resolve(5127,a,5087,a)]. 23.73/23.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A))),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,A)). [resolve(5127,a,5100,a)]. 23.73/23.67 5128 -number_ring(A) | one_one(A) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) # label(fact_174_semiring__norm_I110_J) # label(axiom). [clausify(2660)]. 23.73/23.67 5129 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)) # label(fact_137_double__number__of__Bit0) # label(axiom). [clausify(2664)]. 23.73/23.67 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)). [resolve(5129,a,5066,a)]. 23.73/23.67 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)). [resolve(5129,a,5086,a)]. 23.73/23.67 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)). [resolve(5129,a,5087,a)]. 24.01/23.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)). [resolve(5129,a,5100,a)]. 24.01/23.95 5130 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_177_less__special_I1_J) # label(axiom). [clausify(2725)]. 24.01/23.95 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5130,a,5066,a)]. 24.01/23.95 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5130,a,5086,a)]. 24.01/23.95 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5130,a,5087,a)]. 24.01/23.95 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5130,a,5100,a)]. 24.01/23.95 5131 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_177_less__special_I1_J) # label(axiom). [clausify(2725)]. 24.01/23.95 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5131,a,5066,a)]. 24.01/23.95 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5131,a,5086,a)]. 24.01/23.95 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5131,a,5087,a)]. 24.01/23.95 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5131,a,5100,a)]. 24.01/23.95 5132 -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(int,A,number_number_of(A),B) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) # label(fact_1446_of__nat__number__of__lemma) # label(axiom). [clausify(2943)]. 24.01/23.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,rat,number_number_of(rat),A) = hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,number_number_of(nat),A)). [resolve(5132,a,5066,a)]. 24.01/23.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,complex,number_number_of(complex),A) = hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,number_number_of(nat),A)). [resolve(5132,a,5086,a)]. 24.01/23.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,int,number_number_of(int),A) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)). [resolve(5132,a,5087,a)]. 24.24/24.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,real,number_number_of(real),A) = hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)). [resolve(5132,a,5100,a)]. 24.24/24.18 5133 -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_1446_of__nat__number__of__lemma) # label(axiom). [clausify(2943)]. 24.24/24.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(5133,a,5066,a)]. 24.24/24.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(5133,a,5086,a)]. 24.24/24.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(5133,a,5087,a)]. 24.24/24.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(5133,a,5100,a)]. 24.24/24.18 5134 -number_ring(A) | -field(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) # label(fact_1734_divide__Numeral1) # label(axiom). [clausify(2984)]. 24.24/24.18 5135 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) # label(fact_43_arith__simps_I32_J) # label(axiom). [clausify(3065)]. 24.24/24.18 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5135,a,5066,a)]. 24.24/24.18 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5135,a,5086,a)]. 24.24/24.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5135,a,5087,a)]. 24.24/24.18 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5135,a,5100,a)]. 24.24/24.18 5136 -number_ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,uminus_uminus(int),B)) # label(fact_2040_number__of__minus) # label(axiom). [clausify(3217)]. 24.24/24.18 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,uminus_uminus(int),A)). [resolve(5136,a,5066,a)]. 24.24/24.18 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),A)). [resolve(5136,a,5086,a)]. 24.24/24.18 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(5136,a,5087,a)]. 24.24/24.22 Derived: hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),A)). [resolve(5136,a,5100,a)]. 24.24/24.22 5137 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))) # label(fact_2184_diff__special_I2_J) # label(axiom). [clausify(3221)]. 24.24/24.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))). [resolve(5137,a,5066,a)]. 24.24/24.22 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))). [resolve(5137,a,5086,a)]. 24.24/24.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),A)),one_one(int)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))). [resolve(5137,a,5087,a)]. 24.24/24.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))). [resolve(5137,a,5100,a)]. 24.24/24.22 5138 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),D)) # label(fact_151_add__number__of__left) # label(axiom). [clausify(3254)]. 24.24/24.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),C)). [resolve(5138,a,5066,a)]. 24.24/24.22 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),B)),C)). [resolve(5138,a,5086,a)]. 24.24/24.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),B)),C)). [resolve(5138,a,5087,a)]. 24.24/24.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),C)). [resolve(5138,a,5100,a)]. 24.24/24.22 5139 -number_ring(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),ring_1_Ints(A))) # label(fact_3843_Ints__number__of) # label(axiom). [clausify(3262)]. 24.24/24.22 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,number_number_of(rat),A)),ring_1_Ints(rat))). [resolve(5139,a,5066,a)]. 24.83/24.75 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,number_number_of(complex),A)),ring_1_Ints(complex))). [resolve(5139,a,5086,a)]. 24.83/24.75 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,number_number_of(int),A)),ring_1_Ints(int))). [resolve(5139,a,5087,a)]. 24.83/24.75 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),ring_1_Ints(real))). [resolve(5139,a,5100,a)]. 24.83/24.75 5140 -number_ring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_146_number__of__Pls) # label(axiom). [clausify(3352)]. 24.83/24.75 Derived: hAPP(int,rat,number_number_of(rat),pls) = zero_zero(rat). [resolve(5140,a,5066,a)]. 24.83/24.75 Derived: hAPP(int,complex,number_number_of(complex),pls) = zero_zero(complex). [resolve(5140,a,5086,a)]. 24.83/24.75 Derived: hAPP(int,int,number_number_of(int),pls) = zero_zero(int). [resolve(5140,a,5087,a)]. 24.83/24.75 Derived: hAPP(int,real,number_number_of(real),pls) = zero_zero(real). [resolve(5140,a,5100,a)]. 24.83/24.75 5141 -number_ring(A) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(int,A,number_number_of(A),min_1) # label(fact_2103_arith__simps_I31_J) # label(axiom). [clausify(3508)]. 24.83/24.75 5142 -number_ring(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),min_1))) # label(fact_2605_nonzero__number__of__Min) # label(axiom). [clausify(3711)]. 24.83/24.75 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),min_1))). [resolve(5142,a,5066,a)]. 24.83/24.75 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),min_1))). [resolve(5142,a,5086,a)]. 24.83/24.75 Derived: -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),min_1))). [resolve(5142,a,5087,a)]. 24.83/24.75 Derived: -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),min_1))). [resolve(5142,a,5100,a)]. 24.83/24.75 5143 -number_ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,uminus_uminus(int),B)) # label(fact_2039_arith__simps_I30_J) # label(axiom). [clausify(3832)]. 24.83/24.75 5144 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),B)) # label(fact_15_add__special_I2_J) # label(axiom). [clausify(3879)]. 24.83/24.75 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),A)). [resolve(5144,a,5066,a)]. 24.83/24.75 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),A)). [resolve(5144,a,5086,a)]. 24.83/24.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),A)). [resolve(5144,a,5087,a)]. 24.83/24.75 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),A)). [resolve(5144,a,5100,a)]. 24.83/24.75 5145 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) # label(fact_44_number__of__mult) # label(axiom). [clausify(3898)]. 24.83/24.75 5146 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom). [clausify(3905)]. 24.83/24.81 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5146,b,5066,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5146,b,5086,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(int) | -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,hAPP(int,fun(int,int),inverse_divide(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5146,b,5087,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5146,b,5100,a)]. 24.83/24.81 5147 -linord1117847801e_zero(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom). [clausify(3905)]. 24.83/24.81 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5147,b,5066,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5147,b,5086,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(int) | 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,hAPP(int,fun(int,int),inverse_divide(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5147,b,5087,a)]. 24.83/24.81 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5147,b,5100,a)]. 24.83/24.81 5148 -number_ring(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))),B) # label(fact_110_mult__numeral__1) # label(axiom). [clausify(3966)]. 24.83/24.81 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))),A). [resolve(5148,a,5066,a)]. 24.83/24.81 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))),A). [resolve(5148,a,5086,a)]. 24.91/24.87 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))),A). [resolve(5148,a,5087,a)]. 24.91/24.87 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))),A). [resolve(5148,a,5100,a)]. 24.91/24.87 5149 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)) # label(fact_170_number__of__Bit0) # label(axiom). [clausify(4011)]. 24.91/24.87 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)). [resolve(5149,a,5066,a)]. 24.91/24.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)). [resolve(5149,a,5086,a)]. 24.91/24.87 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)). [resolve(5149,a,5087,a)]. 24.91/24.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)). [resolve(5149,a,5100,a)]. 24.91/24.87 5150 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2185_diff__special_I1_J) # label(axiom). [clausify(4013)]. 24.91/24.87 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5150,a,5066,a)]. 24.91/24.87 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5150,a,5086,a)]. 24.91/24.87 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5150,a,5087,a)]. 24.91/24.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5150,a,5100,a)]. 24.91/24.87 5151 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),C)))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(int,A,number_number_of(A),C))) # label(fact_2174_add__number__of__diff2) # label(axiom). [clausify(4030)]. 24.91/24.87 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)))),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),hAPP(int,rat,number_number_of(rat),B))). [resolve(5151,a,5066,a)]. 25.05/24.98 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)))),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),hAPP(int,complex,number_number_of(complex),B))). [resolve(5151,a,5086,a)]. 25.05/24.98 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,number_number_of(int),B))). [resolve(5151,a,5087,a)]. 25.05/24.98 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)))),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),hAPP(int,real,number_number_of(real),B))). [resolve(5151,a,5100,a)]. 25.05/24.98 5152 -number_ring(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1768_half) # label(axiom). [clausify(4068)]. 25.05/24.98 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5152,a,5066,a)]. 25.05/24.98 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5152,a,5086,a)]. 25.05/24.98 Derived: -linord1117847801e_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),inverse_divide(int),one_one(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5152,a,5087,a)]. 25.05/24.98 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5152,a,5100,a)]. 25.05/24.98 5153 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_591_power2__diff) # label(axiom). [clausify(4149)]. 25.05/24.98 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5153,a,5066,a)]. 25.12/25.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5153,a,5086,a)]. 25.12/25.03 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5153,a,5087,a)]. 25.12/25.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5153,a,5100,a)]. 25.12/25.03 5154 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) # label(fact_179_one__add__one__is__two) # label(axiom). [clausify(4199)]. 25.12/25.03 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). [resolve(5154,a,5066,a)]. 25.12/25.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex)) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). [resolve(5154,a,5086,a)]. 25.12/25.03 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). [resolve(5154,a,5087,a)]. 25.12/25.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). [resolve(5154,a,5100,a)]. 25.20/25.13 5155 -number_ring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_147_semiring__norm_I112_J) # label(axiom). [clausify(4245)]. 25.20/25.13 5156 -number_ring(A) | hAPP(int,A,number_number_of(A),B) != hAPP(int,A,number_number_of(A),C) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2622_eq__number__of__eq) # label(axiom). [clausify(4250)]. 25.20/25.13 Derived: hAPP(int,rat,number_number_of(rat),A) != hAPP(int,rat,number_number_of(rat),B) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5156,a,5066,a)]. 25.20/25.13 Derived: hAPP(int,complex,number_number_of(complex),A) != hAPP(int,complex,number_number_of(complex),B) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5156,a,5086,a)]. 25.20/25.13 Derived: hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5156,a,5087,a)]. 25.20/25.13 Derived: hAPP(int,real,number_number_of(real),A) != hAPP(int,real,number_number_of(real),B) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5156,a,5100,a)]. 25.20/25.13 5157 -number_ring(A) | hAPP(int,A,number_number_of(A),B) = hAPP(int,A,number_number_of(A),C) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2622_eq__number__of__eq) # label(axiom). [clausify(4250)]. 25.20/25.13 Derived: hAPP(int,rat,number_number_of(rat),A) = hAPP(int,rat,number_number_of(rat),B) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5157,a,5066,a)]. 25.20/25.13 Derived: hAPP(int,complex,number_number_of(complex),A) = hAPP(int,complex,number_number_of(complex),B) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5157,a,5086,a)]. 25.20/25.13 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5157,a,5087,a)]. 25.20/25.13 Derived: hAPP(int,real,number_number_of(real),A) = hAPP(int,real,number_number_of(real),B) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,uminus_uminus(int),A))))). [resolve(5157,a,5100,a)]. 25.20/25.13 5158 -number_ring(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(int,A,number_number_of(A),min_1) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B) # label(fact_2443_Parity_Oneg__one__odd__power) # label(axiom). [clausify(4276)]. 25.20/25.13 5159 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_142_mult__2__right) # label(axiom). [clausify(4292)]. 25.20/25.13 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5159,a,5066,a)]. 25.20/25.13 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5159,a,5086,a)]. 25.26/25.25 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5159,a,5087,a)]. 25.26/25.25 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5159,a,5100,a)]. 25.26/25.25 5160 -number_ring(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),pls)) = zero_zero(A) # label(fact_1732_divide__Numeral0) # label(axiom). [clausify(4374)]. 25.26/25.25 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),pls)) = zero_zero(rat). [resolve(5160,a,5066,a)]. 25.26/25.25 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),pls)) = zero_zero(complex). [resolve(5160,a,5086,a)]. 25.26/25.25 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),hAPP(int,int,number_number_of(int),pls)) = zero_zero(int). [resolve(5160,a,5087,a)]. 25.26/25.25 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),pls)) = zero_zero(real). [resolve(5160,a,5100,a)]. 25.26/25.25 5161 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) # label(fact_152_add__number__of__eq) # label(axiom). [clausify(4377)]. 25.26/25.25 5162 -linordered_idom(A) | -number_ring(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),min_1)) # label(fact_1885_abs__minus__one) # label(axiom). [clausify(4378)]. 25.26/25.25 Derived: -linordered_idom(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),min_1)). [resolve(5162,b,5066,a)]. 25.26/25.25 Derived: -linordered_idom(complex) | one_one(complex) = hAPP(complex,complex,abs_abs(complex),hAPP(int,complex,number_number_of(complex),min_1)). [resolve(5162,b,5086,a)]. 25.26/25.25 Derived: -linordered_idom(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),min_1)). [resolve(5162,b,5087,a)]. 25.26/25.25 Derived: -linordered_idom(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),min_1)). [resolve(5162,b,5100,a)]. 25.26/25.25 5163 -number_ring(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),B))))) | one_one(A) = hAPP(int,A,number_number_of(A),B) # label(fact_2504_eq__special_I2_J) # label(axiom). [clausify(4405)]. 25.26/25.25 Derived: -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(rat) = hAPP(int,rat,number_number_of(rat),A). [resolve(5163,a,5066,a)]. 25.26/25.25 Derived: -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(complex) = hAPP(int,complex,number_number_of(complex),A). [resolve(5163,a,5086,a)]. 25.26/25.25 Derived: -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(int) = hAPP(int,int,number_number_of(int),A). [resolve(5163,a,5087,a)]. 25.26/25.25 Derived: -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(real) = hAPP(int,real,number_number_of(real),A). [resolve(5163,a,5100,a)]. 25.26/25.26 5164 -number_ring(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),B))))) | one_one(A) != hAPP(int,A,number_number_of(A),B) # label(fact_2504_eq__special_I2_J) # label(axiom). [clausify(4405)]. 25.26/25.26 Derived: hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(rat) != hAPP(int,rat,number_number_of(rat),A). [resolve(5164,a,5066,a)]. 25.26/25.26 Derived: hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(complex) != hAPP(int,complex,number_number_of(complex),A). [resolve(5164,a,5086,a)]. 25.26/25.26 Derived: hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(int) != hAPP(int,int,number_number_of(int),A). [resolve(5164,a,5087,a)]. 25.26/25.26 Derived: hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),A))))) | one_one(real) != hAPP(int,real,number_number_of(real),A). [resolve(5164,a,5100,a)]. 25.26/25.26 5165 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_27_le__number__of) # label(axiom). [clausify(4409)]. 25.26/25.26 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5165,a,5066,a)]. 25.26/25.26 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5165,a,5086,a)]. 25.26/25.26 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5165,a,5087,a)]. 25.26/25.26 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5165,a,5100,a)]. 25.26/25.26 5166 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_27_le__number__of) # label(axiom). [clausify(4409)]. 25.26/25.26 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5166,a,5066,a)]. 25.26/25.26 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5166,a,5086,a)]. 25.26/25.26 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5166,a,5087,a)]. 25.58/25.52 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5166,a,5100,a)]. 25.58/25.52 5167 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1757_half__gt__zero) # label(axiom). [clausify(4502)]. 25.58/25.52 5168 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_176_less__special_I3_J) # label(axiom). [clausify(4566)]. 25.58/25.52 Derived: -linordered_idom(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5168,a,5066,a)]. 25.58/25.52 Derived: -linordered_idom(complex) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))). [resolve(5168,a,5086,a)]. 25.58/25.52 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),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5168,a,5087,a)]. 25.58/25.52 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),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5168,a,5100,a)]. 25.58/25.52 5169 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_176_less__special_I3_J) # label(axiom). [clausify(4566)]. 25.58/25.52 Derived: -linordered_idom(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5169,a,5066,a)]. 25.58/25.52 Derived: -linordered_idom(complex) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))). [resolve(5169,a,5086,a)]. 25.58/25.52 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),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5169,a,5087,a)]. 25.58/25.52 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),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5169,a,5100,a)]. 25.58/25.52 5170 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) != hAPP(int,A,number_number_of(A),C) | ti(int,B) = ti(int,C) # label(fact_89_eq__number__of) # label(axiom). [clausify(4665)]. 25.58/25.52 Derived: -ring_char_0(rat) | hAPP(int,rat,number_number_of(rat),A) != hAPP(int,rat,number_number_of(rat),B) | ti(int,A) = ti(int,B). [resolve(5170,a,5066,a)]. 25.58/25.52 Derived: -ring_char_0(complex) | hAPP(int,complex,number_number_of(complex),A) != hAPP(int,complex,number_number_of(complex),B) | ti(int,A) = ti(int,B). [resolve(5170,a,5086,a)]. 25.58/25.52 Derived: -ring_char_0(int) | hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B) | ti(int,A) = ti(int,B). [resolve(5170,a,5087,a)]. 25.58/25.52 Derived: -ring_char_0(real) | hAPP(int,real,number_number_of(real),A) != hAPP(int,real,number_number_of(real),B) | ti(int,A) = ti(int,B). [resolve(5170,a,5100,a)]. 25.65/25.58 5171 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) = hAPP(int,A,number_number_of(A),C) | ti(int,B) != ti(int,C) # label(fact_89_eq__number__of) # label(axiom). [clausify(4665)]. 25.65/25.58 Derived: -ring_char_0(rat) | hAPP(int,rat,number_number_of(rat),A) = hAPP(int,rat,number_number_of(rat),B) | ti(int,A) != ti(int,B). [resolve(5171,a,5066,a)]. 25.65/25.58 Derived: -ring_char_0(complex) | hAPP(int,complex,number_number_of(complex),A) = hAPP(int,complex,number_number_of(complex),B) | ti(int,A) != ti(int,B). [resolve(5171,a,5086,a)]. 25.65/25.58 Derived: -ring_char_0(int) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B) | ti(int,A) != ti(int,B). [resolve(5171,a,5087,a)]. 25.65/25.58 Derived: -ring_char_0(real) | hAPP(int,real,number_number_of(real),A) = hAPP(int,real,number_number_of(real),B) | ti(int,A) != ti(int,B). [resolve(5171,a,5100,a)]. 25.65/25.58 5172 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_60_le__special_I2_J) # label(axiom). [clausify(4715)]. 25.65/25.58 Derived: -linordered_idom(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5172,a,5066,a)]. 25.65/25.58 Derived: -linordered_idom(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5172,a,5086,a)]. 25.65/25.58 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5172,a,5087,a)]. 25.65/25.58 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5172,a,5100,a)]. 25.65/25.58 5173 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) # label(fact_60_le__special_I2_J) # label(axiom). [clausify(4715)]. 25.65/25.58 Derived: -linordered_idom(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5173,a,5066,a)]. 25.65/25.58 Derived: -linordered_idom(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5173,a,5086,a)]. 25.65/25.58 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5173,a,5087,a)]. 25.65/25.58 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)). [resolve(5173,a,5100,a)]. 25.65/25.58 5174 -number_ring(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),min_1)) # label(fact_2102_mult__minus1__right) # label(axiom). [clausify(4718)]. 25.65/25.58 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),min_1)). [resolve(5174,a,5066,a)]. 28.41/28.35 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),min_1)). [resolve(5174,a,5086,a)]. 28.41/28.35 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),min_1)). [resolve(5174,a,5087,a)]. 28.41/28.35 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),min_1)). [resolve(5174,a,5100,a)]. 28.41/28.35 5175 -field_inverse_zero(A) | -number_ring(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),min_1)) # label(fact_2105_divide__minus1) # label(axiom). [clausify(4826)]. 28.41/28.35 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),min_1)). [resolve(5175,b,5066,a)]. 28.41/28.35 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),min_1)). [resolve(5175,b,5086,a)]. 28.41/28.35 Derived: -field_inverse_zero(int) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),hAPP(int,int,number_number_of(int),min_1)). [resolve(5175,b,5087,a)]. 28.41/28.35 Derived: -field_inverse_zero(real) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),min_1)). [resolve(5175,b,5100,a)]. 28.41/28.35 5176 -number_ring(A) | hAPP(int,A,number_number_of(A),min_1) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_1474_power__m1__odd) # label(axiom). [clausify(4862)]. 28.41/28.35 Derived: hAPP(int,rat,number_number_of(rat),min_1) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5176,a,5066,a)]. 28.41/28.35 Derived: hAPP(int,complex,number_number_of(complex),min_1) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5176,a,5086,a)]. 28.41/28.35 Derived: hAPP(int,int,number_number_of(int),min_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5176,a,5087,a)]. 28.41/28.35 Derived: hAPP(int,real,number_number_of(real),min_1) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5176,a,5100,a)]. 28.41/28.35 5177 ab_group_add(complex) # label(arity_Complex_Ocomplex___Groups_Oab__group__add) # label(axiom). [assumption]. 28.41/28.35 5178 -ab_group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) # label(fact_794_eq__iff__diff__eq__0) # label(axiom). [clausify(30)]. 28.41/28.35 5179 -ab_group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) # label(fact_794_eq__iff__diff__eq__0) # label(axiom). [clausify(30)]. 28.41/28.35 5180 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_4213_setsum__negf) # label(axiom). [clausify(457)]. 28.41/28.36 5181 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2052_minus__diff__minus) # label(axiom). [clausify(525)]. 28.41/28.36 5182 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_2068_ab__left__minus) # label(axiom). [clausify(639)]. 28.41/28.36 5183 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) # label(fact_2053_minus__diff__eq) # label(axiom). [clausify(1433)]. 28.41/28.36 5184 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom). [clausify(1769)]. 28.41/28.36 5185 -ab_group_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))) # label(fact_4180_sumr__offset) # label(axiom). [clausify(1776)]. 28.41/28.36 5186 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2051_minus__add__distrib) # label(axiom). [clausify(2481)]. 28.41/28.36 5187 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E)) # label(fact_722_add__diff__add) # label(axiom). [clausify(2916)]. 28.41/28.36 5188 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,B) != ti(A,C) | ti(A,D) = ti(A,E) # label(fact_773_diff__eq__diff__eq) # label(axiom). [clausify(3179)]. 28.41/28.36 5189 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,B) = ti(A,C) | ti(A,D) != ti(A,E) # label(fact_773_diff__eq__diff__eq) # label(axiom). [clausify(3179)]. 28.41/28.36 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) = zero_zero(complex). [resolve(5177,a,5178,a)]. 28.41/28.36 Derived: ti(complex,A) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != zero_zero(complex). [resolve(5177,a,5179,a)]. 28.41/28.36 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),uminus_uminus(complex)),B)),C) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)). [resolve(5177,a,5180,a)]. 28.41/28.36 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5177,a,5181,a)]. 28.41/28.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),A) = zero_zero(complex). [resolve(5177,a,5182,a)]. 28.41/28.36 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A). [resolve(5177,a,5183,a)]. 28.41/28.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5177,a,5184,a)]. 28.41/28.36 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5177,a,5185,a)]. 28.41/28.36 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5177,a,5186,a)]. 28.41/28.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D)). [resolve(5177,a,5187,a)]. 28.41/28.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,A) != ti(complex,B) | ti(complex,C) = ti(complex,D). [resolve(5177,a,5188,a)]. 28.56/28.49 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,A) = ti(complex,B) | ti(complex,C) != ti(complex,D). [resolve(5177,a,5189,a)]. 28.56/28.49 5190 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4221_setsum__subtractf) # label(axiom). [clausify(3682)]. 28.56/28.49 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),minus_minus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5190,a,5177,a)]. 28.56/28.49 5191 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_4618_setsum__natinterval__difff) # label(axiom). [clausify(3842)]. 28.56/28.49 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,C,A)),hAPP(nat,complex,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5191,a,5177,a)]. 28.56/28.49 5192 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = zero_zero(A) # label(fact_4618_setsum__natinterval__difff) # label(axiom). [clausify(3842)]. 28.73/28.70 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(complex). [resolve(5192,a,5177,a)]. 28.73/28.70 5193 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption]. 28.73/28.70 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = zero_zero(int). [resolve(5193,a,5178,a)]. 28.73/28.70 Derived: ti(int,A) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != zero_zero(int). [resolve(5193,a,5179,a)]. 28.73/28.70 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(5193,a,5180,a)]. 28.73/28.70 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(5193,a,5181,a)]. 28.73/28.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),A) = zero_zero(int). [resolve(5193,a,5182,a)]. 28.73/28.70 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A). [resolve(5193,a,5183,a)]. 28.73/28.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5193,a,5184,a)]. 28.73/28.70 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5193,a,5185,a)]. 28.81/28.75 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(5193,a,5186,a)]. 28.81/28.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)). [resolve(5193,a,5187,a)]. 28.81/28.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,A) != ti(int,B) | ti(int,C) = ti(int,D). [resolve(5193,a,5188,a)]. 28.81/28.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,A) = ti(int,B) | ti(int,C) != ti(int,D). [resolve(5193,a,5189,a)]. 28.81/28.75 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(5193,a,5190,a)]. 28.81/28.75 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5193,a,5191,a)]. 28.81/28.75 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(int). [resolve(5193,a,5192,a)]. 28.81/28.75 5194 ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oab__group__add) # label(axiom). [assumption]. 28.81/28.75 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = zero_zero(real). [resolve(5194,a,5178,a)]. 28.81/28.75 Derived: ti(real,A) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != zero_zero(real). [resolve(5194,a,5179,a)]. 28.81/28.75 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),uminus_uminus(real)),B)),C) = hAPP(real,real,uminus_uminus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5194,a,5180,a)]. 28.81/28.75 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(5194,a,5181,a)]. 28.81/28.75 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),A) = zero_zero(real). [resolve(5194,a,5182,a)]. 28.81/28.75 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A). [resolve(5194,a,5183,a)]. 28.81/28.75 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5194,a,5184,a)]. 28.81/28.75 Derived: hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5194,a,5185,a)]. 28.81/28.75 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(5194,a,5186,a)]. 28.81/28.75 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)). [resolve(5194,a,5187,a)]. 28.81/28.75 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,A) != ti(real,B) | ti(real,C) = ti(real,D). [resolve(5194,a,5188,a)]. 28.81/28.75 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,A) = ti(real,B) | ti(real,C) != ti(real,D). [resolve(5194,a,5189,a)]. 28.81/28.75 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),minus_minus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5194,a,5190,a)]. 29.01/28.99 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,C,A)),hAPP(nat,real,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5194,a,5191,a)]. 29.01/28.99 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(real). [resolve(5194,a,5192,a)]. 29.01/28.99 5195 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2075_ab__diff__minus) # label(axiom). [clausify(4371)]. 29.01/28.99 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5195,a,5177,a)]. 29.01/28.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(5195,a,5193,a)]. 29.01/28.99 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5195,a,5194,a)]. 29.01/28.99 5196 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)) # label(fact_4233_setsum__diff) # label(axiom). [clausify(4476)]. 29.01/28.99 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)). [resolve(5196,a,5177,a)]. 29.42/29.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)). [resolve(5196,a,5193,a)]. 29.42/29.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)). [resolve(5196,a,5194,a)]. 29.42/29.36 5197 ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oab__group__add) # label(axiom). [assumption]. 29.42/29.36 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) = zero_zero(rat). [resolve(5197,a,5178,a)]. 29.42/29.36 Derived: ti(rat,A) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != zero_zero(rat). [resolve(5197,a,5179,a)]. 29.42/29.36 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),uminus_uminus(rat)),B)),C) = hAPP(rat,rat,uminus_uminus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)). [resolve(5197,a,5180,a)]. 29.42/29.36 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(5197,a,5181,a)]. 29.42/29.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A) = zero_zero(rat). [resolve(5197,a,5182,a)]. 29.42/29.36 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A). [resolve(5197,a,5183,a)]. 29.42/29.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(5197,a,5184,a)]. 29.42/29.36 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(5197,a,5185,a)]. 29.42/29.36 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(5197,a,5186,a)]. 29.42/29.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D)). [resolve(5197,a,5187,a)]. 29.42/29.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,A) != ti(rat,B) | ti(rat,C) = ti(rat,D). [resolve(5197,a,5188,a)]. 29.42/29.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,A) = ti(rat,B) | ti(rat,C) != ti(rat,D). [resolve(5197,a,5189,a)]. 29.42/29.36 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),minus_minus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(5197,a,5190,a)]. 29.42/29.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,C,A)),hAPP(nat,rat,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(5197,a,5191,a)]. 29.42/29.36 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(rat). [resolve(5197,a,5192,a)]. 29.42/29.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(5197,a,5195,a)]. 30.91/30.85 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)). [resolve(5197,a,5196,a)]. 30.91/30.85 5198 archim1727834104eiling(rat) # label(arity_Rat_Orat___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 30.91/30.85 5199 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,int,semiring_1_of_nat(int),B) # label(fact_2875_floor__of__nat) # label(axiom). [clausify(31)]. 30.91/30.85 5200 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) # label(fact_2889_floor__diff__one) # label(axiom). [clausify(38)]. 30.91/30.85 5201 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3595_ceiling__le__iff) # label(axiom). [clausify(124)]. 30.91/30.85 5202 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3595_ceiling__le__iff) # label(axiom). [clausify(124)]. 30.91/30.85 5203 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom). [clausify(244)]. 30.91/30.85 5204 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom). [clausify(244)]. 30.91/30.85 5205 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),B) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B))) # label(fact_3295_ceiling__def) # label(axiom). [clausify(276)]. 30.91/30.85 5206 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom). [clausify(348)]. 30.91/30.85 5207 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom). [clausify(348)]. 30.91/30.85 5208 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),B)) # label(fact_3294_ceiling__minus) # label(axiom). [clausify(374)]. 30.91/30.85 5209 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) # label(fact_3307_ceiling__diff__one) # label(axiom). [clausify(416)]. 30.91/30.85 5210 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_3306_ceiling__add__number__of) # label(axiom). [clausify(417)]. 30.91/30.85 5211 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archimedean_ceiling(A),one_one(A)) # label(fact_3282_ceiling__one) # label(axiom). [clausify(430)]. 30.91/30.85 5212 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) # label(fact_2887_floor__add__one) # label(axiom). [clausify(442)]. 30.91/30.85 5213 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2847_floor__le__one) # label(axiom). [clausify(576)]. 30.91/30.85 5214 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2847_floor__le__one) # label(axiom). [clausify(576)]. 30.91/30.85 5215 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_2885_floor__less__number__of) # label(axiom). [clausify(635)]. 30.91/30.85 5216 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_2885_floor__less__number__of) # label(axiom). [clausify(635)]. 30.91/30.85 5217 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3281_ceiling__mono) # label(axiom). [clausify(636)]. 30.91/30.85 5218 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2882_floor__le__zero) # label(axiom). [clausify(698)]. 30.91/30.85 5219 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2882_floor__le__zero) # label(axiom). [clausify(698)]. 30.91/30.85 5220 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_3280_ceiling__less__cancel) # label(axiom). [clausify(706)]. 30.91/30.85 5221 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3564_ceiling__of__int) # label(axiom). [clausify(932)]. 30.91/30.85 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(5198,a,5199,a)]. 30.91/30.85 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)). [resolve(5198,a,5200,a)]. 30.91/30.85 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(5198,a,5201,a)]. 30.91/30.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(5198,a,5202,a)]. 30.91/30.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(5198,a,5203,a)]. 30.91/30.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(5198,a,5204,a)]. 30.91/30.87 Derived: hAPP(rat,int,archimedean_ceiling(rat),A) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5198,a,5205,a)]. 30.91/30.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(5198,a,5206,a)]. 30.91/30.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(5198,a,5207,a)]. 30.91/30.87 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),A)). [resolve(5198,a,5208,a)]. 30.91/30.87 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)). [resolve(5198,a,5209,a)]. 30.91/30.87 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5198,a,5210,a)]. 30.91/30.87 Derived: one_one(int) = hAPP(rat,int,archimedean_ceiling(rat),one_one(rat)). [resolve(5198,a,5211,a)]. 30.91/30.87 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)). [resolve(5198,a,5212,a)]. 30.91/30.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5198,a,5213,a)]. 30.91/30.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5198,a,5214,a)]. 30.91/30.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(5198,a,5215,a)]. 30.91/30.87 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(5198,a,5216,a)]. 30.91/30.87 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5198,a,5217,a)]. 30.97/30.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(5198,a,5218,a)]. 30.97/30.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(5198,a,5219,a)]. 30.97/30.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5198,a,5220,a)]. 30.97/30.94 Derived: ti(int,A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(5198,a,5221,a)]. 30.97/30.94 5222 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3298_ceiling__le__zero) # label(axiom). [clausify(1080)]. 30.97/30.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5222,a,5198,a)]. 30.97/30.94 5223 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3298_ceiling__le__zero) # label(axiom). [clausify(1080)]. 30.97/30.94 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5223,a,5198,a)]. 30.97/30.94 5224 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,int,semiring_1_of_nat(int),B) # label(fact_3285_ceiling__of__nat) # label(axiom). [clausify(1124)]. 30.97/30.94 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(5224,a,5198,a)]. 30.97/30.94 5225 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),B) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_3357_ceiling__floor) # label(axiom). [clausify(1141)]. 30.97/30.94 Derived: hAPP(rat,int,archim2085082626_floor(rat),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5225,a,5198,a)]. 30.97/30.94 5226 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 30.97/30.94 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(5226,a,5199,a)]. 30.97/30.95 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)). [resolve(5226,a,5200,a)]. 30.97/30.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5226,a,5201,a)]. 30.97/30.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5226,a,5202,a)]. 30.97/30.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5226,a,5203,a)]. 31.05/30.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5226,a,5204,a)]. 31.05/30.97 Derived: hAPP(real,int,archimedean_ceiling(real),A) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A))). [resolve(5226,a,5205,a)]. 31.05/30.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(5226,a,5206,a)]. 31.05/30.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(5226,a,5207,a)]. 31.05/30.97 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),A)). [resolve(5226,a,5208,a)]. 31.05/30.97 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)). [resolve(5226,a,5209,a)]. 31.05/30.97 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5226,a,5210,a)]. 31.05/30.97 Derived: one_one(int) = hAPP(real,int,archimedean_ceiling(real),one_one(real)). [resolve(5226,a,5211,a)]. 31.05/30.97 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)). [resolve(5226,a,5212,a)]. 31.05/30.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5226,a,5213,a)]. 31.05/30.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5226,a,5214,a)]. 31.05/30.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5226,a,5215,a)]. 31.05/30.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(5226,a,5216,a)]. 31.05/30.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5226,a,5217,a)]. 31.05/30.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5226,a,5218,a)]. 31.05/30.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5226,a,5219,a)]. 31.09/31.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5226,a,5220,a)]. 31.09/31.00 Derived: ti(int,A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5226,a,5221,a)]. 31.09/31.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5226,a,5222,a)]. 31.09/31.00 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5226,a,5223,a)]. 31.09/31.00 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(5226,a,5224,a)]. 31.09/31.00 Derived: hAPP(real,int,archim2085082626_floor(real),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5226,a,5225,a)]. 31.09/31.00 5227 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_2890_floor__diff__number__of) # label(axiom). [clausify(1153)]. 31.09/31.00 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5227,a,5198,a)]. 31.09/31.00 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5227,a,5226,a)]. 31.09/31.00 5228 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3576_floor__of__int) # label(axiom). [clausify(1166)]. 31.09/31.00 Derived: ti(int,A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(5228,a,5198,a)]. 31.09/31.00 Derived: ti(int,A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5228,a,5226,a)]. 31.09/31.00 5229 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2884_one__le__floor) # label(axiom). [clausify(1223)]. 31.09/31.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(5229,a,5198,a)]. 31.09/31.00 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5229,a,5226,a)]. 31.09/31.00 5230 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_2884_one__le__floor) # label(axiom). [clausify(1223)]. 31.09/31.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)). [resolve(5230,a,5198,a)]. 31.13/31.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(5230,a,5226,a)]. 31.13/31.07 5231 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) # label(fact_3597_ceiling__add__of__int) # label(axiom). [clausify(1283)]. 31.13/31.07 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B). [resolve(5231,a,5198,a)]. 31.13/31.07 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),B). [resolve(5231,a,5226,a)]. 31.13/31.07 5232 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_3593_le__floor__iff) # label(axiom). [clausify(1302)]. 31.13/31.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5232,a,5198,a)]. 31.13/31.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5232,a,5226,a)]. 31.13/31.07 5233 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_3593_le__floor__iff) # label(axiom). [clausify(1302)]. 31.13/31.07 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5233,a,5198,a)]. 31.13/31.07 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5233,a,5226,a)]. 31.13/31.07 5234 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2893_number__of__less__floor) # label(axiom). [clausify(1400)]. 31.13/31.07 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5234,a,5198,a)]. 31.13/31.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5234,a,5226,a)]. 31.13/31.07 5235 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2893_number__of__less__floor) # label(axiom). [clausify(1400)]. 31.25/31.24 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5235,a,5198,a)]. 31.25/31.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5235,a,5226,a)]. 31.25/31.24 5236 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_3301_one__less__ceiling) # label(axiom). [clausify(1563)]. 31.25/31.24 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(5236,a,5198,a)]. 31.25/31.24 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(5236,a,5226,a)]. 31.25/31.24 5237 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_3301_one__less__ceiling) # label(axiom). [clausify(1563)]. 31.25/31.24 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)). [resolve(5237,a,5198,a)]. 31.25/31.24 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(5237,a,5226,a)]. 31.25/31.24 5238 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) # label(fact_3305_ceiling__add__one) # label(axiom). [clausify(1771)]. 31.25/31.24 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)). [resolve(5238,a,5198,a)]. 31.25/31.24 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)). [resolve(5238,a,5226,a)]. 31.25/31.24 5239 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom). [clausify(1817)]. 31.25/31.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5239,a,5198,a)]. 31.25/31.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5239,a,5226,a)]. 31.25/31.24 5240 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom). [clausify(1817)]. 31.35/31.27 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5240,a,5198,a)]. 31.35/31.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5240,a,5226,a)]. 31.35/31.27 5241 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom). [clausify(1866)]. 31.35/31.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(5241,a,5198,a)]. 31.35/31.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(5241,a,5226,a)]. 31.35/31.27 5242 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom). [clausify(1866)]. 31.35/31.27 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(5242,a,5198,a)]. 31.35/31.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(5242,a,5226,a)]. 31.35/31.27 5243 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom). [clausify(1870)]. 31.35/31.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(5243,a,5198,a)]. 31.35/31.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5243,a,5226,a)]. 31.35/31.27 5244 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom). [clausify(1870)]. 31.35/31.27 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(5244,a,5198,a)]. 31.35/31.27 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(5244,a,5226,a)]. 31.57/31.48 5245 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,int,number_number_of(int),B) # label(fact_2872_floor__number__of) # label(axiom). [clausify(2065)]. 31.57/31.48 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5245,a,5198,a)]. 31.57/31.48 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5245,a,5226,a)]. 31.57/31.48 5246 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3567_of__int__floor__le) # label(axiom). [clausify(2174)]. 31.57/31.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archim2085082626_floor(rat),A))),A)). [resolve(5246,a,5198,a)]. 31.57/31.48 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archim2085082626_floor(real),A))),A)). [resolve(5246,a,5226,a)]. 31.57/31.48 5247 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom). [clausify(2198)]. 31.57/31.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5247,a,5198,a)]. 31.57/31.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5247,a,5226,a)]. 31.57/31.48 5248 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom). [clausify(2198)]. 31.57/31.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5248,a,5198,a)]. 31.57/31.48 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5248,a,5226,a)]. 31.57/31.48 5249 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2879_floor__less__zero) # label(axiom). [clausify(2292)]. 31.57/31.48 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))). [resolve(5249,a,5198,a)]. 31.57/31.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))). [resolve(5249,a,5226,a)]. 31.57/31.48 5250 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2879_floor__less__zero) # label(axiom). [clausify(2292)]. 31.57/31.48 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))). [resolve(5250,a,5198,a)]. 31.80/31.70 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))). [resolve(5250,a,5226,a)]. 31.80/31.70 5251 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2864_floor__less__cancel) # label(axiom). [clausify(2356)]. 31.80/31.70 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5251,a,5198,a)]. 31.80/31.70 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5251,a,5226,a)]. 31.80/31.70 5252 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),B) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3355_floor__ceiling) # label(axiom). [clausify(2403)]. 31.80/31.70 Derived: hAPP(rat,int,archimedean_ceiling(rat),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(5252,a,5198,a)]. 31.80/31.70 Derived: hAPP(real,int,archimedean_ceiling(real),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(5252,a,5226,a)]. 31.80/31.70 5253 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom). [clausify(2522)]. 31.80/31.70 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5253,a,5198,a)]. 31.80/31.70 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5253,a,5226,a)]. 31.80/31.70 5254 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom). [clausify(2522)]. 31.80/31.70 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5254,a,5198,a)]. 31.80/31.70 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5254,a,5226,a)]. 31.80/31.70 5255 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_3311_ceiling__less__number__of) # label(axiom). [clausify(2528)]. 31.80/31.70 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(5255,a,5198,a)]. 31.80/31.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5255,a,5226,a)]. 31.80/31.77 5256 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_3311_ceiling__less__number__of) # label(axiom). [clausify(2528)]. 31.80/31.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(5256,a,5198,a)]. 31.80/31.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5256,a,5226,a)]. 31.80/31.77 5257 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom). [clausify(2566)]. 31.80/31.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)). [resolve(5257,a,5198,a)]. 31.80/31.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)). [resolve(5257,a,5226,a)]. 31.80/31.77 5258 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom). [clausify(2566)]. 31.80/31.77 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)). [resolve(5258,a,5198,a)]. 31.80/31.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),B)). [resolve(5258,a,5226,a)]. 31.80/31.77 5259 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A)))) | ti(int,B) = hAPP(A,int,archim2085082626_floor(A),C) # label(fact_3605_floor__unique) # label(axiom). [clausify(2626)]. 31.80/31.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat)))) | ti(int,A) = hAPP(rat,int,archim2085082626_floor(rat),B). [resolve(5259,a,5198,a)]. 32.11/32.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real)))) | ti(int,A) = hAPP(real,int,archim2085082626_floor(real),B). [resolve(5259,a,5226,a)]. 32.11/32.07 5260 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_3308_ceiling__diff__number__of) # label(axiom). [clausify(2810)]. 32.11/32.07 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5260,a,5198,a)]. 32.11/32.07 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5260,a,5226,a)]. 32.11/32.07 5261 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_3299_ceiling__less__one) # label(axiom). [clausify(2872)]. 32.11/32.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5261,a,5198,a)]. 32.11/32.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5261,a,5226,a)]. 32.11/32.07 5262 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_3299_ceiling__less__one) # label(axiom). [clausify(2872)]. 32.11/32.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5262,a,5198,a)]. 32.11/32.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5262,a,5226,a)]. 32.11/32.07 5263 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B))),one_one(A))),B)) # label(fact_3607_ceiling__correct) # label(axiom). [clausify(2876)]. 32.11/32.07 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A))),one_one(rat))),A)). [resolve(5263,a,5198,a)]. 32.11/32.07 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A))),one_one(real))),A)). [resolve(5263,a,5226,a)]. 32.11/32.07 5264 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3607_ceiling__correct) # label(axiom). [clausify(2876)]. 32.11/32.07 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(rat,int,archimedean_ceiling(rat),A)))). [resolve(5264,a,5198,a)]. 32.18/32.14 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(real,int,archimedean_ceiling(real),A)))). [resolve(5264,a,5226,a)]. 32.18/32.14 5265 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) # label(fact_3599_ceiling__diff__of__int) # label(axiom). [clausify(2894)]. 32.18/32.14 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B). [resolve(5265,a,5198,a)]. 32.18/32.14 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),B). [resolve(5265,a,5226,a)]. 32.18/32.14 5266 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) = zero_zero(int) # label(fact_2863_floor__zero) # label(axiom). [clausify(2960)]. 32.18/32.14 Derived: hAPP(rat,int,archim2085082626_floor(rat),zero_zero(rat)) = zero_zero(int). [resolve(5266,a,5198,a)]. 32.18/32.14 Derived: hAPP(real,int,archim2085082626_floor(real),zero_zero(real)) = zero_zero(int). [resolve(5266,a,5226,a)]. 32.18/32.14 5267 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_2895_one__less__floor) # label(axiom). [clausify(2968)]. 32.18/32.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5267,a,5198,a)]. 32.18/32.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5267,a,5226,a)]. 32.18/32.14 5268 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)) # label(fact_2895_one__less__floor) # label(axiom). [clausify(2968)]. 32.18/32.14 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5268,a,5198,a)]. 32.18/32.14 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)). [resolve(5268,a,5226,a)]. 32.18/32.14 5269 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom). [clausify(2977)]. 32.18/32.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(5269,a,5198,a)]. 32.64/32.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5269,a,5226,a)]. 32.64/32.63 5270 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom). [clausify(2977)]. 32.64/32.63 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(5270,a,5198,a)]. 32.64/32.63 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5270,a,5226,a)]. 32.64/32.63 5271 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) = zero_zero(int) # label(fact_3279_ceiling__zero) # label(axiom). [clausify(2991)]. 32.64/32.63 Derived: hAPP(rat,int,archimedean_ceiling(rat),zero_zero(rat)) = zero_zero(int). [resolve(5271,a,5198,a)]. 32.64/32.63 Derived: hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = zero_zero(int). [resolve(5271,a,5226,a)]. 32.64/32.63 5272 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3302_ceiling__le__one) # label(axiom). [clausify(3220)]. 32.64/32.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(5272,a,5198,a)]. 32.64/32.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))). [resolve(5272,a,5226,a)]. 32.64/32.63 5273 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3302_ceiling__le__one) # label(axiom). [clausify(3220)]. 32.64/32.63 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(5273,a,5198,a)]. 32.64/32.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))). [resolve(5273,a,5226,a)]. 32.64/32.63 5274 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom). [clausify(3509)]. 32.64/32.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5274,a,5198,a)]. 32.64/32.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5274,a,5226,a)]. 33.18/33.12 5275 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom). [clausify(3509)]. 33.18/33.12 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(5275,a,5198,a)]. 33.18/33.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(5275,a,5226,a)]. 33.18/33.12 5276 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2880_zero__le__floor) # label(axiom). [clausify(3702)]. 33.18/33.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5276,a,5198,a)]. 33.18/33.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5276,a,5226,a)]. 33.18/33.12 5277 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2880_zero__le__floor) # label(axiom). [clausify(3702)]. 33.18/33.12 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5277,a,5198,a)]. 33.18/33.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5277,a,5226,a)]. 33.18/33.12 5278 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))))) # label(fact_3612_floor__correct) # label(axiom). [clausify(3908)]. 33.18/33.12 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))))). [resolve(5278,a,5198,a)]. 33.18/33.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))))). [resolve(5278,a,5226,a)]. 33.18/33.12 5279 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3612_floor__correct) # label(axiom). [clausify(3908)]. 33.18/33.12 5280 -archim1727834104eiling(A) | archimedean_ceiling(A) = ti(fun(A,int),archimedean_ceiling(A)) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom). [clausify(4019)]. 33.18/33.12 Derived: archimedean_ceiling(rat) = ti(fun(rat,int),archimedean_ceiling(rat)). [resolve(5280,a,5198,a)]. 33.18/33.12 Derived: archimedean_ceiling(real) = ti(fun(real,int),archimedean_ceiling(real)). [resolve(5280,a,5226,a)]. 33.38/33.29 5281 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3586_le__of__int__ceiling) # label(axiom). [clausify(4032)]. 33.38/33.29 5282 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) # label(fact_3596_floor__add__of__int) # label(axiom). [clausify(4123)]. 33.38/33.29 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B). [resolve(5282,a,5198,a)]. 33.38/33.29 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),B). [resolve(5282,a,5226,a)]. 33.38/33.29 5283 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(int,int,uminus_uminus(int),hAPP(A,int,archimedean_ceiling(A),B)) # label(fact_3293_floor__minus) # label(axiom). [clausify(4145)]. 33.38/33.29 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archimedean_ceiling(rat),A)). [resolve(5283,a,5198,a)]. 33.38/33.29 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(int,int,uminus_uminus(int),hAPP(real,int,archimedean_ceiling(real),A)). [resolve(5283,a,5226,a)]. 33.38/33.29 5284 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom). [clausify(4191)]. 33.38/33.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(5284,a,5198,a)]. 33.38/33.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5284,a,5226,a)]. 33.38/33.29 5285 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom). [clausify(4191)]. 33.38/33.29 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(5285,a,5198,a)]. 33.38/33.29 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(5285,a,5226,a)]. 33.38/33.29 5286 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2865_floor__mono) # label(axiom). [clausify(4196)]. 33.78/33.69 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5286,a,5198,a)]. 33.78/33.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5286,a,5226,a)]. 33.78/33.69 5287 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archim2085082626_floor(A),one_one(A)) # label(fact_2870_floor__one) # label(axiom). [clausify(4214)]. 33.78/33.69 Derived: one_one(int) = hAPP(rat,int,archim2085082626_floor(rat),one_one(rat)). [resolve(5287,a,5198,a)]. 33.78/33.69 Derived: one_one(int) = hAPP(real,int,archim2085082626_floor(real),one_one(real)). [resolve(5287,a,5226,a)]. 33.78/33.69 5288 -archim1727834104eiling(A) | archim2085082626_floor(A) = ti(fun(A,int),archim2085082626_floor(A)) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom). [clausify(4314)]. 33.78/33.69 Derived: archim2085082626_floor(rat) = ti(fun(rat,int),archim2085082626_floor(rat)). [resolve(5288,a,5198,a)]. 33.78/33.69 Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)). [resolve(5288,a,5226,a)]. 33.78/33.69 5289 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3309_ceiling__less__zero) # label(axiom). [clausify(4333)]. 33.78/33.69 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5289,a,5198,a)]. 33.78/33.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5289,a,5226,a)]. 33.78/33.69 5290 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3309_ceiling__less__zero) # label(axiom). [clausify(4333)]. 33.78/33.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5290,a,5198,a)]. 33.78/33.69 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min_1))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5290,a,5226,a)]. 33.78/33.69 5291 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3297_zero__less__ceiling) # label(axiom). [clausify(4565)]. 33.78/33.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5291,a,5198,a)]. 33.78/33.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5291,a,5226,a)]. 33.78/33.69 5292 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3297_zero__less__ceiling) # label(axiom). [clausify(4565)]. 33.92/33.85 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5292,a,5198,a)]. 33.92/33.85 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5292,a,5226,a)]. 33.92/33.85 5293 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(int,A,ring_1_of_int(A),B))) | ti(int,B) = hAPP(A,int,archimedean_ceiling(A),C) # label(fact_3606_ceiling__unique) # label(axiom). [clausify(4637)]. 33.92/33.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(int,rat,ring_1_of_int(rat),A))) | ti(int,A) = hAPP(rat,int,archimedean_ceiling(rat),B). [resolve(5293,a,5198,a)]. 33.92/33.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(int,real,ring_1_of_int(real),A))) | ti(int,A) = hAPP(real,int,archimedean_ceiling(real),B). [resolve(5293,a,5226,a)]. 33.92/33.85 5294 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3300_one__le__ceiling) # label(axiom). [clausify(4694)]. 33.92/33.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(5294,a,5198,a)]. 33.92/33.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(5294,a,5226,a)]. 33.92/33.85 5295 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3300_one__le__ceiling) # label(axiom). [clausify(4694)]. 33.92/33.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(5295,a,5198,a)]. 33.92/33.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(5295,a,5226,a)]. 33.92/33.85 5296 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom). [clausify(4722)]. 33.92/33.85 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(5296,a,5198,a)]. 33.92/33.85 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5296,a,5226,a)]. 34.08/34.00 5297 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom). [clausify(4722)]. 34.08/34.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(5297,a,5198,a)]. 34.08/34.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(5297,a,5226,a)]. 34.08/34.00 5298 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,number_number_of(A),B)) = hAPP(int,int,number_number_of(int),B) # label(fact_3283_ceiling__number__of) # label(axiom). [clausify(4747)]. 34.08/34.00 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5298,a,5198,a)]. 34.08/34.00 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5298,a,5226,a)]. 34.08/34.00 5299 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) # label(fact_2888_floor__add__number__of) # label(axiom). [clausify(4800)]. 34.08/34.00 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(int,rat,number_number_of(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5299,a,5198,a)]. 34.08/34.00 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)). [resolve(5299,a,5226,a)]. 34.08/34.00 5300 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2886_number__of__le__floor) # label(axiom). [clausify(4851)]. 34.08/34.00 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5300,a,5198,a)]. 34.08/34.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5300,a,5226,a)]. 34.08/34.00 5301 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2886_number__of__le__floor) # label(axiom). [clausify(4851)]. 35.49/35.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5301,a,5198,a)]. 35.49/35.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5301,a,5226,a)]. 35.49/35.44 5302 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3592_floor__less__iff) # label(axiom). [clausify(4870)]. 35.49/35.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)). [resolve(5302,a,5198,a)]. 35.49/35.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)). [resolve(5302,a,5226,a)]. 35.49/35.44 5303 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3592_floor__less__iff) # label(axiom). [clausify(4870)]. 35.49/35.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)). [resolve(5303,a,5198,a)]. 35.49/35.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)). [resolve(5303,a,5226,a)]. 35.49/35.44 5304 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,ring_1_of_int(A),C))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) # label(fact_3598_floor__diff__of__int) # label(axiom). [clausify(4871)]. 35.49/35.44 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B). [resolve(5304,a,5198,a)]. 35.49/35.44 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,ring_1_of_int(real),B))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),B). [resolve(5304,a,5226,a)]. 35.49/35.44 5305 real_normed_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 35.49/35.44 5306 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)))) # label(fact_4623_Cauchy__product__sums) # label(axiom). [clausify(32)]. 35.49/35.44 5307 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),sequentially)) # label(fact_4477_LIMSEQ__mult) # label(axiom). [clausify(150)]. 35.49/35.44 5308 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_4678_mult_OscaleR__left) # label(axiom). [clausify(237)]. 35.49/35.44 5309 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_883_mult__left_Oadd) # label(axiom). [clausify(390)]. 35.49/35.44 5310 -real_normed_algebra(A) | -power(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(nat,fun(nat,A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),combc(nat,nat,A),hAPP(fun(nat,A),fun(nat,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(nat,A),fun(nat,fun(nat,A))),combb(A,fun(nat,A),nat),power_power(A)),B)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),sequentially)) # label(fact_4467_LIMSEQ__pow) # label(axiom). [clausify(451)]. 35.49/35.44 5311 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f102(A,B)))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom). [clausify(512)]. 35.49/35.44 5312 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f102(A,B))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom). [clausify(512)]. 35.49/35.44 5313 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_887_mult_Odiff__right) # label(axiom). [clausify(561)]. 35.49/35.44 5314 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4000_mult__left_Osummable) # label(axiom). [clausify(583)]. 35.49/35.44 5315 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4081_mult__right_Osums) # label(axiom). [clausify(616)]. 35.49/35.44 5316 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),C)) # label(fact_4908_mult__left_OisCont) # label(axiom). [clausify(667)]. 35.49/35.44 5317 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3988_mult__right_Osuminf) # label(axiom). [clausify(818)]. 35.49/35.44 5318 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom). [clausify(827)]. 35.49/35.44 5319 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_884_mult__left_Odiff) # label(axiom). [clausify(867)]. 35.49/35.44 5320 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4551_mult__left_Ocont) # label(axiom). [clausify(896)]. 35.49/35.44 5321 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_881_mult__right_Oadd) # label(axiom). [clausify(913)]. 35.49/35.44 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)))). [resolve(5305,a,5306,a)]. 35.49/35.45 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),C),D),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),sequentially)). [resolve(5305,a,5307,a)]. 35.49/35.45 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(5305,a,5308,a)]. 35.49/35.45 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5305,a,5309,a)]. 35.49/35.45 Derived: -power(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),hAPP(fun(nat,real),fun(nat,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(nat,real),fun(nat,fun(nat,real))),combb(real,fun(nat,real),nat),power_power(real)),A)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),sequentially)). [resolve(5305,a,5310,a)]. 35.49/35.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f102(real,A)))). [resolve(5305,a,5311,a)]. 35.49/35.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f102(real,A))). [resolve(5305,a,5312,a)]. 35.49/35.45 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)). [resolve(5305,a,5313,a)]. 35.49/35.45 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5305,a,5314,a)]. 35.49/35.45 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),C)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5305,a,5315,a)]. 35.57/35.47 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),B)). [resolve(5305,a,5316,a)]. 35.57/35.47 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5305,a,5317,a)]. 35.57/35.47 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))). [resolve(5305,a,5318,a)]. 35.57/35.47 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B). [resolve(5305,a,5319,a)]. 35.57/35.47 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5305,a,5320,a)]. 35.57/35.47 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(5305,a,5321,a)]. 35.57/35.47 5322 -real_normed_algebra(A) | -comm_ring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f170(B,A,C,D,E)),E)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom). [clausify(969)]. 35.57/35.47 Derived: -comm_ring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f170(A,real,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)). [resolve(5322,a,5305,a)]. 35.61/35.51 5323 -real_normed_algebra(A) | -comm_ring_1(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(B,fun(nat,A),C,f170(B,A,C,D,E))),hAPP(B,A,D,f170(B,A,C,D,E))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom). [clausify(969)]. 35.61/35.51 Derived: -comm_ring_1(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(A,fun(nat,real),B,f170(A,real,B,C,D))),hAPP(A,real,C,f170(A,real,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(A,bool),fun(nat,real),hAPP(fun(nat,fun(fun(A,bool),real)),fun(fun(A,bool),fun(nat,real)),combc(nat,fun(A,bool),real),hAPP(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(nat,fun(A,real)),fun(nat,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),nat),big_co302546470etprod(A,real)),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),B))),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D)),sequentially)). [resolve(5323,a,5305,a)]. 35.61/35.51 5324 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f173(A)))) # label(fact_1805_mult_Opos__bounded) # label(axiom). [clausify(1009)]. 35.61/35.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f173(real)))). [resolve(5324,a,5305,a)]. 35.61/35.51 5325 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f173(A))) # label(fact_1805_mult_Opos__bounded) # label(axiom). [clausify(1009)]. 35.61/35.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f173(real))). [resolve(5325,a,5305,a)]. 35.61/35.51 5326 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2036_mult_Ominus__left) # label(axiom). [clausify(1062)]. 35.61/35.51 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5326,a,5305,a)]. 35.61/35.51 5327 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom). [clausify(1088)]. 35.63/35.54 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5327,a,5305,a)]. 35.63/35.54 5328 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4191_mult__right_Osetsum) # label(axiom). [clausify(1111)]. 35.63/35.54 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5328,a,5305,a)]. 35.63/35.54 5329 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),E)) # label(fact_4474_mult_Otendsto) # label(axiom). [clausify(1117)]. 35.63/35.54 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),F)),D)). [resolve(5329,a,5305,a)]. 35.63/35.54 5330 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f198(A,C)))) # label(fact_1812_mult__left_Obounded) # label(axiom). [clausify(1128)]. 35.63/35.54 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f198(real,B)))). [resolve(5330,a,5305,a)]. 35.63/35.54 5331 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f207(A)))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom). [clausify(1244)]. 35.63/35.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f207(real)))). [resolve(5331,a,5305,a)]. 35.63/35.58 5332 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f207(A))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom). [clausify(1244)]. 35.63/35.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f207(real))). [resolve(5332,a,5305,a)]. 35.63/35.58 5333 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f219(A,B))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom). [clausify(1291)]. 35.63/35.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f219(real,A))). [resolve(5333,a,5305,a)]. 35.63/35.58 5334 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f219(A,C)))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom). [clausify(1291)]. 35.63/35.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f219(real,B)))). [resolve(5334,a,5305,a)]. 35.63/35.58 5335 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3997_summable__mult) # label(axiom). [clausify(1325)]. 35.63/35.58 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5335,a,5305,a)]. 35.63/35.58 5336 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),hAPP(B,filter(B),at(B),E))) # label(fact_4549_mult__left_OLIM) # label(axiom). [clausify(1342)]. 35.63/35.58 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5336,a,5305,a)]. 35.63/35.58 5337 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_4100_mult__right_OCauchy) # label(axiom). [clausify(1381)]. 35.72/35.65 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5337,a,5305,a)]. 35.72/35.65 5338 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4575_LIM__mult__left__zero) # label(axiom). [clausify(1460)]. 35.72/35.65 5339 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3990_suminf__mult) # label(axiom). [clausify(1516)]. 35.72/35.65 5340 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f278(A,B)))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom). [clausify(1545)]. 35.72/35.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f278(real,A)))). [resolve(5340,a,5305,a)]. 35.72/35.65 5341 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f278(A,B))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom). [clausify(1545)]. 35.72/35.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f278(real,A))). [resolve(5341,a,5305,a)]. 35.72/35.65 5342 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_4621_Cauchy__product) # label(axiom). [clausify(1615)]. 35.72/35.65 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5342,a,5305,a)]. 35.79/35.74 5343 -real_normed_algebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E))) # label(fact_1789_norm__mult__less) # label(axiom). [clausify(1693)]. 35.79/35.74 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5343,a,5305,a)]. 35.79/35.74 5344 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),F),V6),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),D),V6)),hAPP(A,filter(A),at(A),E))) # label(fact_4548_LIM__mult) # label(axiom). [clausify(1735)]. 35.79/35.74 5345 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),times_times(A),B)),C)) # label(fact_4907_mult__right_OisCont) # label(axiom). [clausify(1744)]. 35.79/35.74 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),times_times(real),A)),B)). [resolve(5345,a,5305,a)]. 35.79/35.74 5346 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3999_mult__right_Osummable) # label(axiom). [clausify(1804)]. 35.79/35.74 5347 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),E)),C)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4573_LIM__mult__right__zero) # label(axiom). [clausify(1892)]. 35.92/35.84 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),D)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5347,a,5305,a)]. 35.92/35.84 5348 real_normed_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 35.92/35.84 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)))). [resolve(5348,a,5306,a)]. 35.92/35.84 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),C),D),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)),sequentially)). [resolve(5348,a,5307,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5348,a,5308,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B). [resolve(5348,a,5309,a)]. 35.94/35.85 Derived: -power(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(nat,fun(nat,complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),combc(nat,nat,complex),hAPP(fun(nat,complex),fun(nat,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(nat,complex),fun(nat,fun(nat,complex))),combb(complex,fun(nat,complex),nat),power_power(complex)),A)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),sequentially)). [resolve(5348,a,5310,a)]. 35.94/35.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f102(complex,A)))). [resolve(5348,a,5311,a)]. 35.94/35.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f102(complex,A))). [resolve(5348,a,5312,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)). [resolve(5348,a,5313,a)]. 35.94/35.85 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5348,a,5314,a)]. 35.94/35.85 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),C)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))). [resolve(5348,a,5315,a)]. 35.94/35.85 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),B)). [resolve(5348,a,5316,a)]. 35.94/35.85 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5348,a,5317,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))). [resolve(5348,a,5318,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),B). [resolve(5348,a,5319,a)]. 35.94/35.85 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5348,a,5320,a)]. 35.94/35.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)). [resolve(5348,a,5321,a)]. 35.94/35.85 Derived: -comm_ring_1(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f170(A,complex,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)). [resolve(5348,a,5322,a)]. 35.94/35.85 Derived: -comm_ring_1(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(A,fun(nat,complex),B,f170(A,complex,B,C,D))),hAPP(A,complex,C,f170(A,complex,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(A,bool),fun(nat,complex),hAPP(fun(nat,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(nat,complex)),combc(nat,fun(A,bool),complex),hAPP(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(nat,fun(A,complex)),fun(nat,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),nat),big_co302546470etprod(A,complex)),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),B))),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),D)),sequentially)). [resolve(5348,a,5323,a)]. 35.94/35.86 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f173(complex)))). [resolve(5348,a,5324,a)]. 35.94/35.86 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f173(complex))). [resolve(5348,a,5325,a)]. 35.94/35.86 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B). [resolve(5348,a,5326,a)]. 35.94/35.86 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5348,a,5327,a)]. 35.94/35.86 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5348,a,5328,a)]. 35.94/35.86 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),F)),D)). [resolve(5348,a,5329,a)]. 35.94/35.86 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f198(complex,B)))). [resolve(5348,a,5330,a)]. 35.94/35.86 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f207(complex)))). [resolve(5348,a,5331,a)]. 35.94/35.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f207(complex))). [resolve(5348,a,5332,a)]. 35.94/35.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f219(complex,A))). [resolve(5348,a,5333,a)]. 35.94/35.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f219(complex,B)))). [resolve(5348,a,5334,a)]. 35.94/35.87 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5348,a,5335,a)]. 35.94/35.87 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5348,a,5336,a)]. 35.94/35.87 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5348,a,5337,a)]. 35.94/35.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f278(complex,A)))). [resolve(5348,a,5340,a)]. 35.94/35.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f278(complex,A))). [resolve(5348,a,5341,a)]. 35.94/35.87 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5348,a,5342,a)]. 36.21/36.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5348,a,5343,a)]. 36.21/36.12 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B)). [resolve(5348,a,5345,a)]. 36.21/36.12 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),D)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5348,a,5347,a)]. 36.21/36.12 5349 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_882_mult_Oadd__left) # label(axiom). [clausify(2172)]. 36.21/36.12 5350 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2035_mult__left_Ominus) # label(axiom). [clausify(2333)]. 36.21/36.12 5351 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2037_mult__right_Ominus) # label(axiom). [clausify(2464)]. 36.21/36.12 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5351,a,5305,a)]. 36.21/36.12 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5351,a,5348,a)]. 36.21/36.12 5352 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),E)) # label(fact_4476_mult__right_Otendsto) # label(axiom). [clausify(2580)]. 36.21/36.12 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),E)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C)),D)). [resolve(5352,a,5305,a)]. 36.24/36.20 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),E)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C)),D)). [resolve(5352,a,5348,a)]. 36.24/36.20 5353 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),E)) # label(fact_4475_mult__left_Otendsto) # label(axiom). [clausify(2633)]. 36.24/36.20 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),D)). [resolve(5353,a,5305,a)]. 36.24/36.20 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),D)). [resolve(5353,a,5348,a)]. 36.24/36.20 5354 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),sequentially)) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom). [clausify(2665)]. 36.24/36.20 5355 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_3998_summable__mult2) # label(axiom). [clausify(2668)]. 36.24/36.20 5356 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f474(A)))) # label(fact_1811_mult_Obounded) # label(axiom). [clausify(2721)]. 36.24/36.20 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f474(real)))). [resolve(5356,a,5305,a)]. 36.53/36.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f474(complex)))). [resolve(5356,a,5348,a)]. 36.53/36.44 5357 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)))) # label(fact_1788_norm__mult__ineq) # label(axiom). [clausify(2813)]. 36.53/36.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)))). [resolve(5357,a,5305,a)]. 36.53/36.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)))). [resolve(5357,a,5348,a)]. 36.53/36.44 5358 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_878_mult_Ozero__right) # label(axiom). [clausify(2833)]. 36.53/36.44 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)) = zero_zero(real). [resolve(5358,a,5305,a)]. 36.53/36.44 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5358,a,5348,a)]. 36.53/36.44 5359 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2038_mult_Ominus__right) # label(axiom). [clausify(2930)]. 36.53/36.44 5360 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f530(A,B)))) # label(fact_1813_mult__right_Obounded) # label(axiom). [clausify(2953)]. 36.53/36.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f530(real,A)))). [resolve(5360,a,5305,a)]. 36.53/36.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f530(complex,A)))). [resolve(5360,a,5348,a)]. 36.53/36.44 5361 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3987_mult__left_Osuminf) # label(axiom). [clausify(2974)]. 36.53/36.44 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5361,a,5305,a)]. 36.69/36.59 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5361,a,5348,a)]. 36.69/36.59 5362 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4101_mult__left_OCauchy) # label(axiom). [clausify(3012)]. 36.69/36.59 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5362,a,5305,a)]. 36.69/36.59 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5362,a,5348,a)]. 36.69/36.59 5363 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3989_suminf__mult2) # label(axiom). [clausify(3041)]. 36.69/36.59 5364 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),hAPP(B,filter(B),at(B),E))) # label(fact_4550_mult__right_OLIM) # label(axiom). [clausify(3060)]. 36.69/36.59 5365 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_4674_mult_OscaleR__right) # label(axiom). [clausify(3151)]. 36.69/36.59 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5365,a,5305,a)]. 36.69/36.59 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5365,a,5348,a)]. 36.95/36.84 5366 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4079_sums__mult) # label(axiom). [clausify(3155)]. 36.95/36.84 5367 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_4676_mult__right_OscaleR) # label(axiom). [clausify(3307)]. 36.95/36.84 5368 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_886_mult__right_Odiff) # label(axiom). [clausify(3320)]. 36.95/36.84 5369 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4910_mult_OisCont) # label(axiom). [clausify(3380)]. 36.95/36.84 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),C)). [resolve(5369,b,5305,a)]. 36.95/36.84 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),C)). [resolve(5369,b,5348,a)]. 36.95/36.84 5370 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),E)),C)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom). [clausify(3443)]. 36.95/36.84 5371 -topological_space(A) | -power(B) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),F)),hAPP(nat,B,hAPP(B,fun(nat,B),power_power(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4556_LIM__power) # label(axiom). [clausify(3520)]. 36.95/36.84 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),E)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5371,c,5305,a)]. 36.99/36.88 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),E)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5371,c,5348,a)]. 36.99/36.88 5372 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),times_times(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,filter(A),at(A),C))) # label(fact_4552_mult__right_Ocont) # label(axiom). [clausify(3534)]. 36.99/36.88 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),times_times(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,filter(real),at(real),B))). [resolve(5372,a,5305,a)]. 36.99/36.88 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5372,a,5348,a)]. 36.99/36.88 5373 -real_normed_algebra(A) | -metric_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),E),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4577_LIM__mult__zero) # label(axiom). [clausify(3578)]. 36.99/36.88 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),D),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5373,a,5305,a)]. 36.99/36.88 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),D),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5373,a,5348,a)]. 37.35/37.27 5374 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4190_mult__left_Osetsum) # label(axiom). [clausify(3627)]. 37.35/37.27 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5374,a,5305,a)]. 37.35/37.27 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C). [resolve(5374,a,5348,a)]. 37.35/37.27 5375 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_877_mult__left_Ozero) # label(axiom). [clausify(3774)]. 37.35/37.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A) = zero_zero(real). [resolve(5375,a,5305,a)]. 37.35/37.27 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5375,a,5348,a)]. 37.35/37.27 5376 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_4679_mult__left_OscaleR) # label(axiom). [clausify(3983)]. 37.35/37.27 5377 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_885_mult_Odiff__left) # label(axiom). [clausify(4050)]. 37.35/37.27 5378 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),E),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(A,fun(B,B)),fun(fun(A,B),fun(A,B)),combs(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),D)) # label(fact_4909_isCont__mult) # label(axiom). [clausify(4095)]. 37.96/37.89 5379 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4080_sums__mult2) # label(axiom). [clausify(4189)]. 37.96/37.89 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5379,a,5305,a)]. 37.96/37.89 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(5379,a,5348,a)]. 37.96/37.89 5380 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4082_mult__left_Osums) # label(axiom). [clausify(4477)]. 37.96/37.89 5381 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_880_mult_Oadd__right) # label(axiom). [clausify(4511)]. 37.96/37.89 5382 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_879_mult__right_Ozero) # label(axiom). [clausify(4548)]. 37.96/37.89 5383 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),sequentially)) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom). [clausify(4629)]. 37.96/37.89 5384 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_876_mult_Ozero__left) # label(axiom). [clausify(4762)]. 37.96/37.89 5385 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f832(A,C)))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom). [clausify(4834)]. 37.96/37.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f832(real,B)))). [resolve(5385,a,5305,a)]. 37.96/37.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f832(complex,B)))). [resolve(5385,a,5348,a)]. 39.55/39.45 5386 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f832(A,B))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom). [clausify(4834)]. 39.55/39.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f832(real,A))). [resolve(5386,a,5305,a)]. 39.55/39.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f832(complex,A))). [resolve(5386,a,5348,a)]. 39.55/39.45 5387 -topological_space(A) | -real_normed_algebra(B) | -power(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),E)),D)) # label(fact_4902_isCont__power) # label(axiom). [clausify(4891)]. 39.55/39.45 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),D)),C)). [resolve(5387,b,5305,a)]. 39.55/39.45 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),D)),C)). [resolve(5387,b,5348,a)]. 39.55/39.45 5388 linorder(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Orderings_Olinorder) # label(axiom). [assumption]. 39.55/39.45 5389 -linorder(A) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | ti(A,C) = ti(A,E) # label(fact_4195_atLeastLessThan__inj_I2_J) # label(axiom). [clausify(33)]. 39.55/39.45 5390 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4951_min__max_Oless__supI1) # label(axiom). [clausify(34)]. 39.55/39.45 5391 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4968_min__max_Osup__left__idem) # label(axiom). [clausify(116)]. 39.55/39.45 5392 -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_1590_linorder__antisym__conv1) # label(axiom). [clausify(178)]. 39.55/39.45 5393 -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_1590_linorder__antisym__conv1) # label(axiom). [clausify(178)]. 39.55/39.45 5394 -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_1544_linorder__le__cases) # label(axiom). [clausify(231)]. 39.55/39.45 5395 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_4801_min__max_Oless__infI2) # label(axiom). [clausify(275)]. 39.55/39.46 5396 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4812_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(281)]. 39.55/39.46 5397 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_4964_min__max_Osup__assoc) # label(axiom). [clausify(295)]. 39.55/39.46 5398 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) # label(fact_4941_min__max_Oinf__sup__absorb) # label(axiom). [clausify(297)]. 39.55/39.46 5399 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f71(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2824_pinf_I6_J) # label(axiom). [clausify(303)]. 39.55/39.46 5400 -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_1558_linorder__linear) # label(axiom). [clausify(505)]. 39.55/39.46 5401 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom). [clausify(552)]. 39.55/39.46 5402 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom). [clausify(552)]. 39.55/39.46 5403 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_4828_min__max_Oinf__le2) # label(axiom). [clausify(565)]. 39.55/39.46 5404 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f112(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2829_pinf_I8_J) # label(axiom). [clausify(571)]. 39.55/39.46 5405 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4938_min__max_Osup__inf__distrib2) # label(axiom). [clausify(686)]. 39.55/39.46 Derived: hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),C),D) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,D). [resolve(5388,a,5389,a)]. 39.55/39.46 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))). [resolve(5388,a,5390,a)]. 39.55/39.46 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B). [resolve(5388,a,5391,a)]. 39.55/39.47 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,A). [resolve(5388,a,5392,a)]. 39.55/39.47 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,A). [resolve(5388,a,5393,a)]. 39.55/39.47 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5388,a,5394,a)]. 39.55/39.47 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),C),A)),B)). [resolve(5388,a,5395,a)]. 39.55/39.47 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)). [resolve(5388,a,5396,a)]. 39.55/39.47 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)). [resolve(5388,a,5397,a)]. 39.55/39.47 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)). [resolve(5388,a,5398,a)]. 39.55/39.47 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f71(quickcheck_code_int,A)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5388,a,5399,a)]. 39.55/39.47 Derived: -hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),C),D))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5388,a,5401,a)]. 39.55/39.49 Derived: -hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),C),D))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5388,a,5402,a)]. 39.55/39.49 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),B)). [resolve(5388,a,5403,a)]. 39.55/39.49 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f112(quickcheck_code_int,A)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5388,a,5404,a)]. 39.55/39.49 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),B). [resolve(5388,a,5405,a)]. 39.55/39.49 5406 -linorder(A) | ord_max(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_4991_dual__min) # label(axiom). [clausify(773)]. 39.55/39.49 Derived: ord_max(quickcheck_code_int) = hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),min(quickcheck_code_int),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),combc(quickcheck_code_int,quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int))). [resolve(5406,a,5388,a)]. 39.55/39.49 5407 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),D) # label(fact_4205_ivl__diff) # label(axiom). [clausify(859)]. 39.55/39.49 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hAPP(fun(quickcheck_code_int,bool),fun(quickcheck_code_int,bool),hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),fun(quickcheck_code_int,bool)),minus_minus(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B)) = hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),B),C). [resolve(5407,a,5388,a)]. 39.55/39.52 5408 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_4798_min__less__iff__disj) # label(axiom). [clausify(880)]. 39.55/39.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(5408,a,5388,a)]. 39.55/39.52 5409 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_4798_min__less__iff__disj) # label(axiom). [clausify(880)]. 39.55/39.52 5410 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_4798_min__less__iff__disj) # label(axiom). [clausify(880)]. 39.55/39.52 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(5410,a,5388,a)]. 39.55/39.52 5411 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(984)]. 39.55/39.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5411,a,5388,a)]. 39.55/39.52 5412 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(984)]. 39.55/39.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5412,a,5388,a)]. 39.55/39.52 5413 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -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),B),D)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(984)]. 39.64/39.55 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5413,a,5388,a)]. 39.64/39.55 5414 -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_1589_not__leE) # label(axiom). [clausify(1044)]. 39.64/39.55 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)). [resolve(5414,a,5388,a)]. 39.64/39.55 5415 -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),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),C))) # label(fact_4799_min__less__iff__conj) # label(axiom). [clausify(1081)]. 39.64/39.55 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),C),B))). [resolve(5415,a,5388,a)]. 39.64/39.55 5416 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),C))) # label(fact_4799_min__less__iff__conj) # label(axiom). [clausify(1081)]. 39.64/39.55 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),C),B))). [resolve(5416,a,5388,a)]. 39.64/39.55 5417 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_4799_min__less__iff__conj) # label(axiom). [clausify(1081)]. 39.64/39.55 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))). [resolve(5417,a,5388,a)]. 39.64/39.55 5418 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4981_min__max_Ole__supI2) # label(axiom). [clausify(1090)]. 39.64/39.55 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B))). [resolve(5418,a,5388,a)]. 39.70/39.60 5419 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_4825_min__max_Ole__infI1) # label(axiom). [clausify(1106)]. 39.70/39.60 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),B)). [resolve(5419,a,5388,a)]. 39.70/39.60 5420 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4971_min__max_Osup_Ocommute) # label(axiom). [clausify(1137)]. 39.70/39.60 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A). [resolve(5420,a,5388,a)]. 39.70/39.60 5421 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4975_min__max_Ole__supE) # label(axiom). [clausify(1181)]. 39.70/39.60 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5421,a,5388,a)]. 39.70/39.60 5422 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4975_min__max_Ole__supE) # label(axiom). [clausify(1181)]. 39.70/39.60 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(5422,a,5388,a)]. 39.70/39.60 5423 -linorder(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom). [clausify(1235)]. 39.70/39.60 Derived: ti(quickcheck_code_int,A) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5423,a,5388,a)]. 39.70/39.60 5424 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom). [clausify(1235)]. 39.70/39.60 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5424,a,5388,a)]. 39.70/39.60 5425 -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_1564_linorder__antisym__conv3) # label(axiom). [clausify(1282)]. 39.70/39.61 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B). [resolve(5425,a,5388,a)]. 39.70/39.61 5426 -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_1564_linorder__antisym__conv3) # label(axiom). [clausify(1282)]. 39.70/39.61 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B). [resolve(5426,a,5388,a)]. 39.70/39.61 5427 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4817_min__max_Oinf_Oidem) # label(axiom). [clausify(1296)]. 39.70/39.61 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),A). [resolve(5427,a,5388,a)]. 39.70/39.61 5428 -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),D),E)) | ti(A,B) != ti(A,D) | ti(A,C) != ti(A,E) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(1314)]. 39.70/39.61 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,C) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,D) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),C),D). [resolve(5428,a,5388,a)]. 39.70/39.61 5429 -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),D),E)) | ti(A,B) = ti(A,D) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(1314)]. 39.70/39.61 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),hAPP(quickcheck_code_int,fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),ord_atLeastLessThan(quickcheck_code_int),C),D). [resolve(5429,a,5388,a)]. 39.70/39.61 5430 -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),D),E)) | ti(A,C) = ti(A,E) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(1314)]. 39.70/39.61 5431 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(1326)]. 39.79/39.68 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B))). [resolve(5431,a,5388,a)]. 39.79/39.68 5432 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(1326)]. 39.79/39.68 5433 -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),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(1326)]. 39.79/39.68 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B))). [resolve(5433,a,5388,a)]. 39.79/39.68 5434 -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_1582_linorder__not__less) # label(axiom). [clausify(1332)]. 39.79/39.68 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)). [resolve(5434,a,5388,a)]. 39.79/39.68 5435 -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_1582_linorder__not__less) # label(axiom). [clausify(1332)]. 39.79/39.68 5436 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_4956_Max_Oidem) # label(axiom). [clausify(1334)]. 39.79/39.68 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),A). [resolve(5436,a,5388,a)]. 39.79/39.68 5437 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_1561_linorder__neq__iff) # label(axiom). [clausify(1426)]. 39.79/39.68 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B). [resolve(5437,a,5388,a)]. 39.79/39.68 5438 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_1561_linorder__neq__iff) # label(axiom). [clausify(1426)]. 39.79/39.68 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,A). [resolve(5438,a,5388,a)]. 39.79/39.68 5439 -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_1561_linorder__neq__iff) # label(axiom). [clausify(1426)]. 39.79/39.68 5440 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4980_min__max_Osup__absorb2) # label(axiom). [clausify(1487)]. 39.79/39.68 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B). [resolve(5440,a,5388,a)]. 39.79/39.72 5441 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption]. 39.79/39.72 Derived: hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D) | -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)) | ti(nat,B) = ti(nat,D). [resolve(5441,a,5389,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(5441,a,5390,a)]. 39.79/39.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(5441,a,5391,a)]. 39.79/39.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(5441,a,5392,a)]. 39.79/39.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(5441,a,5393,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)). [resolve(5441,a,5395,a)]. 39.79/39.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(5441,a,5396,a)]. 39.79/39.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)). [resolve(5441,a,5397,a)]. 39.79/39.72 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)). [resolve(5441,a,5398,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f71(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5441,a,5399,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5441,a,5401,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5441,a,5402,a)]. 39.79/39.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),B)). [resolve(5441,a,5403,a)]. 39.79/39.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f112(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5441,a,5404,a)]. 39.79/39.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(5441,a,5405,a)]. 39.84/39.74 Derived: ord_max(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))). [resolve(5441,a,5406,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C). [resolve(5441,a,5407,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | 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),A),C)). [resolve(5441,a,5408,a)]. 39.84/39.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(5441,a,5410,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5441,a,5411,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5441,a,5412,a)]. 39.84/39.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -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),A),C)). [resolve(5441,a,5413,a)]. 39.84/39.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(5441,a,5414,a)]. 39.84/39.74 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),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B))). [resolve(5441,a,5415,a)]. 39.84/39.74 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),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B))). [resolve(5441,a,5416,a)]. 39.84/39.74 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),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(5441,a,5417,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(5441,a,5418,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B)). [resolve(5441,a,5419,a)]. 39.84/39.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(5441,a,5420,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5441,a,5421,a)]. 39.84/39.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5441,a,5422,a)]. 39.84/39.74 Derived: ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5441,a,5423,a)]. 39.87/39.77 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5441,a,5424,a)]. 39.87/39.77 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) = ti(nat,B). [resolve(5441,a,5425,a)]. 39.87/39.77 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) != ti(nat,B). [resolve(5441,a,5426,a)]. 39.87/39.77 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A). [resolve(5441,a,5427,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | ti(nat,A) != ti(nat,C) | ti(nat,B) != ti(nat,D) | hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D). [resolve(5441,a,5428,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | ti(nat,A) = ti(nat,C) | hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D). [resolve(5441,a,5429,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(5441,a,5431,a)]. 39.87/39.77 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(5441,a,5433,a)]. 39.87/39.77 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(5441,a,5434,a)]. 39.87/39.77 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A). [resolve(5441,a,5436,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B). [resolve(5441,a,5437,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(5441,a,5438,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(5441,a,5440,a)]. 39.87/39.77 5442 linorder(rat) # label(arity_Rat_Orat___Orderings_Olinorder) # label(axiom). [assumption]. 39.87/39.77 Derived: hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B) != hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,B) = ti(rat,D). [resolve(5442,a,5389,a)]. 39.87/39.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))). [resolve(5442,a,5390,a)]. 39.87/39.77 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B). [resolve(5442,a,5391,a)]. 39.87/39.77 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) = ti(rat,A). [resolve(5442,a,5392,a)]. 39.87/39.77 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) != ti(rat,A). [resolve(5442,a,5393,a)]. 39.87/39.77 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5442,a,5394,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),C),A)),B)). [resolve(5442,a,5395,a)]. 39.87/39.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)). [resolve(5442,a,5396,a)]. 39.87/39.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)). [resolve(5442,a,5397,a)]. 39.87/39.80 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)). [resolve(5442,a,5398,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f71(rat,A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5442,a,5399,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5442,a,5401,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5442,a,5402,a)]. 39.87/39.80 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),B)). [resolve(5442,a,5403,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f112(rat,A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5442,a,5404,a)]. 39.87/39.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(5442,a,5405,a)]. 39.87/39.80 Derived: ord_max(rat) = hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,rat)),min(rat),hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,bool)),combc(rat,rat,bool),ord_less_eq(rat))). [resolve(5442,a,5406,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,bool),fun(fun(rat,bool),fun(rat,bool)),minus_minus(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),C)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),B),C). [resolve(5442,a,5407,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(5442,a,5408,a)]. 39.87/39.80 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(5442,a,5410,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5442,a,5411,a)]. 39.87/39.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5442,a,5412,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5442,a,5413,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5442,a,5414,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),C),B))). [resolve(5442,a,5415,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),C),B))). [resolve(5442,a,5416,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))). [resolve(5442,a,5417,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B))). [resolve(5442,a,5418,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B)). [resolve(5442,a,5419,a)]. 39.87/39.82 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A). [resolve(5442,a,5420,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5442,a,5421,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5442,a,5422,a)]. 39.87/39.82 Derived: ti(rat,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5442,a,5423,a)]. 39.87/39.82 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5442,a,5424,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | ti(rat,A) = ti(rat,B). [resolve(5442,a,5425,a)]. 39.87/39.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | ti(rat,A) != ti(rat,B). [resolve(5442,a,5426,a)]. 39.87/39.82 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),A). [resolve(5442,a,5427,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,A) != ti(rat,C) | ti(rat,B) != ti(rat,D) | hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D). [resolve(5442,a,5428,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,A) = ti(rat,C) | hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B) != hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D). [resolve(5442,a,5429,a)]. 39.87/39.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B))). [resolve(5442,a,5431,a)]. 39.99/39.90 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B))). [resolve(5442,a,5433,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5442,a,5434,a)]. 39.99/39.90 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),A). [resolve(5442,a,5436,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,A) != ti(rat,B). [resolve(5442,a,5437,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) != ti(rat,A). [resolve(5442,a,5438,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B). [resolve(5442,a,5440,a)]. 39.99/39.90 5443 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_4800_min__max_Oless__infI1) # label(axiom). [clausify(1562)]. 39.99/39.90 5444 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_4819_min__max_Oinf__mono) # label(axiom). [clausify(1632)]. 39.99/39.90 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),D))). [resolve(5444,a,5388,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))). [resolve(5444,a,5441,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),D))). [resolve(5444,a,5442,a)]. 39.99/39.90 5445 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4822_min__max_Oinf__absorb2) # label(axiom). [clausify(1741)]. 39.99/39.90 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),A). [resolve(5445,a,5388,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(5445,a,5441,a)]. 39.99/39.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),A). [resolve(5445,a,5442,a)]. 39.99/39.92 5446 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom). [assumption]. 39.99/39.92 Derived: hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B) != hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | ti(real,B) = ti(real,D). [resolve(5446,a,5389,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))). [resolve(5446,a,5390,a)]. 39.99/39.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B). [resolve(5446,a,5391,a)]. 39.99/39.92 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(5446,a,5392,a)]. 39.99/39.92 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(5446,a,5393,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),C),A)),B)). [resolve(5446,a,5395,a)]. 39.99/39.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)). [resolve(5446,a,5396,a)]. 39.99/39.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)). [resolve(5446,a,5397,a)]. 39.99/39.92 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)). [resolve(5446,a,5398,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f71(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5446,a,5399,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5446,a,5401,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5446,a,5402,a)]. 39.99/39.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),B)). [resolve(5446,a,5403,a)]. 39.99/39.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f112(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5446,a,5404,a)]. 39.99/39.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(5446,a,5405,a)]. 40.06/39.95 Derived: ord_max(real) = hAPP(fun(real,fun(real,bool)),fun(real,fun(real,real)),min(real),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real))). [resolve(5446,a,5406,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,bool),fun(real,bool)),minus_minus(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),C)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),B),C). [resolve(5446,a,5407,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5446,a,5408,a)]. 40.06/39.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5446,a,5410,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5446,a,5411,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5446,a,5412,a)]. 40.06/39.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))) | -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),A),C)). [resolve(5446,a,5413,a)]. 40.06/39.95 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(5446,a,5414,a)]. 40.06/39.95 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),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),C),B))). [resolve(5446,a,5415,a)]. 40.06/39.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),C),B))). [resolve(5446,a,5416,a)]. 40.06/39.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))). [resolve(5446,a,5417,a)]. 40.06/39.95 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),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5446,a,5418,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B)). [resolve(5446,a,5419,a)]. 40.06/39.95 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A). [resolve(5446,a,5420,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5446,a,5421,a)]. 40.06/39.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5446,a,5422,a)]. 40.08/39.98 Derived: ti(real,A) != hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5446,a,5423,a)]. 40.08/39.98 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5446,a,5424,a)]. 40.08/39.98 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)) | ti(real,A) = ti(real,B). [resolve(5446,a,5425,a)]. 40.08/39.98 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)) | ti(real,A) != ti(real,B). [resolve(5446,a,5426,a)]. 40.08/39.98 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),A). [resolve(5446,a,5427,a)]. 40.08/39.98 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)) | ti(real,A) != ti(real,C) | ti(real,B) != ti(real,D) | hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D). [resolve(5446,a,5428,a)]. 40.08/39.98 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)) | ti(real,A) = ti(real,C) | hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B) != hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D). [resolve(5446,a,5429,a)]. 40.08/39.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5446,a,5431,a)]. 40.08/39.98 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),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5446,a,5433,a)]. 40.08/39.98 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(5446,a,5434,a)]. 40.08/39.98 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),A). [resolve(5446,a,5436,a)]. 40.08/39.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) != ti(real,B). [resolve(5446,a,5437,a)]. 40.08/39.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A). [resolve(5446,a,5438,a)]. 40.08/39.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B). [resolve(5446,a,5440,a)]. 40.08/39.98 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,hAPP(real,fun(real,real),ord_min(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),D))). [resolve(5446,a,5444,a)]. 40.08/39.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),A). [resolve(5446,a,5445,a)]. 40.08/39.98 5447 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4813_min__max_Oinf__left__idem) # label(axiom). [clausify(1775)]. 40.08/39.98 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B). [resolve(5447,a,5388,a)]. 40.15/40.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B). [resolve(5447,a,5441,a)]. 40.15/40.04 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B). [resolve(5447,a,5442,a)]. 40.15/40.04 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B). [resolve(5447,a,5446,a)]. 40.15/40.04 5448 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom). [clausify(1834)]. 40.15/40.04 5449 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom). [clausify(1834)]. 40.15/40.04 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B). [resolve(5449,a,5388,a)]. 40.15/40.04 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(5449,a,5441,a)]. 40.15/40.04 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B). [resolve(5449,a,5442,a)]. 40.15/40.04 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B). [resolve(5449,a,5446,a)]. 40.15/40.04 5450 -linorder(A) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | ti(A,B) = ti(A,D) # label(fact_4196_atLeastLessThan__inj_I1_J) # label(axiom). [clausify(1836)]. 40.15/40.04 5451 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1893)]. 40.15/40.04 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5451,a,5388,a)]. 40.15/40.04 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5451,a,5441,a)]. 40.15/40.04 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5451,a,5442,a)]. 40.15/40.04 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5451,a,5446,a)]. 40.25/40.15 5452 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1893)]. 40.25/40.15 5453 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1893)]. 40.25/40.15 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5453,a,5388,a)]. 40.25/40.15 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5453,a,5441,a)]. 40.25/40.15 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5453,a,5442,a)]. 40.25/40.15 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5453,a,5446,a)]. 40.25/40.15 5454 -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_1563_linorder__less__linear) # label(axiom). [clausify(1918)]. 40.25/40.15 5455 -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),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_4821_min__max_Ole__infI) # label(axiom). [clausify(1985)]. 40.25/40.15 5456 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4979_min__max_Osup__absorb1) # label(axiom). [clausify(2027)]. 40.25/40.15 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A). [resolve(5456,a,5388,a)]. 40.25/40.15 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(5456,a,5441,a)]. 40.25/40.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A). [resolve(5456,a,5442,a)]. 40.25/40.15 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A). [resolve(5456,a,5446,a)]. 40.25/40.15 5457 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4816_min__max_Oinf_Ocommute) # label(axiom). [clausify(2115)]. 40.25/40.15 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),A). [resolve(5457,a,5388,a)]. 40.25/40.15 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(5457,a,5441,a)]. 40.29/40.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),A). [resolve(5457,a,5442,a)]. 40.29/40.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),A). [resolve(5457,a,5446,a)]. 40.29/40.22 5458 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4952_min__max_Oless__supI2) # label(axiom). [clausify(2225)]. 40.29/40.22 5459 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4937_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(2236)]. 40.29/40.22 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)). [resolve(5459,a,5388,a)]. 40.29/40.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(5459,a,5441,a)]. 40.29/40.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)). [resolve(5459,a,5442,a)]. 40.29/40.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)). [resolve(5459,a,5446,a)]. 40.29/40.22 5460 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_atMost(A),B) = hAPP(A,fun(A,bool),ord_atMost(A),C) # label(fact_4962_atMost__eq__iff) # label(axiom). [clausify(2260)]. 40.29/40.22 Derived: ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_atMost(quickcheck_code_int),A) = hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_atMost(quickcheck_code_int),B). [resolve(5460,a,5388,a)]. 40.29/40.22 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_atMost(nat),A) = hAPP(nat,fun(nat,bool),ord_atMost(nat),B). [resolve(5460,a,5441,a)]. 40.29/40.22 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,fun(rat,bool),ord_atMost(rat),A) = hAPP(rat,fun(rat,bool),ord_atMost(rat),B). [resolve(5460,a,5442,a)]. 40.29/40.22 Derived: ti(real,A) != ti(real,B) | hAPP(real,fun(real,bool),ord_atMost(real),A) = hAPP(real,fun(real,bool),ord_atMost(real),B). [resolve(5460,a,5446,a)]. 40.29/40.22 5461 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_atMost(A),B) != hAPP(A,fun(A,bool),ord_atMost(A),C) # label(fact_4962_atMost__eq__iff) # label(axiom). [clausify(2260)]. 40.29/40.22 Derived: ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_atMost(quickcheck_code_int),A) != hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_atMost(quickcheck_code_int),B). [resolve(5461,a,5388,a)]. 40.29/40.22 Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_atMost(nat),A) != hAPP(nat,fun(nat,bool),ord_atMost(nat),B). [resolve(5461,a,5441,a)]. 40.54/40.42 Derived: ti(rat,A) = ti(rat,B) | hAPP(rat,fun(rat,bool),ord_atMost(rat),A) != hAPP(rat,fun(rat,bool),ord_atMost(rat),B). [resolve(5461,a,5442,a)]. 40.54/40.42 Derived: ti(real,A) = ti(real,B) | hAPP(real,fun(real,bool),ord_atMost(real),A) != hAPP(real,fun(real,bool),ord_atMost(real),B). [resolve(5461,a,5446,a)]. 40.54/40.42 5462 -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),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_4820_min__max_Oinf__greatest) # label(axiom). [clausify(2311)]. 40.54/40.42 5463 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f424(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2828_minf_I6_J) # label(axiom). [clausify(2344)]. 40.54/40.42 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f424(quickcheck_code_int,B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5463,a,5388,a)]. 40.54/40.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f424(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5463,a,5441,a)]. 40.54/40.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f424(rat,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5463,a,5442,a)]. 40.54/40.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f424(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5463,a,5446,a)]. 40.54/40.42 5464 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_4946_min__max_Odistrib__sup__le) # label(axiom). [clausify(2505)]. 40.54/40.42 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)))). [resolve(5464,a,5388,a)]. 40.54/40.42 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)))). [resolve(5464,a,5441,a)]. 40.54/40.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)))). [resolve(5464,a,5442,a)]. 40.54/40.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)))). [resolve(5464,a,5446,a)]. 40.90/40.78 5465 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4809_min__max_Oinf__assoc) # label(axiom). [clausify(2533)]. 40.90/40.78 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)). [resolve(5465,a,5388,a)]. 40.90/40.78 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(5465,a,5441,a)]. 40.90/40.78 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)). [resolve(5465,a,5442,a)]. 40.90/40.78 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)). [resolve(5465,a,5446,a)]. 40.90/40.78 5466 -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_1584_linorder__le__less__linear) # label(axiom). [clausify(2662)]. 40.90/40.78 5467 -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_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(2684)]. 40.90/40.78 5468 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(2684)]. 40.90/40.78 5469 -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_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(2684)]. 40.90/40.78 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)). [resolve(5469,a,5388,a)]. 40.90/40.78 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(5469,a,5441,a)]. 40.90/40.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5469,a,5442,a)]. 40.90/40.78 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(5469,a,5446,a)]. 40.90/40.78 5470 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4818_min__max_Ole__infE) # label(axiom). [clausify(2822)]. 40.90/40.78 5471 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4818_min__max_Ole__infE) # label(axiom). [clausify(2822)]. 40.90/40.78 5472 -linorder(A) | ord_min(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_4834_dual__max) # label(axiom). [clausify(2903)]. 41.21/41.10 Derived: ord_min(quickcheck_code_int) = hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),max(quickcheck_code_int),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),combc(quickcheck_code_int,quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int))). [resolve(5472,a,5388,a)]. 41.21/41.10 Derived: ord_min(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),max(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))). [resolve(5472,a,5441,a)]. 41.21/41.10 Derived: ord_min(rat) = hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,rat)),max(rat),hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,bool)),combc(rat,rat,bool),ord_less_eq(rat))). [resolve(5472,a,5442,a)]. 41.21/41.10 Derived: ord_min(real) = hAPP(fun(real,fun(real,bool)),fun(real,fun(real,real)),max(real),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real))). [resolve(5472,a,5446,a)]. 41.21/41.10 5473 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4939_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(2954)]. 41.21/41.10 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)). [resolve(5473,a,5388,a)]. 41.21/41.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(5473,a,5441,a)]. 41.21/41.10 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)). [resolve(5473,a,5442,a)]. 41.21/41.10 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)). [resolve(5473,a,5446,a)]. 41.21/41.10 5474 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_4965_min__max_Osup_Oassoc) # label(axiom). [clausify(2972)]. 41.21/41.10 5475 -linorder(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_50_le__number__of__eq__not__less) # label(axiom). [clausify(3321)]. 41.21/41.10 5476 -linorder(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_50_le__number__of__eq__not__less) # label(axiom). [clausify(3321)]. 41.36/41.27 5477 -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),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4982_min__max_Ole__supI1) # label(axiom). [clausify(3362)]. 41.36/41.27 5478 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_4986_le__maxI1) # label(axiom). [clausify(3513)]. 41.36/41.27 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B))). [resolve(5478,a,5388,a)]. 41.36/41.27 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))). [resolve(5478,a,5441,a)]. 41.36/41.27 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B))). [resolve(5478,a,5442,a)]. 41.36/41.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B))). [resolve(5478,a,5446,a)]. 41.36/41.27 5479 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom). [clausify(3535)]. 41.36/41.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5479,a,5388,a)]. 41.36/41.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5479,a,5441,a)]. 41.36/41.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5479,a,5442,a)]. 41.36/41.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5479,a,5446,a)]. 41.36/41.27 5480 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom). [clausify(3535)]. 41.36/41.27 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5480,a,5388,a)]. 41.36/41.27 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5480,a,5441,a)]. 41.62/41.51 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5480,a,5442,a)]. 41.62/41.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5480,a,5446,a)]. 41.62/41.51 5481 -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_1588_leI) # label(axiom). [clausify(3587)]. 41.62/41.51 5482 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4978_min__max_Ole__supI) # label(axiom). [clausify(3591)]. 41.62/41.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),B)). [resolve(5482,a,5388,a)]. 41.62/41.51 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),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B)). [resolve(5482,a,5441,a)]. 41.62/41.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B)). [resolve(5482,a,5442,a)]. 41.62/41.51 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),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B)). [resolve(5482,a,5446,a)]. 41.62/41.51 5483 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4814_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(3763)]. 41.62/41.51 5484 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3776)]. 41.62/41.51 5485 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3776)]. 41.62/41.51 5486 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -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),B),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3776)]. 41.62/41.51 5487 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_4985_le__maxI2) # label(axiom). [clausify(3806)]. 41.62/41.51 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A))). [resolve(5487,a,5388,a)]. 41.74/41.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))). [resolve(5487,a,5441,a)]. 41.74/41.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A))). [resolve(5487,a,5442,a)]. 41.74/41.67 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A))). [resolve(5487,a,5446,a)]. 41.74/41.67 5488 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1595_linorder__antisym__conv2) # label(axiom). [clausify(3920)]. 41.74/41.67 5489 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1595_linorder__antisym__conv2) # label(axiom). [clausify(3920)]. 41.74/41.67 5490 -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),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),B)),C)) # label(fact_4949_max__less__iff__conj) # label(axiom). [clausify(3964)]. 41.74/41.67 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),A)),B)). [resolve(5490,a,5388,a)]. 41.74/41.67 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),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),A)),B)). [resolve(5490,a,5441,a)]. 41.74/41.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),A)),B)). [resolve(5490,a,5442,a)]. 41.74/41.67 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),A)),B)). [resolve(5490,a,5446,a)]. 41.74/41.67 5491 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),B)),C)) # label(fact_4949_max__less__iff__conj) # label(axiom). [clausify(3964)]. 41.74/41.67 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),A)),B)). [resolve(5491,a,5388,a)]. 41.74/41.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),A)),B)). [resolve(5491,a,5441,a)]. 41.74/41.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),A)),B)). [resolve(5491,a,5442,a)]. 41.74/41.67 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),A)),B)). [resolve(5491,a,5446,a)]. 41.90/41.77 5492 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4949_max__less__iff__conj) # label(axiom). [clausify(3964)]. 41.90/41.77 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),B)). [resolve(5492,a,5388,a)]. 41.90/41.77 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B)). [resolve(5492,a,5441,a)]. 41.90/41.77 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B)). [resolve(5492,a,5442,a)]. 41.90/41.77 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(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B)). [resolve(5492,a,5446,a)]. 41.90/41.77 5493 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) # label(fact_4942_min__max_Osup__inf__absorb) # label(axiom). [clausify(3994)]. 41.90/41.77 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)). [resolve(5493,a,5388,a)]. 41.90/41.77 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)). [resolve(5493,a,5441,a)]. 41.90/41.77 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)). [resolve(5493,a,5442,a)]. 41.90/41.77 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)). [resolve(5493,a,5446,a)]. 41.90/41.77 5494 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4969_min__max_Osup_Oleft__idem) # label(axiom). [clausify(4010)]. 41.90/41.77 5495 -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_1565_linorder__neqE) # label(axiom). [clausify(4059)]. 41.90/41.77 5496 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_4945_min__max_Odistrib__inf__le) # label(axiom). [clausify(4066)]. 41.90/41.77 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)))). [resolve(5496,a,5388,a)]. 41.96/41.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)))). [resolve(5496,a,5441,a)]. 41.96/41.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)))). [resolve(5496,a,5442,a)]. 41.96/41.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C))),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)))). [resolve(5496,a,5446,a)]. 41.96/41.88 5497 -linorder(A) | -dvd(A) | -plus(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(4088)]. 41.96/41.88 Derived: -dvd(quickcheck_code_int) | -plus(quickcheck_code_int) | plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)). [resolve(5497,a,5388,a)]. 41.96/41.88 Derived: -dvd(nat) | -plus(nat) | plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(5497,a,5441,a)]. 41.96/41.88 Derived: -dvd(rat) | -plus(rat) | plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)). [resolve(5497,a,5442,a)]. 41.96/41.88 Derived: -dvd(real) | -plus(real) | plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(5497,a,5446,a)]. 41.96/41.88 5498 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4802_Min_Oidem) # label(axiom). [clausify(4097)]. 41.96/41.88 5499 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_4829_min__max_Oinf__le1) # label(axiom). [clausify(4174)]. 41.96/41.88 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),A)). [resolve(5499,a,5388,a)]. 41.96/41.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),A)). [resolve(5499,a,5441,a)]. 41.96/41.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),A)). [resolve(5499,a,5442,a)]. 41.96/41.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),A)). [resolve(5499,a,5446,a)]. 41.96/41.88 5500 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_4966_min__max_Osup__left__commute) # label(axiom). [clausify(4183)]. 41.96/41.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)). [resolve(5500,a,5388,a)]. 41.96/41.88 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)). [resolve(5500,a,5441,a)]. 41.96/41.89 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)). [resolve(5500,a,5442,a)]. 41.96/41.89 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)). [resolve(5500,a,5446,a)]. 41.96/41.89 5501 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption]. 41.96/41.89 Derived: hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B) != hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | ti(int,B) = ti(int,D). [resolve(5501,a,5389,a)]. 41.96/41.89 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),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(5501,a,5390,a)]. 41.96/41.89 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(5501,a,5391,a)]. 41.96/41.89 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(5501,a,5392,a)]. 41.96/41.89 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(5501,a,5393,a)]. 41.96/41.89 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5501,a,5394,a)]. 41.96/41.89 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)). [resolve(5501,a,5395,a)]. 41.96/41.89 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(5501,a,5396,a)]. 41.96/41.89 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)). [resolve(5501,a,5397,a)]. 41.96/41.89 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)). [resolve(5501,a,5398,a)]. 41.96/41.89 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f71(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5501,a,5399,a)]. 41.96/41.89 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5501,a,5401,a)]. 41.96/41.89 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5501,a,5402,a)]. 41.96/41.90 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),B)). [resolve(5501,a,5403,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f112(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5404,a)]. 41.96/41.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(5501,a,5405,a)]. 41.96/41.90 Derived: ord_max(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),min(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))). [resolve(5501,a,5406,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),C)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),B),C). [resolve(5501,a,5407,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(5501,a,5408,a)]. 41.96/41.90 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(5501,a,5410,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5411,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5501,a,5412,a)]. 41.96/41.90 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | -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),A),C)). [resolve(5501,a,5413,a)]. 41.96/41.90 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(5501,a,5414,a)]. 41.96/41.90 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),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B))). [resolve(5501,a,5415,a)]. 41.96/41.90 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),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B))). [resolve(5501,a,5416,a)]. 41.96/41.90 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),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))). [resolve(5501,a,5417,a)]. 41.96/41.90 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),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(5501,a,5418,a)]. 41.96/41.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)). [resolve(5501,a,5419,a)]. 41.96/41.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(5501,a,5420,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5501,a,5421,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(5501,a,5422,a)]. 41.96/41.92 Derived: ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5423,a)]. 41.96/41.92 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5424,a)]. 41.96/41.92 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)) | ti(int,A) = ti(int,B). [resolve(5501,a,5425,a)]. 41.96/41.92 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)) | ti(int,A) != ti(int,B). [resolve(5501,a,5426,a)]. 41.96/41.92 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A). [resolve(5501,a,5427,a)]. 41.96/41.92 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)) | ti(int,A) != ti(int,C) | ti(int,B) != ti(int,D) | hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D). [resolve(5501,a,5428,a)]. 41.96/41.92 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)) | ti(int,A) = ti(int,C) | hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B) != hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D). [resolve(5501,a,5429,a)]. 41.96/41.92 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),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(5501,a,5431,a)]. 41.96/41.92 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),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(5501,a,5433,a)]. 41.96/41.92 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(5501,a,5434,a)]. 41.96/41.92 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A). [resolve(5501,a,5436,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B). [resolve(5501,a,5437,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A). [resolve(5501,a,5438,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(5501,a,5440,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),D))). [resolve(5501,a,5444,a)]. 41.96/41.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A). [resolve(5501,a,5445,a)]. 41.96/41.92 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B). [resolve(5501,a,5447,a)]. 41.96/41.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(5501,a,5449,a)]. 41.96/41.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5451,a)]. 41.96/41.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5453,a)]. 41.96/41.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(5501,a,5456,a)]. 41.96/41.94 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A). [resolve(5501,a,5457,a)]. 41.96/41.94 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(5501,a,5459,a)]. 41.96/41.94 Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_atMost(int),A) = hAPP(int,fun(int,bool),ord_atMost(int),B). [resolve(5501,a,5460,a)]. 41.96/41.94 Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_atMost(int),A) != hAPP(int,fun(int,bool),ord_atMost(int),B). [resolve(5501,a,5461,a)]. 41.96/41.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f424(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5501,a,5463,a)]. 41.96/41.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)))). [resolve(5501,a,5464,a)]. 41.96/41.94 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(5501,a,5465,a)]. 41.96/41.94 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(5501,a,5469,a)]. 41.96/41.94 Derived: ord_min(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),max(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))). [resolve(5501,a,5472,a)]. 41.96/41.94 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(5501,a,5473,a)]. 41.96/41.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B))). [resolve(5501,a,5478,a)]. 41.96/41.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5501,a,5479,a)]. 41.96/41.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5501,a,5480,a)]. 41.96/41.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B)). [resolve(5501,a,5482,a)]. 41.96/41.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A))). [resolve(5501,a,5487,a)]. 42.07/41.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),A)),B)). [resolve(5501,a,5490,a)]. 42.07/41.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),A)),B)). [resolve(5501,a,5491,a)]. 42.07/41.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B)). [resolve(5501,a,5492,a)]. 42.07/41.97 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)). [resolve(5501,a,5493,a)]. 42.07/41.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)))). [resolve(5501,a,5496,a)]. 42.07/41.97 Derived: -dvd(int) | -plus(int) | plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(5501,a,5497,a)]. 42.07/41.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),A)). [resolve(5501,a,5499,a)]. 42.07/41.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)). [resolve(5501,a,5500,a)]. 42.07/41.97 5502 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_4972_min__max_Osup_Oidem) # label(axiom). [clausify(4190)]. 42.07/41.97 5503 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(4208)]. 42.07/41.97 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(5503,a,5388,a)]. 42.07/41.97 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5503,a,5441,a)]. 42.07/41.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5503,a,5442,a)]. 42.07/41.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5503,a,5446,a)]. 42.07/41.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(5503,a,5501,a)]. 42.22/42.14 5504 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(4208)]. 42.22/42.14 5505 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(4208)]. 42.22/42.14 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(5505,a,5388,a)]. 42.22/42.14 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5505,a,5441,a)]. 42.22/42.14 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5505,a,5442,a)]. 42.22/42.14 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5505,a,5446,a)]. 42.22/42.14 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(5505,a,5501,a)]. 42.22/42.14 5506 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4810_min__max_Oinf_Oassoc) # label(axiom). [clausify(4234)]. 42.22/42.14 5507 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4811_min__max_Oinf__left__commute) # label(axiom). [clausify(4241)]. 42.22/42.14 5508 -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_1583_linorder__not__le) # label(axiom). [clausify(4293)]. 42.22/42.14 5509 -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_1583_linorder__not__le) # label(axiom). [clausify(4293)]. 42.22/42.14 5510 linorder(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Orderings_Olinorder) # label(axiom). [assumption]. 42.22/42.14 Derived: hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B) != hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),C),D) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,B) = ti(code_code_numeral,D). [resolve(5510,a,5389,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))). [resolve(5510,a,5390,a)]. 42.22/42.14 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B). [resolve(5510,a,5391,a)]. 42.22/42.14 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) = ti(code_code_numeral,A). [resolve(5510,a,5392,a)]. 42.22/42.14 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) != ti(code_code_numeral,A). [resolve(5510,a,5393,a)]. 42.22/42.14 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),A)). [resolve(5510,a,5394,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),C),A)),B)). [resolve(5510,a,5395,a)]. 42.22/42.14 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)). [resolve(5510,a,5396,a)]. 42.22/42.14 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)). [resolve(5510,a,5397,a)]. 42.22/42.14 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)). [resolve(5510,a,5398,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f71(code_code_numeral,A)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),A)). [resolve(5510,a,5399,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),C),D))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),A)). [resolve(5510,a,5401,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),C),D))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),A)). [resolve(5510,a,5402,a)]. 42.22/42.14 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),B)). [resolve(5510,a,5403,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f112(code_code_numeral,A)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5404,a)]. 42.22/42.14 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),B). [resolve(5510,a,5405,a)]. 42.22/42.14 Derived: ord_max(code_code_numeral) = hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),min(code_code_numeral),hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,bool)),combc(code_code_numeral,code_code_numeral,bool),ord_less_eq(code_code_numeral))). [resolve(5510,a,5406,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hAPP(fun(code_code_numeral,bool),fun(code_code_numeral,bool),hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),fun(code_code_numeral,bool)),minus_minus(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),C)),hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B)) = hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),B),C). [resolve(5510,a,5407,a)]. 42.22/42.14 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(5510,a,5408,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(5510,a,5410,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5411,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5510,a,5412,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5510,a,5413,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)). [resolve(5510,a,5414,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),C),B))). [resolve(5510,a,5415,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),C),B))). [resolve(5510,a,5416,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))). [resolve(5510,a,5417,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B))). [resolve(5510,a,5418,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),B)). [resolve(5510,a,5419,a)]. 42.22/42.15 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A). [resolve(5510,a,5420,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5510,a,5421,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(5510,a,5422,a)]. 42.22/42.15 Derived: ti(code_code_numeral,A) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5423,a)]. 42.22/42.15 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5424,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)) | ti(code_code_numeral,A) = ti(code_code_numeral,B). [resolve(5510,a,5425,a)]. 42.22/42.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)) | ti(code_code_numeral,A) != ti(code_code_numeral,B). [resolve(5510,a,5426,a)]. 42.22/42.15 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),A). [resolve(5510,a,5427,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,A) != ti(code_code_numeral,C) | ti(code_code_numeral,B) != ti(code_code_numeral,D) | hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B) = hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),C),D). [resolve(5510,a,5428,a)]. 42.22/42.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,A) = ti(code_code_numeral,C) | hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),A),B) != hAPP(code_code_numeral,fun(code_code_numeral,bool),hAPP(code_code_numeral,fun(code_code_numeral,fun(code_code_numeral,bool)),ord_atLeastLessThan(code_code_numeral),C),D). [resolve(5510,a,5429,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B))). [resolve(5510,a,5431,a)]. 42.22/42.16 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B))). [resolve(5510,a,5433,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)). [resolve(5510,a,5434,a)]. 42.22/42.16 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),A). [resolve(5510,a,5436,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | ti(code_code_numeral,A) != ti(code_code_numeral,B). [resolve(5510,a,5437,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | ti(code_code_numeral,B) != ti(code_code_numeral,A). [resolve(5510,a,5438,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B). [resolve(5510,a,5440,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),D))). [resolve(5510,a,5444,a)]. 42.22/42.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),A). [resolve(5510,a,5445,a)]. 42.22/42.16 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B). [resolve(5510,a,5447,a)]. 42.22/42.16 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B). [resolve(5510,a,5449,a)]. 42.22/42.17 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5451,a)]. 42.22/42.17 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5453,a)]. 42.22/42.17 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A). [resolve(5510,a,5456,a)]. 42.22/42.17 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),A). [resolve(5510,a,5457,a)]. 42.22/42.17 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)). [resolve(5510,a,5459,a)]. 42.22/42.17 Derived: ti(code_code_numeral,A) != ti(code_code_numeral,B) | hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_atMost(code_code_numeral),A) = hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_atMost(code_code_numeral),B). [resolve(5510,a,5460,a)]. 42.22/42.17 Derived: ti(code_code_numeral,A) = ti(code_code_numeral,B) | hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_atMost(code_code_numeral),A) != hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_atMost(code_code_numeral),B). [resolve(5510,a,5461,a)]. 42.22/42.17 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f424(code_code_numeral,B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5510,a,5463,a)]. 42.22/42.17 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)))). [resolve(5510,a,5464,a)]. 42.32/42.18 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)). [resolve(5510,a,5465,a)]. 42.32/42.18 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)). [resolve(5510,a,5469,a)]. 42.32/42.18 Derived: ord_min(code_code_numeral) = hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),max(code_code_numeral),hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,bool)),combc(code_code_numeral,code_code_numeral,bool),ord_less_eq(code_code_numeral))). [resolve(5510,a,5472,a)]. 42.32/42.18 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)). [resolve(5510,a,5473,a)]. 42.32/42.18 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B))). [resolve(5510,a,5478,a)]. 42.32/42.18 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5510,a,5479,a)]. 42.32/42.18 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5510,a,5480,a)]. 42.32/42.18 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),B)). [resolve(5510,a,5482,a)]. 42.32/42.18 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A))). [resolve(5510,a,5487,a)]. 42.32/42.19 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),A)),B)). [resolve(5510,a,5490,a)]. 42.32/42.19 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),A)),B)). [resolve(5510,a,5491,a)]. 42.32/42.19 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),B)). [resolve(5510,a,5492,a)]. 42.32/42.19 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)). [resolve(5510,a,5493,a)]. 42.32/42.19 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)))). [resolve(5510,a,5496,a)]. 42.32/42.19 Derived: -dvd(code_code_numeral) | -plus(code_code_numeral) | plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)). [resolve(5510,a,5497,a)]. 42.32/42.19 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),A)). [resolve(5510,a,5499,a)]. 42.32/42.19 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)). [resolve(5510,a,5500,a)]. 42.32/42.19 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(5510,a,5503,a)]. 42.36/42.25 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(5510,a,5505,a)]. 42.36/42.25 5511 -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_1593_leD) # label(axiom). [clausify(4362)]. 42.36/42.25 5512 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) = hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_4316_lessThan__eq__iff) # label(axiom). [clausify(4373)]. 42.36/42.25 Derived: ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A) = hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B). [resolve(5512,a,5388,a)]. 42.36/42.25 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),B). [resolve(5512,a,5441,a)]. 42.36/42.25 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,fun(rat,bool),ord_lessThan(rat),A) = hAPP(rat,fun(rat,bool),ord_lessThan(rat),B). [resolve(5512,a,5442,a)]. 42.36/42.25 Derived: ti(real,A) != ti(real,B) | hAPP(real,fun(real,bool),ord_lessThan(real),A) = hAPP(real,fun(real,bool),ord_lessThan(real),B). [resolve(5512,a,5446,a)]. 42.36/42.25 Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) = hAPP(int,fun(int,bool),ord_lessThan(int),B). [resolve(5512,a,5501,a)]. 42.36/42.25 Derived: ti(code_code_numeral,A) != ti(code_code_numeral,B) | hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A) = hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B). [resolve(5512,a,5510,a)]. 42.36/42.25 5513 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) != hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_4316_lessThan__eq__iff) # label(axiom). [clausify(4373)]. 42.36/42.25 Derived: ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B) | hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A) != hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B). [resolve(5513,a,5388,a)]. 42.36/42.25 Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) != hAPP(nat,fun(nat,bool),ord_lessThan(nat),B). [resolve(5513,a,5441,a)]. 42.36/42.25 Derived: ti(rat,A) = ti(rat,B) | hAPP(rat,fun(rat,bool),ord_lessThan(rat),A) != hAPP(rat,fun(rat,bool),ord_lessThan(rat),B). [resolve(5513,a,5442,a)]. 42.36/42.25 Derived: ti(real,A) = ti(real,B) | hAPP(real,fun(real,bool),ord_lessThan(real),A) != hAPP(real,fun(real,bool),ord_lessThan(real),B). [resolve(5513,a,5446,a)]. 42.36/42.25 Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) != hAPP(int,fun(int,bool),ord_lessThan(int),B). [resolve(5513,a,5501,a)]. 42.36/42.25 Derived: ti(code_code_numeral,A) = ti(code_code_numeral,B) | hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A) != hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B). [resolve(5513,a,5510,a)]. 42.36/42.25 5514 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_4976_min__max_Osup__mono) # label(axiom). [clausify(4418)]. 42.36/42.25 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),D))). [resolve(5514,a,5388,a)]. 42.53/42.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))). [resolve(5514,a,5441,a)]. 42.53/42.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),D))). [resolve(5514,a,5442,a)]. 42.53/42.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),D))). [resolve(5514,a,5446,a)]. 42.53/42.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),D))). [resolve(5514,a,5501,a)]. 42.53/42.47 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),D))). [resolve(5514,a,5510,a)]. 42.53/42.47 5515 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4815_min__max_Oinf__commute) # label(axiom). [clausify(4452)]. 42.53/42.47 5516 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_4967_min__max_Osup_Oleft__commute) # label(axiom). [clausify(4480)]. 42.53/42.47 5517 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4940_min__max_Osup__inf__distrib1) # label(axiom). [clausify(4634)]. 42.53/42.47 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)). [resolve(5517,a,5388,a)]. 42.68/42.58 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(5517,a,5441,a)]. 42.68/42.58 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)). [resolve(5517,a,5442,a)]. 42.68/42.58 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)). [resolve(5517,a,5446,a)]. 42.68/42.58 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(5517,a,5501,a)]. 42.68/42.58 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)). [resolve(5517,a,5510,a)]. 42.68/42.58 5518 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f806(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2830_minf_I8_J) # label(axiom). [clausify(4663)]. 42.68/42.58 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f806(quickcheck_code_int,B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5518,a,5388,a)]. 42.68/42.58 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f806(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5518,a,5441,a)]. 42.68/42.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f806(rat,B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5518,a,5442,a)]. 42.68/42.58 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f806(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5518,a,5446,a)]. 42.68/42.58 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f806(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5518,a,5501,a)]. 42.68/42.58 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f806(code_code_numeral,B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),A)). [resolve(5518,a,5510,a)]. 42.68/42.58 5519 -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_1581_linorder__cases) # label(axiom). [clausify(4690)]. 42.68/42.58 5520 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4970_min__max_Osup__commute) # label(axiom). [clausify(4740)]. 42.68/42.58 5521 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4977_min__max_Osup__least) # label(axiom). [clausify(4749)]. 42.77/42.63 5522 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4319_lessThan__subset__iff) # label(axiom). [clausify(4793)]. 42.77/42.63 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5522,a,5388,a)]. 42.77/42.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5522,a,5441,a)]. 42.77/42.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5522,a,5442,a)]. 42.77/42.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5522,a,5446,a)]. 42.77/42.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5522,a,5501,a)]. 42.77/42.63 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5522,a,5510,a)]. 42.77/42.63 5523 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4319_lessThan__subset__iff) # label(axiom). [clausify(4793)]. 42.77/42.63 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5523,a,5388,a)]. 42.77/42.63 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5523,a,5441,a)]. 42.77/42.63 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5523,a,5442,a)]. 45.05/44.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5523,a,5446,a)]. 45.05/44.91 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5523,a,5501,a)]. 45.05/44.91 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5523,a,5510,a)]. 45.05/44.91 5524 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4823_min__max_Oinf__absorb1) # label(axiom). [clausify(4822)]. 45.05/44.91 5525 -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),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_4824_min__max_Ole__infI2) # label(axiom). [clausify(4895)]. 45.05/44.91 5526 real_normed_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__field) # label(axiom). [assumption]. 45.05/44.91 5527 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F))) # label(fact_3822_DERIV__diff) # label(axiom). [clausify(43)]. 45.05/44.91 5528 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),hAPP(nat,nat,suc,E))),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(nat,A,semiring_1_of_nat(A),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),E))))) # label(fact_3887_DERIV__power__Suc) # label(axiom). [clausify(63)]. 45.05/44.91 5529 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4008_divide_Osummable) # label(axiom). [clausify(117)]. 45.05/44.91 5530 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,E) != ti(A,D) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2634_DERIV__cong) # label(axiom). [clausify(213)]. 45.05/44.91 5531 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom). [clausify(223)]. 45.05/44.91 5532 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,D) != ti(A,E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom). [clausify(227)]. 45.05/44.91 5533 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),E))) # label(fact_3836_DERIV__cdivide) # label(axiom). [clausify(315)]. 45.05/44.91 5534 -real_normed_field(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),C)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B))),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),E)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(A,real,norm_norm(A),B)))) # label(fact_1773_lemma__termdiff3) # label(axiom). [clausify(345)]. 45.05/44.91 5535 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),exp(A)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),hAPP(A,A,B,C))),D))) # label(fact_3864_DERIV__fun__exp) # label(axiom). [clausify(362)]. 45.05/44.91 5536 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom). [clausify(446)]. 45.05/44.91 5537 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom). [clausify(446)]. 45.05/44.91 5538 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),exp(A)),B)) # label(fact_4891_isCont__exp) # label(axiom). [clausify(517)]. 45.05/44.91 5539 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f106(A,C)))) # label(fact_1810_divide_Obounded) # label(axiom). [clausify(537)]. 45.05/44.91 5540 -real_normed_field(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),inverse_inverse(A)),B),hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3888_DERIV__inverse) # label(axiom). [clausify(704)]. 45.05/44.91 5541 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3983_suminf__add) # label(axiom). [clausify(750)]. 45.05/44.91 5542 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2586_mult__exp__exp) # label(axiom). [clausify(795)]. 45.05/44.91 5543 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3889_DERIV__power) # label(axiom). [clausify(856)]. 45.05/44.91 5544 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4564_divide_Ocont) # label(axiom). [clausify(857)]. 45.05/44.91 5545 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1656_divide_Ozero) # label(axiom). [clausify(883)]. 45.05/44.91 5546 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4086_sums__divide) # label(axiom). [clausify(903)]. 45.05/44.91 5547 -real_normed_field(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),hAPP(B,filter(B),at(B),E))) # label(fact_4563_divide_OLIM) # label(axiom). [clausify(1023)]. 45.05/44.91 5548 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),B),C)) | ti(A,D) != hAPP(A,A,B,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,E,f214(A,E,C,D,B))),hAPP(A,A,E,C)) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,f214(A,E,C,D,B))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),f214(A,E,C,D,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),D)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1274)]. 45.05/44.91 5549 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),f215(A,B,C,D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1274)]. 45.05/44.91 5550 -real_normed_field(A) | ti(A,B) = hAPP(A,A,f215(A,C,D,B),D) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),C),D),B)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1274)]. 45.05/44.91 5551 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,C)),hAPP(A,A,B,D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,f215(A,B,D,E),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),D),E)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1274)]. 45.05/44.91 5552 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),sequentially)) # label(fact_4449_divide_OLIMSEQ) # label(axiom). [clausify(1290)]. 45.05/44.91 5553 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),power_power(A),B))) # label(fact_4026_summable__geometric) # label(axiom). [clausify(1382)]. 45.05/44.91 5554 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),one_one(A)),B)))) # label(fact_4098_geometric__sums) # label(axiom). [clausify(1419)]. 45.05/44.91 5555 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f259(B,A,D,E,F,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(1445)]. 45.05/44.91 5556 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(B,fun(A,A),hAPP(fun(A,fun(B,A)),fun(B,fun(A,A)),combc(A,B,A),D),f259(B,A,D,E,F,C))),E),hAPP(B,A,hAPP(A,fun(B,A),F,E),f259(B,A,D,E,F,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(1445)]. 45.05/44.91 5557 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f263(A,C)))) # label(fact_1802_divide_Opos__bounded) # label(axiom). [clausify(1450)]. 45.05/44.91 5558 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f263(A,B))) # label(fact_1802_divide_Opos__bounded) # label(axiom). [clausify(1450)]. 45.05/44.91 5559 -real_normed_field(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2017_divide_Ominus) # label(axiom). [clausify(1593)]. 45.05/44.91 5560 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1661_divide_Oadd) # label(axiom). [clausify(1674)]. 45.05/44.91 5561 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_4087_sums__add) # label(axiom). [clausify(1675)]. 45.05/44.91 5562 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),hAPP(A,A,uminus_uminus(A),C))) # label(fact_4083_sums__minus) # label(axiom). [clausify(1740)]. 45.05/44.91 5563 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C))) # label(fact_4012_summable__diff) # label(axiom). [clausify(1806)]. 45.05/44.91 5564 -real_normed_field(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4586_divide_OLIM__zero) # label(axiom). [clausify(1838)]. 45.05/44.91 5565 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),E)) # label(fact_4456_divide_Otendsto) # label(axiom). [clausify(1841)]. 45.05/44.91 5566 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),hAPP(A,A,B,C)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),E),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))) # label(fact_3862_DERIV__chain_H) # label(axiom). [clausify(1971)]. 45.05/44.91 5567 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2585_exp__add) # label(axiom). [clausify(2005)]. 45.05/44.91 5568 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),E))),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,uminus_uminus(A),F)))) # label(fact_3816_DERIV__add__minus) # label(axiom). [clausify(2013)]. 45.05/44.91 5569 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f370(A,C)))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom). [clausify(2058)]. 45.05/44.91 5570 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f370(A,B))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom). [clausify(2058)]. 45.05/44.91 5571 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),hAPP(A,A,C,D)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),C),D),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),C)),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),F))) # label(fact_3861_DERIV__chain2) # label(axiom). [clausify(2084)]. 45.05/44.91 5572 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),B) != zero_zero(A) # label(fact_2537_exp__not__eq__zero) # label(axiom). [clausify(2118)]. 45.05/44.91 5573 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4620_DERIV__D) # label(axiom). [clausify(2158)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),E))). [resolve(5526,a,5527,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),hAPP(nat,nat,suc,D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(nat,complex,semiring_1_of_nat(complex),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),D))))). [resolve(5526,a,5528,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5526,a,5529,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,D) != ti(complex,C) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)). [resolve(5526,a,5530,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5526,a,5531,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,C) != ti(complex,D) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)). [resolve(5526,a,5532,a)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),D))). [resolve(5526,a,5533,a)]. 45.05/44.92 Derived: ti(complex,A) = zero_zero(complex) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(complex,real,norm_norm(complex),A)))). [resolve(5526,a,5534,a)]. 45.05/44.92 Derived: -banach(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),exp(complex)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),hAPP(complex,complex,A,B))),C))). [resolve(5526,a,5535,b)]. 45.05/44.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5526,a,5536,a)]. 45.07/44.93 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5526,a,5537,a)]. 45.07/44.93 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),exp(complex)),A)). [resolve(5526,a,5538,a)]. 45.07/44.93 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f106(complex,B)))). [resolve(5526,a,5539,a)]. 45.07/44.93 Derived: ti(complex,A) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),inverse_inverse(complex)),A),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5526,a,5540,a)]. 45.07/44.93 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5526,a,5541,a)]. 45.07/44.93 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)). [resolve(5526,a,5542,a)]. 45.07/44.93 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5526,a,5543,a)]. 45.07/44.94 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5526,a,5544,a)]. 45.07/44.94 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5526,a,5545,a)]. 45.07/44.94 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))). [resolve(5526,a,5546,a)]. 45.07/44.94 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5526,a,5547,a)]. 45.07/44.94 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),A),B)) | ti(complex,C) != hAPP(complex,complex,A,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,D,f214(complex,D,B,C,A))),hAPP(complex,complex,D,B)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,f214(complex,D,B,C,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),f214(complex,D,B,C,A)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),C)). [resolve(5526,a,5548,a)]. 45.07/44.94 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),f215(complex,A,B,C)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)). [resolve(5526,a,5549,a)]. 45.07/44.94 Derived: ti(complex,A) = hAPP(complex,complex,f215(complex,B,C,A),C) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),B),C),A)). [resolve(5526,a,5550,a)]. 45.07/44.95 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,B)),hAPP(complex,complex,A,C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,f215(complex,A,C,D),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),C),D)). [resolve(5526,a,5551,a)]. 45.07/44.95 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)),sequentially)). [resolve(5526,a,5552,a)]. 45.07/44.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),power_power(complex),A))). [resolve(5526,a,5553,a)]. 45.07/44.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),one_one(complex)),A)))). [resolve(5526,a,5554,a)]. 45.07/44.95 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f259(A,complex,C,D,E,B)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5526,a,5555,a)]. 45.07/44.95 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(A,fun(complex,complex),hAPP(fun(complex,fun(A,complex)),fun(A,fun(complex,complex)),combc(complex,A,complex),C),f259(A,complex,C,D,E,B))),D),hAPP(A,complex,hAPP(complex,fun(A,complex),E,D),f259(A,complex,C,D,E,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5526,a,5556,a)]. 45.07/44.96 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f263(complex,B)))). [resolve(5526,a,5557,a)]. 45.07/44.96 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f263(complex,A))). [resolve(5526,a,5558,a)]. 45.07/44.96 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B). [resolve(5526,a,5559,a)]. 45.07/44.96 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5526,a,5560,a)]. 45.07/44.96 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D))). [resolve(5526,a,5561,a)]. 45.07/44.96 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),hAPP(complex,complex,uminus_uminus(complex),B))). [resolve(5526,a,5562,a)]. 45.07/44.96 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B))). [resolve(5526,a,5563,a)]. 45.07/44.96 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5526,a,5564,a)]. 45.07/44.96 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),D)). [resolve(5526,a,5565,a)]. 45.07/44.97 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),hAPP(complex,complex,A,B)),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),D),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C))). [resolve(5526,a,5566,a)]. 45.07/44.97 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,uminus_uminus(complex),E)))). [resolve(5526,a,5568,a)]. 45.07/44.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f370(complex,B)))). [resolve(5526,a,5569,a)]. 45.07/44.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f370(complex,A))). [resolve(5526,a,5570,a)]. 45.07/44.97 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),A) != zero_zero(complex). [resolve(5526,a,5572,a)]. 45.07/44.97 5574 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C))),D)),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C)))))) # label(fact_3877_DERIV__inverse_H) # label(axiom). [clausify(2185)]. 45.07/44.97 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B))),C)),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B)))))). [resolve(5574,a,5526,a)]. 45.07/44.98 5575 -banach(A) | -real_normed_field(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4751_exp__def) # label(axiom). [clausify(2192)]. 45.07/44.98 Derived: -banach(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))) = hAPP(complex,complex,exp(complex),A). [resolve(5575,b,5526,a)]. 45.07/44.98 5576 real_normed_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__field) # label(axiom). [assumption]. 45.07/44.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),E))). [resolve(5576,a,5527,a)]. 45.07/44.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),hAPP(nat,nat,suc,D))),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),D))))). [resolve(5576,a,5528,a)]. 45.07/44.98 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5576,a,5529,a)]. 45.07/44.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,D) != ti(real,C) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)). [resolve(5576,a,5530,a)]. 45.07/44.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5576,a,5531,a)]. 45.07/44.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,C) != ti(real,D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)). [resolve(5576,a,5532,a)]. 45.07/44.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),D))). [resolve(5576,a,5533,a)]. 45.07/44.99 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,norm_norm(real),A)))). [resolve(5576,a,5534,a)]. 45.07/44.99 Derived: -banach(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),exp(real)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),hAPP(real,real,A,B))),C))). [resolve(5576,a,5535,b)]. 45.07/44.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5576,a,5536,a)]. 45.07/44.99 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5576,a,5537,a)]. 45.07/44.99 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),exp(real)),A)). [resolve(5576,a,5538,a)]. 45.07/44.99 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f106(real,B)))). [resolve(5576,a,5539,a)]. 45.07/44.99 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),inverse_inverse(real)),A),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5576,a,5540,a)]. 45.07/44.99 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5576,a,5541,a)]. 45.07/44.99 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)). [resolve(5576,a,5542,a)]. 45.07/44.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5576,a,5543,a)]. 45.07/45.00 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5576,a,5544,a)]. 45.07/45.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),zero_zero(real)),A) = zero_zero(real). [resolve(5576,a,5545,a)]. 45.07/45.00 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5576,a,5546,a)]. 45.07/45.00 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5576,a,5547,a)]. 45.07/45.00 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),A),B)) | ti(real,C) != hAPP(real,real,A,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,D,f214(real,D,B,C,A))),hAPP(real,real,D,B)) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,f214(real,D,B,C,A))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),f214(real,D,B,C,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),C)). [resolve(5576,a,5548,a)]. 45.07/45.00 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),f215(real,A,B,C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)). [resolve(5576,a,5549,a)]. 45.07/45.00 Derived: ti(real,A) = hAPP(real,real,f215(real,B,C,A),C) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),B),C),A)). [resolve(5576,a,5550,a)]. 45.07/45.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,B)),hAPP(real,real,A,C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,f215(real,A,C,D),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),C),D)). [resolve(5576,a,5551,a)]. 45.07/45.00 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),sequentially)). [resolve(5576,a,5552,a)]. 45.07/45.02 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),power_power(real),A))). [resolve(5576,a,5553,a)]. 45.07/45.02 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),A)))). [resolve(5576,a,5554,a)]. 45.07/45.02 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f259(A,real,C,D,E,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5576,a,5555,a)]. 45.07/45.02 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(A,fun(real,real),hAPP(fun(real,fun(A,real)),fun(A,fun(real,real)),combc(real,A,real),C),f259(A,real,C,D,E,B))),D),hAPP(A,real,hAPP(real,fun(A,real),E,D),f259(A,real,C,D,E,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5576,a,5556,a)]. 45.07/45.02 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f263(real,B)))). [resolve(5576,a,5557,a)]. 45.07/45.02 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f263(real,A))). [resolve(5576,a,5558,a)]. 45.07/45.02 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5576,a,5559,a)]. 45.07/45.02 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5576,a,5560,a)]. 45.07/45.02 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(5576,a,5561,a)]. 45.17/45.03 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),hAPP(real,real,uminus_uminus(real),B))). [resolve(5576,a,5562,a)]. 45.17/45.03 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B))). [resolve(5576,a,5563,a)]. 45.17/45.03 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5576,a,5564,a)]. 45.17/45.03 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),D)). [resolve(5576,a,5565,a)]. 45.17/45.03 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),hAPP(real,real,A,B)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),D),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))). [resolve(5576,a,5566,a)]. 45.17/45.03 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),D))),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,uminus_uminus(real),E)))). [resolve(5576,a,5568,a)]. 45.17/45.03 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f370(real,B)))). [resolve(5576,a,5569,a)]. 45.17/45.03 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f370(real,A))). [resolve(5576,a,5570,a)]. 45.17/45.04 Derived: -banach(real) | hAPP(real,real,exp(real),A) != zero_zero(real). [resolve(5576,a,5572,a)]. 45.17/45.04 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B))),C)),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B)))))). [resolve(5576,a,5574,a)]. 45.17/45.04 Derived: -banach(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))) = hAPP(real,real,exp(real),A). [resolve(5576,a,5575,b)]. 45.17/45.04 5577 -real_normed_field(A) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) # label(fact_4601_DERIV__iff2) # label(axiom). [clausify(2228)]. 45.17/45.04 Derived: -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)). [resolve(5577,a,5526,a)]. 45.17/45.04 Derived: -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)). [resolve(5577,a,5576,a)]. 45.33/45.20 5578 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) # label(fact_4601_DERIV__iff2) # label(axiom). [clausify(2228)]. 45.33/45.20 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)). [resolve(5578,a,5526,a)]. 45.33/45.20 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)). [resolve(5578,a,5576,a)]. 45.33/45.20 5579 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_3996_powser__insidea) # label(axiom). [clausify(2453)]. 45.35/45.22 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5579,b,5526,a)]. 45.35/45.22 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5579,b,5576,a)]. 45.35/45.22 5580 -real_normed_vector(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | ti(B,f443(A,B,D,E,C)) != zero_zero(B) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2495)]. 45.35/45.22 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | ti(complex,f443(A,complex,C,D,B)) != zero_zero(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5580,b,5526,a)]. 45.35/45.22 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | ti(real,f443(A,real,C,D,B)) != zero_zero(real) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5580,b,5576,a)]. 45.37/45.24 5581 -real_normed_vector(A) | -real_normed_field(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(B,real,norm_norm(B),f443(A,B,D,E,C))),C)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2495)]. 45.37/45.24 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f443(A,complex,C,D,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5581,b,5526,a)]. 45.37/45.24 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f443(A,real,C,D,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5581,b,5576,a)]. 45.37/45.24 5582 -real_normed_vector(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(B,A,D,f443(A,B,D,E,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(B,real,norm_norm(B),f443(A,B,D,E,C))))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2495)]. 45.37/45.24 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(complex,A,C,f443(A,complex,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(complex,real,norm_norm(complex),f443(A,complex,C,D,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5582,b,5526,a)]. 45.37/45.24 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,C,f443(A,real,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(real,real,norm_norm(real),f443(A,real,C,D,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5582,b,5576,a)]. 45.37/45.24 5583 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C))))) # label(fact_3817_DERIV__mult) # label(axiom). [clausify(2519)]. 45.37/45.25 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B))))). [resolve(5583,a,5526,a)]. 45.37/45.25 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B))))). [resolve(5583,a,5576,a)]. 45.37/45.25 5584 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | ti(A,V6) = zero_zero(A) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),V6)),E)) # label(fact_4452_tendsto__divide) # label(axiom). [clausify(2557)]. 45.37/45.25 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | ti(complex,F) = zero_zero(complex) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),F)),D)). [resolve(5584,a,5526,a)]. 45.37/45.25 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | ti(real,F) = zero_zero(real) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),F)),D)). [resolve(5584,a,5576,a)]. 45.37/45.32 5585 -real_normed_field(A) | ti(A,B) = zero_zero(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),C)),hAPP(A,real,norm_norm(A),B)) # label(fact_1790_nonzero__norm__divide) # label(axiom). [clausify(2558)]. 45.37/45.32 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),B)),hAPP(complex,real,norm_norm(complex),A)). [resolve(5585,a,5526,a)]. 45.37/45.32 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),B)),hAPP(real,real,norm_norm(real),A)). [resolve(5585,a,5576,a)]. 45.37/45.32 5586 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),combk(A,A),B)),C),zero_zero(A))) # label(fact_3840_DERIV__const) # label(axiom). [clausify(2648)]. 45.37/45.32 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),B),zero_zero(complex))). [resolve(5586,a,5526,a)]. 45.37/45.32 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),combk(real,real),A)),B),zero_zero(real))). [resolve(5586,a,5576,a)]. 45.37/45.32 5587 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,C)),hAPP(A,A,E,C))))) # label(fact_3811_DERIV__divide) # label(axiom). [clausify(2690)]. 45.37/45.32 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,B)),hAPP(complex,complex,D,B))))). [resolve(5587,a,5526,a)]. 45.56/45.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,B)),hAPP(real,real,D,B))))). [resolve(5587,a,5576,a)]. 45.56/45.48 5588 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) | ti(A,D) = ti(A,E) # label(fact_2633_DERIV__unique) # label(axiom). [clausify(2739)]. 45.56/45.48 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)) | ti(complex,C) = ti(complex,D). [resolve(5588,a,5526,a)]. 45.56/45.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)) | ti(real,C) = ti(real,D). [resolve(5588,a,5576,a)]. 45.56/45.48 5589 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4102_divide_OCauchy) # label(axiom). [clausify(2799)]. 45.56/45.48 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5589,a,5526,a)]. 45.56/45.48 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5589,a,5576,a)]. 45.56/45.48 5590 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),zero_zero(A)),sequentially)) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom). [clausify(2820)]. 45.56/45.48 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),zero_zero(complex)),sequentially)). [resolve(5590,a,5526,a)]. 45.78/45.67 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),zero_zero(real)),sequentially)). [resolve(5590,a,5576,a)]. 45.78/45.67 5591 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1664_divide_Odiff) # label(axiom). [clausify(2838)]. 45.78/45.67 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5591,a,5526,a)]. 45.78/45.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5591,a,5576,a)]. 45.78/45.67 5592 -banach(A) | -real_normed_field(A) | one_one(A) = hAPP(A,A,exp(A),zero_zero(A)) # label(fact_2583_exp__zero) # label(axiom). [clausify(2842)]. 45.78/45.67 Derived: -banach(complex) | one_one(complex) = hAPP(complex,complex,exp(complex),zero_zero(complex)). [resolve(5592,b,5526,a)]. 45.78/45.67 Derived: -banach(real) | one_one(real) = hAPP(real,real,exp(real),zero_zero(real)). [resolve(5592,b,5576,a)]. 45.78/45.67 5593 -real_normed_field(A) | -field_inverse_zero(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) # label(fact_1783_norm__divide) # label(axiom). [clausify(3009)]. 45.78/45.67 Derived: -field_inverse_zero(complex) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)). [resolve(5593,a,5526,a)]. 45.78/45.67 Derived: -field_inverse_zero(real) | hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)). [resolve(5593,a,5576,a)]. 45.78/45.67 5594 -banach(A) | -real_normed_field(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2589_exp__diff) # label(axiom). [clausify(3080)]. 45.78/45.67 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)). [resolve(5594,b,5526,a)]. 45.78/45.67 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)). [resolve(5594,b,5576,a)]. 45.78/45.67 5595 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),B)),C),hAPP(A,A,uminus_uminus(A),D))) # label(fact_3856_DERIV__minus) # label(axiom). [clausify(3122)]. 45.95/45.86 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),C))). [resolve(5595,a,5526,a)]. 45.95/45.86 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),A)),B),hAPP(real,real,uminus_uminus(real),C))). [resolve(5595,a,5576,a)]. 45.95/45.86 5596 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),times_times(A),B)),C),B)) # label(fact_2636_DERIV__cmult__Id) # label(axiom). [clausify(3140)]. 45.95/45.86 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B),A)). [resolve(5596,a,5526,a)]. 45.95/45.86 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),times_times(real),A)),B),A)). [resolve(5596,a,5576,a)]. 45.95/45.86 5597 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4009_summable__divide) # label(axiom). [clausify(3193)]. 45.95/45.86 5598 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),C)) # label(fact_4897_divide_OisCont) # label(axiom). [clausify(3299)]. 45.95/45.86 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),B)). [resolve(5598,a,5526,a)]. 45.95/45.86 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),B)). [resolve(5598,a,5576,a)]. 45.95/45.86 5599 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(A,A,exp(A),B))) # label(fact_4752_exp__converges) # label(axiom). [clausify(3404)]. 45.95/45.86 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(complex,complex,exp(complex),A))). [resolve(5599,a,5526,a)]. 46.09/45.99 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(real,real,exp(real),A))). [resolve(5599,a,5576,a)]. 46.09/45.99 5600 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_4002_summable__minus) # label(axiom). [clausify(3517)]. 46.09/45.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A))). [resolve(5600,a,5526,a)]. 46.09/45.99 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))). [resolve(5600,a,5576,a)]. 46.09/45.99 5601 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3985_divide_Osuminf) # label(axiom). [clausify(3521)]. 46.09/45.99 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5601,a,5526,a)]. 46.09/45.99 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5601,a,5576,a)]. 46.09/45.99 5602 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),hAPP(A,fun(A,A),times_times(A),E)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_3863_DERIV__cmult) # label(axiom). [clausify(3575)]. 46.09/45.99 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),D)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),C))). [resolve(5602,a,5526,a)]. 46.18/46.06 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),D)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C))). [resolve(5602,a,5576,a)]. 46.18/46.06 5603 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4750_lemma__exp__ext) # label(axiom). [clausify(3588)]. 46.18/46.06 5604 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4085_divide_Osums) # label(axiom). [clausify(3599)]. 46.18/46.06 5605 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3986_suminf__minus) # label(axiom). [clausify(3647)]. 46.18/46.06 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5605,a,5526,a)]. 46.18/46.06 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)) = hAPP(real,real,uminus_uminus(real),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5605,a,5576,a)]. 46.18/46.06 5606 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_4088_sums__diff) # label(axiom). [clausify(3679)]. 46.18/46.06 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))). [resolve(5606,a,5526,a)]. 46.25/46.12 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))). [resolve(5606,a,5576,a)]. 46.25/46.12 5607 -banach(A) | -real_normed_field(A) | exp(A) = ti(fun(A,A),exp(A)) # label(tsy_c_Transcendental_Oexp_res) # label(axiom). [clausify(3726)]. 46.25/46.12 Derived: -banach(complex) | exp(complex) = ti(fun(complex,complex),exp(complex)). [resolve(5607,b,5526,a)]. 46.25/46.12 Derived: -banach(real) | exp(real) = ti(fun(real,real),exp(real)). [resolve(5607,b,5576,a)]. 46.25/46.12 5608 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),B),C)) # label(fact_4886_DERIV__isCont) # label(axiom). [clausify(3748)]. 46.25/46.12 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),A),B)). [resolve(5608,a,5526,a)]. 46.25/46.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),A),B)). [resolve(5608,a,5576,a)]. 46.25/46.13 5609 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | ti(A,f660(B,A,E,D,C)) != zero_zero(A) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(3767)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | ti(complex,f660(A,complex,D,C,B)) != zero_zero(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5609,a,5526,a)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | ti(real,f660(A,real,D,C,B)) != zero_zero(real) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5609,a,5576,a)]. 46.25/46.13 5610 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f660(B,A,E,D,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(3767)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f660(A,complex,D,C,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5610,a,5526,a)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f660(A,real,D,C,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5610,a,5576,a)]. 46.25/46.13 5611 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(nat,B,hAPP(A,fun(nat,B),E,f660(B,A,E,D,C)),f661(B,A,E,D,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,D,f661(B,A,E,D,C))),hAPP(A,real,norm_norm(A),f660(B,A,E,D,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(3767)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(complex,fun(nat,A),D,f660(A,complex,D,C,B)),f661(A,complex,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f661(A,complex,D,C,B))),hAPP(complex,real,norm_norm(complex),f660(A,complex,D,C,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5611,a,5526,a)]. 46.25/46.13 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(real,fun(nat,A),D,f660(A,real,D,C,B)),f661(A,real,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f661(A,real,D,C,B))),hAPP(real,real,norm_norm(real),f660(A,real,D,C,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5611,a,5576,a)]. 46.39/46.27 5612 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3984_suminf__divide) # label(axiom). [clausify(3866)]. 46.39/46.27 5613 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D)))) # label(fact_4024_powser__inside) # label(axiom). [clausify(3919)]. 46.39/46.27 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C)))). [resolve(5613,b,5526,a)]. 46.39/46.27 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C)))). [resolve(5613,b,5576,a)]. 46.39/46.27 5614 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),power_power(A)))),D),hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_4124_termdiffs) # label(axiom). [clausify(3947)]. 46.39/46.27 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),power_power(complex)))),C),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5614,b,5526,a)]. 46.39/46.32 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),power_power(real)))),C),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5614,b,5576,a)]. 46.39/46.32 5615 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(A,fun(nat,A))),fun(fun(A,A),fun(A,fun(nat,A))),combs(A,A,fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(A,fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(A,fun(nat,A)),A),combc(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),hAPP(A,fun(A,A),plus_plus(A),D))))),hAPP(A,fun(nat,A),power_power(A),D))))),combi(A))))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(A)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4532_termdiffs__aux) # label(axiom). [clausify(4015)]. 46.48/46.32 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(complex,fun(nat,complex))),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combs(complex,complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),complex),combc(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),hAPP(complex,fun(complex,complex),plus_plus(complex),C))))),hAPP(complex,fun(nat,complex),power_power(complex),C))))),combi(complex))))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5615,b,5526,a)]. 46.48/46.33 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(real,fun(nat,real))),fun(fun(real,real),fun(real,fun(nat,real))),combs(real,real,fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(real,fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(real,fun(nat,real)),real),combc(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(real,fun(real,real),plus_plus(real),C))))),hAPP(real,fun(nat,real),power_power(real),C))))),combi(real))))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(real)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5615,b,5576,a)]. 46.55/46.40 5616 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,exp(A),B)) # label(fact_2535_exp__minus) # label(axiom). [clausify(4073)]. 46.55/46.40 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,exp(complex),A)). [resolve(5616,a,5526,a)]. 46.55/46.40 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,exp(real),A)). [resolve(5616,a,5576,a)]. 46.55/46.40 5617 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3982_suminf__diff) # label(axiom). [clausify(4099)]. 46.55/46.40 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5617,a,5526,a)]. 46.55/46.40 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5617,a,5576,a)]. 46.55/46.40 5618 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_4707_divide_OscaleR) # label(axiom). [clausify(4120)]. 46.64/46.52 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5618,a,5526,a)]. 46.64/46.52 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5618,a,5576,a)]. 46.64/46.52 5619 -banach(A) | -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),exp(A)),B),hAPP(A,A,exp(A),B))) # label(fact_2632_DERIV__exp) # label(axiom). [clausify(4163)]. 46.64/46.52 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),exp(complex)),A),hAPP(complex,complex,exp(complex),A))). [resolve(5619,b,5526,a)]. 46.64/46.52 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),exp(real)),A),hAPP(real,real,exp(real),A))). [resolve(5619,b,5576,a)]. 46.64/46.52 5620 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C))) # label(fact_4011_summable__add) # label(axiom). [clausify(4258)]. 46.64/46.52 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B))). [resolve(5620,a,5526,a)]. 46.64/46.52 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B))). [resolve(5620,a,5576,a)]. 46.64/46.52 5621 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | ti(A,E) = zero_zero(A) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),E)),sequentially)) # label(fact_4451_LIMSEQ__divide) # label(axiom). [clausify(4266)]. 46.64/46.52 5622 -real_normed_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4184_divide_Osetsum) # label(axiom). [clausify(4267)]. 46.71/46.55 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C). [resolve(5622,a,5526,a)]. 46.71/46.55 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5622,a,5576,a)]. 46.71/46.55 5623 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),combi(A)),B),one_one(A))) # label(fact_3839_DERIV__ident) # label(axiom). [clausify(4269)]. 46.71/46.55 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),combi(complex)),A),one_one(complex))). [resolve(5623,a,5526,a)]. 46.71/46.55 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),combi(real)),A),one_one(real))). [resolve(5623,a,5576,a)]. 46.71/46.55 5624 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))))) # label(fact_3818_DERIV__mult_H) # label(axiom). [clausify(4313)]. 46.71/46.55 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))))). [resolve(5624,a,5526,a)]. 46.71/46.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))))). [resolve(5624,a,5576,a)]. 46.93/46.77 5625 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,E,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3899_DERIV__quotient) # label(axiom). [clausify(4482)]. 46.93/46.77 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5625,a,5526,a)]. 46.93/46.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5625,a,5576,a)]. 46.93/46.77 5626 -real_normed_field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D))),hAPP(A,A,inverse_inverse(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))),D) # label(fact_2620_DERIV__inverse__lemma) # label(axiom). [clausify(4588)]. 46.93/46.82 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C))),hAPP(complex,complex,inverse_inverse(complex),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B))),C). [resolve(5626,a,5526,a)]. 46.93/46.82 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C))),hAPP(real,real,inverse_inverse(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))),C). [resolve(5626,a,5576,a)]. 46.93/46.82 5627 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4231_sums__group) # label(axiom). [clausify(4651)]. 46.93/46.82 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,complex),complex,suminf(complex),A))). [resolve(5627,a,5526,a)]. 47.01/46.91 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,real),real,suminf(real),A))). [resolve(5627,a,5576,a)]. 47.01/46.91 5628 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(real,A,of_real(A),B)) = hAPP(real,A,of_real(A),hAPP(real,real,exp(real),B)) # label(fact_2799_exp__of__real) # label(axiom). [clausify(4697)]. 47.01/46.91 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(real,complex,of_real(complex),A)) = hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),A)). [resolve(5628,a,5526,a)]. 47.01/46.91 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,of_real(real),A)) = hAPP(real,real,of_real(real),hAPP(real,real,exp(real),A)). [resolve(5628,a,5576,a)]. 47.01/46.91 5629 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_3823_DERIV__add) # label(axiom). [clausify(4764)]. 47.01/46.91 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))). [resolve(5629,a,5526,a)]. 47.01/46.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))). [resolve(5629,a,5576,a)]. 49.45/49.31 5630 -real_normed_field(A) | deriv(A) = ti(fun(fun(A,A),fun(A,fun(A,bool))),deriv(A)) # label(tsy_c_Deriv_Oderiv_res) # label(axiom). [clausify(4852)]. 49.45/49.31 Derived: deriv(complex) = ti(fun(fun(complex,complex),fun(complex,fun(complex,bool))),deriv(complex)). [resolve(5630,a,5526,a)]. 49.45/49.31 Derived: deriv(real) = ti(fun(fun(real,real),fun(real,fun(real,bool))),deriv(real)). [resolve(5630,a,5576,a)]. 49.45/49.31 5631 comm_semiring_1(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 49.45/49.31 5632 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(57)]. 49.45/49.31 5633 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(70)]. 49.45/49.31 5634 -no_zero_divisors(A) | -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) != zero_zero(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f43(B,A,D,C)),C)) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(158)]. 49.45/49.31 5635 -no_zero_divisors(A) | -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) != zero_zero(A) | hAPP(B,A,D,f43(B,A,D,C)) = zero_zero(A) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(158)]. 49.45/49.31 5636 -no_zero_divisors(A) | -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(B,A,D,E) != zero_zero(A) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(158)]. 49.45/49.31 5637 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(282)]. 49.45/49.31 5638 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),plus_plus(A),B)),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),D))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),one_one(nat)))),C)))) # label(fact_4324_arith__series__general) # label(axiom). [clausify(329)]. 49.45/49.31 5639 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(378)]. 49.45/49.31 5640 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))) # label(fact_282_dvd__0__right) # label(axiom). [clausify(395)]. 49.45/49.31 5641 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(615)]. 49.45/49.31 5642 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) # label(fact_255_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(651)]. 49.45/49.31 5643 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(699)]. 49.45/49.31 5644 -comm_semiring_1(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),zero_zero(nat)) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(772)]. 49.45/49.31 5645 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_334_dvd__mult2) # label(axiom). [clausify(966)]. 49.45/49.31 5646 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(1017)]. 49.45/49.31 5647 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) # label(fact_1311_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom). [clausify(1024)]. 49.45/49.31 5648 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),semiring_1_of_nat(A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),B))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),one_one(A))) # label(fact_4617_gauss__sum) # label(axiom). [clausify(1099)]. 49.45/49.31 5649 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(1160)]. 49.45/49.31 5650 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_332_dvd__triv__left) # label(axiom). [clausify(1169)]. 49.45/49.31 5651 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) # label(fact_1310_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom). [clausify(1251)]. 49.45/49.31 5652 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_343_dvd__power__same) # label(axiom). [clausify(1279)]. 49.45/49.32 5653 -comm_semiring_1(A) | one_one(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_462_dvd__power) # label(axiom). [clausify(1328)]. 49.45/49.32 5654 -comm_semiring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_462_dvd__power) # label(axiom). [clausify(1328)]. 49.45/49.32 5655 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_338_dvd__mult__left) # label(axiom). [clausify(1582)]. 49.45/49.32 5656 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_340_dvd__add) # label(axiom). [clausify(1654)]. 49.45/49.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5631,a,5632,a)]. 49.45/49.32 Derived: ti(code_code_numeral,A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),one_one(nat)). [resolve(5631,a,5633,a)]. 49.45/49.32 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) != zero_zero(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,code_code_numeral,C,B)),B)). [resolve(5631,a,5634,b)]. 49.45/49.32 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) != zero_zero(code_code_numeral) | hAPP(A,code_code_numeral,C,f43(A,code_code_numeral,C,B)) = zero_zero(code_code_numeral). [resolve(5631,a,5635,b)]. 49.45/49.32 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,code_code_numeral,C,D) != zero_zero(code_code_numeral). [resolve(5631,a,5636,b)]. 49.45/49.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)). [resolve(5631,a,5637,a)]. 49.45/49.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combb(code_code_numeral,code_code_numeral,nat),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A)),hAPP(code_code_numeral,fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),combc(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),semiring_1_of_nat(code_code_numeral))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5631,a,5638,a)]. 49.48/49.33 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),zero_zero(code_code_numeral))). [resolve(5631,a,5640,a)]. 49.48/49.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D))). [resolve(5631,a,5641,a)]. 49.48/49.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral))),B). [resolve(5631,a,5642,a)]. 49.48/49.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D)). [resolve(5631,a,5643,a)]. 49.48/49.33 Derived: one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),zero_zero(nat)). [resolve(5631,a,5644,a)]. 49.49/49.34 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(5631,a,5645,a)]. 49.49/49.34 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A). [resolve(5631,a,5646,a)]. 49.49/49.34 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)). [resolve(5631,a,5647,a)]. 49.49/49.34 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),semiring_1_of_nat(code_code_numeral)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),one_one(code_code_numeral))). [resolve(5631,a,5648,a)]. 49.49/49.34 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)). [resolve(5631,a,5649,a)]. 49.49/49.34 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(5631,a,5650,a)]. 49.49/49.34 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C))). [resolve(5631,a,5652,a)]. 49.49/49.34 Derived: one_one(code_code_numeral) != ti(code_code_numeral,A) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))). [resolve(5631,a,5653,a)]. 49.58/49.46 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A))). [resolve(5631,a,5654,a)]. 49.58/49.46 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(5631,a,5655,a)]. 49.58/49.46 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C))). [resolve(5631,a,5656,a)]. 49.58/49.46 5657 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(1689)]. 49.58/49.46 5658 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))) # label(fact_345_dvd__power__le) # label(axiom). [clausify(1799)]. 49.58/49.46 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),D))). [resolve(5658,a,5631,a)]. 49.58/49.46 5659 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(1911)]. 49.58/49.46 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)). [resolve(5659,a,5631,a)]. 49.58/49.46 5660 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),zero_zero(A)),B)) | ti(A,B) = zero_zero(A) # label(fact_329_dvd__0__left) # label(axiom). [clausify(1933)]. 49.58/49.46 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = zero_zero(code_code_numeral). [resolve(5660,a,5631,a)]. 49.58/49.46 5661 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),E)),D)) # label(fact_344_power__le__dvd) # label(axiom). [clausify(1967)]. 49.79/49.70 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),D)),C)). [resolve(5661,a,5631,a)]. 49.79/49.70 5662 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(2287)]. 49.79/49.70 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5662,a,5631,a)]. 49.79/49.70 5663 comm_semiring_1(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 49.79/49.70 Derived: ti(complex,A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),one_one(nat)). [resolve(5663,a,5633,a)]. 49.79/49.70 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) != zero_zero(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,complex,C,B)),B)). [resolve(5663,a,5634,b)]. 49.79/49.70 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) != zero_zero(complex) | hAPP(A,complex,C,f43(A,complex,C,B)) = zero_zero(complex). [resolve(5663,a,5635,b)]. 49.79/49.70 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) = zero_zero(complex) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,complex,C,D) != zero_zero(complex). [resolve(5663,a,5636,b)]. 49.79/49.70 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)). [resolve(5663,a,5637,a)]. 49.79/49.70 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),plus_plus(complex),A)),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5663,a,5638,a)]. 49.79/49.71 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),zero_zero(complex))). [resolve(5663,a,5640,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D))). [resolve(5663,a,5641,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),B). [resolve(5663,a,5642,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)). [resolve(5663,a,5643,a)]. 49.79/49.71 Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),zero_zero(nat)). [resolve(5663,a,5644,a)]. 49.79/49.71 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(5663,a,5645,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(5663,a,5646,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)). [resolve(5663,a,5647,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),semiring_1_of_nat(complex)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),one_one(complex))). [resolve(5663,a,5648,a)]. 49.79/49.71 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)). [resolve(5663,a,5649,a)]. 49.88/49.74 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))). [resolve(5663,a,5650,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C))). [resolve(5663,a,5652,a)]. 49.88/49.74 Derived: one_one(complex) != ti(complex,A) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))). [resolve(5663,a,5653,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A))). [resolve(5663,a,5654,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(5663,a,5655,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C))). [resolve(5663,a,5656,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))). [resolve(5663,a,5658,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),zero_zero(complex)),A)) | ti(complex,A) = zero_zero(complex). [resolve(5663,a,5660,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),D)),C)). [resolve(5663,a,5661,a)]. 49.88/49.74 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B). [resolve(5663,a,5662,a)]. 49.88/49.74 5664 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_312_dvd__trans) # label(axiom). [clausify(2369)]. 49.88/49.74 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)). [resolve(5664,a,5631,a)]. 49.88/49.74 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),C)). [resolve(5664,a,5663,a)]. 49.94/49.85 5665 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(2450)]. 49.94/49.85 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),D)). [resolve(5665,a,5631,a)]. 49.94/49.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),D)). [resolve(5665,a,5663,a)]. 49.94/49.85 5666 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(2480)]. 49.94/49.85 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5666,a,5631,a)]. 49.94/49.85 5667 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_335_dvd__mult) # label(axiom). [clausify(2549)]. 49.94/49.85 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(5667,a,5631,a)]. 49.94/49.85 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))). [resolve(5667,a,5663,a)]. 49.94/49.85 5668 comm_semiring_1(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 49.94/49.85 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),zero_zero(rat)) = zero_zero(rat). [resolve(5668,a,5632,a)]. 49.94/49.85 Derived: ti(rat,A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),one_one(nat)). [resolve(5668,a,5633,a)]. 49.94/49.85 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) != zero_zero(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,rat,C,B)),B)). [resolve(5668,a,5634,b)]. 49.94/49.85 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) != zero_zero(rat) | hAPP(A,rat,C,f43(A,rat,C,B)) = zero_zero(rat). [resolve(5668,a,5635,b)]. 50.02/49.86 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) = zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,rat,C,D) != zero_zero(rat). [resolve(5668,a,5636,b)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)). [resolve(5668,a,5637,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),hAPP(rat,fun(rat,rat),plus_plus(rat),A)),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),semiring_1_of_nat(rat))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5668,a,5638,a)]. 50.02/49.86 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),zero_zero(rat))). [resolve(5668,a,5640,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D))). [resolve(5668,a,5641,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),B). [resolve(5668,a,5642,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)). [resolve(5668,a,5643,a)]. 50.02/49.86 Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),zero_zero(nat)). [resolve(5668,a,5644,a)]. 50.02/49.86 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(5668,a,5645,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(5668,a,5646,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)). [resolve(5668,a,5647,a)]. 50.02/49.86 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),semiring_1_of_nat(rat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),one_one(rat))). [resolve(5668,a,5648,a)]. 50.02/49.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)). [resolve(5668,a,5649,a)]. 50.02/49.88 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(5668,a,5650,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))). [resolve(5668,a,5652,a)]. 50.02/49.88 Derived: one_one(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(5668,a,5653,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5668,a,5654,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(5668,a,5655,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(5668,a,5656,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),D))). [resolve(5668,a,5658,a)]. 50.02/49.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)). [resolve(5668,a,5659,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),zero_zero(rat)),A)) | ti(rat,A) = zero_zero(rat). [resolve(5668,a,5660,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),D)),C)). [resolve(5668,a,5661,a)]. 50.02/49.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),B). [resolve(5668,a,5662,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),C)). [resolve(5668,a,5664,a)]. 50.02/49.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),D)). [resolve(5668,a,5665,a)]. 50.02/49.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(5668,a,5666,a)]. 50.02/49.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(5668,a,5667,a)]. 50.34/50.20 5669 -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C))) # label(fact_3953_dvd__setprod) # label(axiom). [clausify(2624)]. 50.34/50.20 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,D,C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B))). [resolve(5669,a,5631,a)]. 50.34/50.20 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,D,C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B))). [resolve(5669,a,5663,a)]. 50.34/50.20 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B))). [resolve(5669,a,5668,a)]. 50.34/50.20 5670 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_339_dvd__mult__right) # label(axiom). [clausify(2735)]. 50.34/50.20 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(5670,a,5631,a)]. 50.34/50.20 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(5670,a,5663,a)]. 50.34/50.20 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(5670,a,5668,a)]. 50.34/50.20 5671 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(2892)]. 50.34/50.20 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5671,a,5631,a)]. 50.34/50.20 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),B). [resolve(5671,a,5668,a)]. 50.77/50.62 5672 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_333_dvd__triv__right) # label(axiom). [clausify(3062)]. 50.77/50.62 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A))). [resolve(5672,a,5631,a)]. 50.77/50.62 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A))). [resolve(5672,a,5663,a)]. 50.77/50.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(5672,a,5668,a)]. 50.77/50.62 5673 -comm_semiring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_346_le__imp__power__dvd) # label(axiom). [clausify(3108)]. 50.77/50.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),A)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),B))). [resolve(5673,a,5631,a)]. 50.77/50.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),A)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),B))). [resolve(5673,a,5663,a)]. 50.77/50.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),B))). [resolve(5673,a,5668,a)]. 50.77/50.62 5674 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(3184)]. 50.77/50.62 5675 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),one_one(A)),B)) # label(fact_342_one__dvd) # label(axiom). [clausify(3281)]. 50.77/50.62 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),one_one(code_code_numeral)),A)). [resolve(5675,a,5631,a)]. 50.77/50.62 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),one_one(complex)),A)). [resolve(5675,a,5663,a)]. 50.77/50.62 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),one_one(rat)),A)). [resolve(5675,a,5668,a)]. 50.77/50.62 5676 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_336_mult__dvd__mono) # label(axiom). [clausify(3436)]. 50.77/50.62 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(5676,a,5631,a)]. 50.91/50.75 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D))). [resolve(5676,a,5663,a)]. 50.91/50.75 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5676,a,5668,a)]. 50.91/50.75 5677 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(3500)]. 50.91/50.75 5678 -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,E) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = zero_zero(A) # label(fact_3950_setprod__zero) # label(axiom). [clausify(3522)]. 50.91/50.75 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,D) != zero_zero(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) = zero_zero(code_code_numeral). [resolve(5678,a,5631,a)]. 50.91/50.75 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,D) != zero_zero(complex) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) = zero_zero(complex). [resolve(5678,a,5663,a)]. 50.91/50.75 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,D) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) = zero_zero(rat). [resolve(5678,a,5668,a)]. 50.91/50.75 5679 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))) # label(fact_1457_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom). [clausify(3583)]. 50.91/50.75 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5679,a,5631,a)]. 51.07/50.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5679,a,5663,a)]. 51.07/50.92 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5679,a,5668,a)]. 51.07/50.92 5680 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(3713)]. 51.07/50.92 5681 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(3730)]. 51.07/50.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5681,a,5631,a)]. 51.07/50.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5681,a,5663,a)]. 51.07/50.92 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5681,a,5668,a)]. 51.07/50.92 5682 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) # label(fact_1309_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom). [clausify(3778)]. 51.07/50.92 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),A) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)). [resolve(5682,a,5631,a)]. 51.07/50.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)). [resolve(5682,a,5663,a)]. 51.07/50.92 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)). [resolve(5682,a,5668,a)]. 51.07/50.92 5683 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(3780)]. 51.13/50.99 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5683,a,5631,a)]. 51.13/50.99 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5683,a,5663,a)]. 51.13/50.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5683,a,5668,a)]. 51.13/50.99 5684 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(3797)]. 51.13/50.99 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(5684,a,5631,a)]. 51.13/50.99 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5684,a,5663,a)]. 51.13/50.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)). [resolve(5684,a,5668,a)]. 51.13/50.99 5685 -comm_semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f678(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4773_dvd__setsum) # label(axiom). [clausify(3849)]. 51.13/50.99 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(5685,a,5631,a)]. 51.13/50.99 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,complex,B,C,D)),D)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D))). [resolve(5685,a,5663,a)]. 51.13/50.99 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(5685,a,5668,a)]. 51.52/51.39 5686 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(C,A,D,f678(C,A,B,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),E))) # label(fact_4773_dvd__setsum) # label(axiom). [clausify(3849)]. 51.52/51.39 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(B,code_code_numeral,C,f678(B,code_code_numeral,A,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),C),D))). [resolve(5686,a,5631,a)]. 51.52/51.39 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(B,complex,C,f678(B,complex,A,C,D)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),C),D))). [resolve(5686,a,5663,a)]. 51.52/51.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(B,rat,C,f678(B,rat,A,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),C),D))). [resolve(5686,a,5668,a)]. 51.52/51.39 5687 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(3871)]. 51.52/51.39 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5687,a,5631,a)]. 51.52/51.39 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),B). [resolve(5687,a,5663,a)]. 51.52/51.39 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B). [resolve(5687,a,5668,a)]. 51.52/51.39 5688 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(4299)]. 51.52/51.39 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)). [resolve(5688,a,5631,a)]. 51.61/51.53 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5688,a,5663,a)]. 51.61/51.53 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(5688,a,5668,a)]. 51.61/51.53 5689 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) # label(fact_253_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(4348)]. 51.61/51.53 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),A). [resolve(5689,a,5631,a)]. 51.61/51.53 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),A). [resolve(5689,a,5663,a)]. 51.61/51.53 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),A). [resolve(5689,a,5668,a)]. 51.61/51.53 5690 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),one_one(A))),B) # label(fact_254_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(4352)]. 51.61/51.53 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),one_one(code_code_numeral))),A). [resolve(5690,a,5631,a)]. 51.61/51.53 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),one_one(complex))),A). [resolve(5690,a,5663,a)]. 51.61/51.53 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),one_one(rat))),A). [resolve(5690,a,5668,a)]. 51.61/51.53 5691 -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f759(B,A,E,F,D,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom). [clausify(4438)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,code_code_numeral,D,E,C,B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),E),B))). [resolve(5691,a,5631,a)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,complex,D,E,C,B)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),E),B))). [resolve(5691,a,5663,a)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,rat,D,E,C,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),E),B))). [resolve(5691,a,5668,a)]. 51.61/51.53 5692 -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,E,f759(B,A,E,F,D,C))),hAPP(B,A,F,f759(B,A,E,F,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom). [clausify(4438)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(A,code_code_numeral,D,f759(A,code_code_numeral,D,E,C,B))),hAPP(A,code_code_numeral,E,f759(A,code_code_numeral,D,E,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),E),B))). [resolve(5692,a,5631,a)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,D,f759(A,complex,D,E,C,B))),hAPP(A,complex,E,f759(A,complex,D,E,C,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),C)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),E),B))). [resolve(5692,a,5663,a)]. 51.61/51.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,f759(A,rat,D,E,C,B))),hAPP(A,rat,E,f759(A,rat,D,E,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),E),B))). [resolve(5692,a,5668,a)]. 51.87/51.72 5693 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(4469)]. 51.87/51.72 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),zero_zero(code_code_numeral)). [resolve(5693,a,5631,a)]. 51.87/51.72 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),zero_zero(complex)). [resolve(5693,a,5663,a)]. 51.87/51.72 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),zero_zero(rat)). [resolve(5693,a,5668,a)]. 51.87/51.72 5694 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(4535)]. 51.87/51.72 5695 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 51.87/51.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(5695,a,5632,a)]. 51.87/51.72 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)). [resolve(5695,a,5633,a)]. 51.87/51.72 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) != zero_zero(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,nat,C,B)),B)). [resolve(5695,a,5634,b)]. 51.87/51.72 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) != zero_zero(nat) | hAPP(A,nat,C,f43(A,nat,C,B)) = zero_zero(nat). [resolve(5695,a,5635,b)]. 51.87/51.72 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = zero_zero(nat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,nat,C,D) != zero_zero(nat). [resolve(5695,a,5636,b)]. 51.87/51.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5695,a,5637,a)]. 51.87/51.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),A)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),semiring_1_of_nat(nat))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5695,a,5638,a)]. 51.89/51.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),zero_zero(nat))). [resolve(5695,a,5640,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D))). [resolve(5695,a,5641,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B). [resolve(5695,a,5642,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)). [resolve(5695,a,5643,a)]. 51.89/51.73 Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),zero_zero(nat)). [resolve(5695,a,5644,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(5695,a,5645,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(5695,a,5646,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)). [resolve(5695,a,5647,a)]. 51.89/51.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),semiring_1_of_nat(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),one_one(nat))). [resolve(5695,a,5648,a)]. 51.89/51.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(5695,a,5650,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(5695,a,5652,a)]. 51.89/51.73 Derived: one_one(nat) != ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(5695,a,5653,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A))). [resolve(5695,a,5654,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(5695,a,5655,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(5695,a,5656,a)]. 51.89/51.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),D))). [resolve(5695,a,5658,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5695,a,5659,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A)) | ti(nat,A) = zero_zero(nat). [resolve(5695,a,5660,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),D)),C)). [resolve(5695,a,5661,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5695,a,5662,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)). [resolve(5695,a,5664,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),D)). [resolve(5695,a,5665,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5695,a,5666,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5695,a,5667,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B))). [resolve(5695,a,5669,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(5695,a,5670,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5695,a,5671,a)]. 51.89/51.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A))). [resolve(5695,a,5672,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(5695,a,5673,a)]. 51.89/51.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A)). [resolve(5695,a,5675,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(5695,a,5676,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,D) != zero_zero(nat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = zero_zero(nat). [resolve(5695,a,5678,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5695,a,5679,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5695,a,5681,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B)). [resolve(5695,a,5682,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5695,a,5683,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(5695,a,5684,a)]. 51.89/51.74 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(5695,a,5685,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(B,nat,C,f678(B,nat,A,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),C),D))). [resolve(5695,a,5686,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5695,a,5687,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5695,a,5688,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A). [resolve(5695,a,5689,a)]. 51.89/51.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),A). [resolve(5695,a,5690,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,nat,D,E,C,B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B))). [resolve(5695,a,5691,a)]. 51.89/51.74 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,D,f759(A,nat,D,E,C,B))),hAPP(A,nat,E,f759(A,nat,D,E,C,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B))). [resolve(5695,a,5692,a)]. 51.89/51.80 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)). [resolve(5695,a,5693,a)]. 51.89/51.80 5696 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(4648)]. 51.89/51.80 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A). [resolve(5696,a,5631,a)]. 51.89/51.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A). [resolve(5696,a,5663,a)]. 51.89/51.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A). [resolve(5696,a,5668,a)]. 51.89/51.80 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A). [resolve(5696,a,5695,a)]. 51.89/51.80 5697 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(4655)]. 51.89/51.80 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D)). [resolve(5697,a,5631,a)]. 51.89/51.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D)). [resolve(5697,a,5663,a)]. 51.89/51.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D)). [resolve(5697,a,5668,a)]. 51.89/51.80 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(5697,a,5695,a)]. 51.89/51.80 5698 comm_semiring_1(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 51.89/51.80 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5698,a,5632,a)]. 51.89/51.80 Derived: ti(quickcheck_code_int,A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),one_one(nat)). [resolve(5698,a,5633,a)]. 51.89/51.80 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,quickcheck_code_int,C,B)),B)). [resolve(5698,a,5634,b)]. 51.89/51.80 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) != zero_zero(quickcheck_code_int) | hAPP(A,quickcheck_code_int,C,f43(A,quickcheck_code_int,C,B)) = zero_zero(quickcheck_code_int). [resolve(5698,a,5635,b)]. 51.89/51.80 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,quickcheck_code_int,C,D) != zero_zero(quickcheck_code_int). [resolve(5698,a,5636,b)]. 51.89/51.80 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)). [resolve(5698,a,5637,a)]. 51.89/51.80 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combb(quickcheck_code_int,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),combc(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),semiring_1_of_nat(quickcheck_code_int))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5698,a,5638,a)]. 51.89/51.81 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),zero_zero(quickcheck_code_int))). [resolve(5698,a,5640,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D))). [resolve(5698,a,5641,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int))),B). [resolve(5698,a,5642,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D)). [resolve(5698,a,5643,a)]. 51.89/51.81 Derived: one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),zero_zero(nat)). [resolve(5698,a,5644,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(5698,a,5645,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A). [resolve(5698,a,5646,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)). [resolve(5698,a,5647,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),semiring_1_of_nat(quickcheck_code_int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),one_one(quickcheck_code_int))). [resolve(5698,a,5648,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)). [resolve(5698,a,5649,a)]. 51.89/51.81 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(5698,a,5650,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C))). [resolve(5698,a,5652,a)]. 51.89/51.81 Derived: one_one(quickcheck_code_int) != ti(quickcheck_code_int,A) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))). [resolve(5698,a,5653,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A))). [resolve(5698,a,5654,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(5698,a,5655,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C))). [resolve(5698,a,5656,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),D))). [resolve(5698,a,5658,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)). [resolve(5698,a,5659,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int). [resolve(5698,a,5660,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),D)),C)). [resolve(5698,a,5661,a)]. 51.89/51.81 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5698,a,5662,a)]. 51.89/51.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)). [resolve(5698,a,5664,a)]. 51.89/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),D)). [resolve(5698,a,5665,a)]. 51.89/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5698,a,5666,a)]. 51.89/51.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(5698,a,5667,a)]. 51.89/51.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B))). [resolve(5698,a,5669,a)]. 51.89/51.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(5698,a,5670,a)]. 51.89/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5698,a,5671,a)]. 51.89/51.82 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A))). [resolve(5698,a,5672,a)]. 51.89/51.82 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),A)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),B))). [resolve(5698,a,5673,a)]. 51.99/51.82 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),one_one(quickcheck_code_int)),A)). [resolve(5698,a,5675,a)]. 51.99/51.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(5698,a,5676,a)]. 51.99/51.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,D) != zero_zero(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) = zero_zero(quickcheck_code_int). [resolve(5698,a,5678,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5698,a,5679,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5698,a,5681,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),A) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B)). [resolve(5698,a,5682,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5698,a,5683,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(5698,a,5684,a)]. 51.99/51.82 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(5698,a,5685,a)]. 51.99/51.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(B,quickcheck_code_int,C,f678(B,quickcheck_code_int,A,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),C),D))). [resolve(5698,a,5686,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5698,a,5687,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)). [resolve(5698,a,5688,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),A). [resolve(5698,a,5689,a)]. 51.99/51.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),one_one(quickcheck_code_int))),A). [resolve(5698,a,5690,a)]. 51.99/51.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,quickcheck_code_int,D,E,C,B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),E),B))). [resolve(5698,a,5691,a)]. 51.99/51.85 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,f759(A,quickcheck_code_int,D,E,C,B))),hAPP(A,quickcheck_code_int,E,f759(A,quickcheck_code_int,D,E,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),E),B))). [resolve(5698,a,5692,a)]. 51.99/51.85 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),zero_zero(quickcheck_code_int)). [resolve(5698,a,5693,a)]. 51.99/51.85 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A). [resolve(5698,a,5696,a)]. 51.99/51.85 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D)). [resolve(5698,a,5697,a)]. 51.99/51.85 5699 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(4711)]. 51.99/51.85 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5699,a,5631,a)]. 52.07/51.91 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5699,a,5663,a)]. 52.07/51.91 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5699,a,5668,a)]. 52.07/51.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5699,a,5695,a)]. 52.07/51.91 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5699,a,5698,a)]. 52.07/51.91 5700 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(4726)]. 52.07/51.91 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(5700,a,5631,a)]. 52.07/51.91 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),A). [resolve(5700,a,5663,a)]. 52.07/51.91 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),A). [resolve(5700,a,5668,a)]. 52.07/51.91 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A). [resolve(5700,a,5695,a)]. 52.07/51.91 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(5700,a,5698,a)]. 52.07/51.91 5701 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),B)) # label(fact_311_dvd__refl) # label(axiom). [clausify(4745)]. 52.07/51.91 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),A)). [resolve(5701,a,5631,a)]. 52.07/51.91 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),A)). [resolve(5701,a,5663,a)]. 52.07/51.91 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),A)). [resolve(5701,a,5668,a)]. 52.07/51.91 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),A)). [resolve(5701,a,5695,a)]. 52.07/51.91 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),A)). [resolve(5701,a,5698,a)]. 52.07/51.91 5702 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 52.07/51.91 Derived: ti(real,A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),one_one(nat)). [resolve(5702,a,5633,a)]. 52.07/51.92 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) != zero_zero(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,real,C,B)),B)). [resolve(5702,a,5634,b)]. 52.07/51.92 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) != zero_zero(real) | hAPP(A,real,C,f43(A,real,C,B)) = zero_zero(real). [resolve(5702,a,5635,b)]. 52.07/51.92 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) = zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,real,C,D) != zero_zero(real). [resolve(5702,a,5636,b)]. 52.07/51.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(5702,a,5637,a)]. 52.07/51.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),A)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5702,a,5638,a)]. 52.07/51.92 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),zero_zero(real))). [resolve(5702,a,5640,a)]. 52.07/51.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D))). [resolve(5702,a,5641,a)]. 52.07/51.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B). [resolve(5702,a,5642,a)]. 52.07/51.92 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)). [resolve(5702,a,5643,a)]. 52.07/51.92 Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),zero_zero(nat)). [resolve(5702,a,5644,a)]. 52.07/51.92 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5702,a,5645,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(5702,a,5646,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)). [resolve(5702,a,5647,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),semiring_1_of_nat(real)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,semiring_1_of_nat(real),A)),one_one(real))). [resolve(5702,a,5648,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)). [resolve(5702,a,5649,a)]. 52.07/51.93 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(5702,a,5650,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))). [resolve(5702,a,5652,a)]. 52.07/51.93 Derived: one_one(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(5702,a,5653,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5702,a,5654,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(5702,a,5655,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(5702,a,5656,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))). [resolve(5702,a,5658,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),zero_zero(real)),A)) | ti(real,A) = zero_zero(real). [resolve(5702,a,5660,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),D)),C)). [resolve(5702,a,5661,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5702,a,5662,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),C)). [resolve(5702,a,5664,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),D)). [resolve(5702,a,5665,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5702,a,5667,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,D,C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B))). [resolve(5702,a,5669,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(5702,a,5670,a)]. 52.07/51.93 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(5702,a,5672,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(5702,a,5673,a)]. 52.07/51.93 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),one_one(real)),A)). [resolve(5702,a,5675,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5702,a,5676,a)]. 52.07/51.93 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,D) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) = zero_zero(real). [resolve(5702,a,5678,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5702,a,5679,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5702,a,5681,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)). [resolve(5702,a,5682,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5702,a,5683,a)]. 52.07/51.93 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5702,a,5684,a)]. 52.07/51.94 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(5702,a,5685,a)]. 52.07/51.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(B,real,C,f678(B,real,A,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),D))). [resolve(5702,a,5686,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B). [resolve(5702,a,5687,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(5702,a,5688,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),A). [resolve(5702,a,5689,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),one_one(real))),A). [resolve(5702,a,5690,a)]. 52.07/51.94 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,real,D,E,C,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),E),B))). [resolve(5702,a,5691,a)]. 52.07/51.94 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,D,f759(A,real,D,E,C,B))),hAPP(A,real,E,f759(A,real,D,E,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),E),B))). [resolve(5702,a,5692,a)]. 52.07/51.94 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)). [resolve(5702,a,5693,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A). [resolve(5702,a,5696,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)). [resolve(5702,a,5697,a)]. 52.07/51.94 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5702,a,5699,a)]. 52.07/51.94 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A). [resolve(5702,a,5700,a)]. 52.20/52.06 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),A)). [resolve(5702,a,5701,a)]. 52.20/52.06 5703 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)) = zero_zero(int). [resolve(5703,a,5632,a)]. 52.20/52.06 Derived: ti(int,A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)). [resolve(5703,a,5633,a)]. 52.20/52.06 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) != zero_zero(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f43(A,int,C,B)),B)). [resolve(5703,a,5634,b)]. 52.20/52.06 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) != zero_zero(int) | hAPP(A,int,C,f43(A,int,C,B)) = zero_zero(int). [resolve(5703,a,5635,b)]. 52.20/52.06 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,int,C,D) != zero_zero(int). [resolve(5703,a,5636,b)]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(5703,a,5637,a)]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),A)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),B))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),C))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),one_one(nat)))),B)))). [resolve(5703,a,5638,a)]. 52.20/52.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),zero_zero(int))). [resolve(5703,a,5640,a)]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D))). [resolve(5703,a,5641,a)]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B). [resolve(5703,a,5642,a)]. 52.20/52.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)). [resolve(5703,a,5643,a)]. 52.20/52.06 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),zero_zero(nat)). [resolve(5703,a,5644,a)]. 52.20/52.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(5703,a,5645,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(5703,a,5646,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)). [resolve(5703,a,5647,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),one_one(int))). [resolve(5703,a,5648,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)). [resolve(5703,a,5649,a)]. 52.20/52.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(5703,a,5650,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(5703,a,5652,a)]. 52.20/52.07 Derived: one_one(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(5703,a,5653,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5703,a,5654,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5703,a,5655,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(5703,a,5656,a)]. 52.20/52.07 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A). [resolve(5703,a,5657,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),D))). [resolve(5703,a,5658,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(5703,a,5659,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),zero_zero(int)),A)) | ti(int,A) = zero_zero(int). [resolve(5703,a,5660,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),D)),C)). [resolve(5703,a,5661,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5703,a,5662,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)). [resolve(5703,a,5664,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),D)). [resolve(5703,a,5665,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A) = zero_zero(int). [resolve(5703,a,5666,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(5703,a,5667,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B))). [resolve(5703,a,5669,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5703,a,5670,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5703,a,5671,a)]. 52.20/52.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(5703,a,5672,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(5703,a,5673,a)]. 52.20/52.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),one_one(int)),A)). [resolve(5703,a,5675,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5703,a,5676,a)]. 52.20/52.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,D) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = zero_zero(int). [resolve(5703,a,5678,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). [resolve(5703,a,5679,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5703,a,5681,a)]. 52.20/52.07 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)). [resolve(5703,a,5682,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(5703,a,5683,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(5703,a,5684,a)]. 52.20/52.08 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f678(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(5703,a,5685,a)]. 52.20/52.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(B,int,C,f678(B,int,A,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),C),D))). [resolve(5703,a,5686,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5703,a,5687,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(5703,a,5688,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A). [resolve(5703,a,5689,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A). [resolve(5703,a,5690,a)]. 52.20/52.08 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f759(A,int,D,E,C,B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B))). [resolve(5703,a,5691,a)]. 52.20/52.08 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,D,f759(A,int,D,E,C,B))),hAPP(A,int,E,f759(A,int,D,E,C,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B))). [resolve(5703,a,5692,a)]. 52.20/52.08 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)). [resolve(5703,a,5693,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A). [resolve(5703,a,5696,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(5703,a,5697,a)]. 52.20/52.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5703,a,5699,a)]. 54.56/54.38 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A). [resolve(5703,a,5700,a)]. 54.56/54.38 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),A)). [resolve(5703,a,5701,a)]. 54.56/54.38 5704 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(4918)]. 54.56/54.38 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),C) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5631,a)]. 54.56/54.38 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),C) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5663,a)]. 54.56/54.38 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),C) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5668,a)]. 54.56/54.38 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5695,a)]. 54.56/54.38 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),C) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5698,a)]. 54.56/54.38 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),C) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5702,a)]. 54.56/54.38 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5704,a,5703,a)]. 54.56/54.38 5705 ordered_ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 54.56/54.38 5706 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2059_neg__0__le__iff__le) # label(axiom). [clausify(61)]. 54.56/54.38 5707 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2059_neg__0__le__iff__le) # label(axiom). [clausify(61)]. 54.56/54.38 5708 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4803_min__diff__distrib__left) # label(axiom). [clausify(409)]. 54.56/54.38 5709 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_825_le__iff__diff__le__0) # label(axiom). [clausify(633)]. 54.56/54.38 5710 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_825_le__iff__diff__le__0) # label(axiom). [clausify(633)]. 54.56/54.38 5711 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f193(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(B,A,E,D) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(1087)]. 54.56/54.38 5712 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f193(B,A,E,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(B,A,D,E) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(1087)]. 54.56/54.38 5713 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2029_le__imp__neg__le) # label(axiom). [clausify(1201)]. 54.56/54.38 5714 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(nat,A),bool,monoseq(A),B)) | hBOOL(hAPP(fun(nat,A),bool,monoseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_3921_monoseq__minus) # label(axiom). [clausify(1366)]. 54.56/54.38 5715 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom). [clausify(1434)]. 54.56/54.38 5716 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom). [clausify(1434)]. 54.56/54.38 5717 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom). [clausify(1596)]. 54.56/54.38 5718 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom). [clausify(1596)]. 54.56/54.38 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5705,a,5706,a)]. 54.56/54.38 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5705,a,5707,a)]. 54.56/54.38 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(5705,a,5708,a)]. 54.56/54.38 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5705,a,5709,a)]. 54.72/54.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5705,a,5710,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f193(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,rat,D,C) = zero_zero(rat). [resolve(5705,a,5711,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f193(A,rat,D,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,rat,C,D) = zero_zero(rat). [resolve(5705,a,5712,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5705,a,5713,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),A)) | hBOOL(hAPP(fun(nat,rat),bool,monoseq(rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),A))). [resolve(5705,a,5714,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)). [resolve(5705,a,5715,a)]. 54.72/54.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)). [resolve(5705,a,5717,a)]. 54.72/54.59 5719 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom). [clausify(1706)]. 54.72/54.59 Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5719,a,5705,a)]. 54.72/54.59 5720 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_4958_max__diff__distrib__left) # label(axiom). [clausify(2137)]. 54.72/54.59 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(5720,a,5705,a)]. 54.72/54.59 5721 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom). [clausify(2330)]. 54.72/54.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5721,a,5705,a)]. 54.99/54.82 5722 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom). [clausify(2330)]. 54.99/54.82 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5722,a,5705,a)]. 54.99/54.82 5723 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom). [clausify(2477)]. 54.99/54.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5723,a,5705,a)]. 54.99/54.82 5724 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom). [clausify(2477)]. 54.99/54.82 5725 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 54.99/54.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5725,a,5706,a)]. 54.99/54.82 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5725,a,5707,a)]. 54.99/54.82 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(5725,a,5708,a)]. 54.99/54.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5725,a,5709,a)]. 54.99/54.82 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5725,a,5710,a)]. 54.99/54.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f193(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,real,D,C) = zero_zero(real). [resolve(5725,a,5711,a)]. 54.99/54.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f193(A,real,D,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,real,C,D) = zero_zero(real). [resolve(5725,a,5712,a)]. 54.99/54.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5725,a,5713,a)]. 54.99/54.82 Derived: -hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A)) | hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))). [resolve(5725,a,5714,a)]. 55.26/55.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(5725,a,5715,a)]. 55.26/55.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(5725,a,5717,a)]. 55.26/55.09 Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(5725,a,5719,a)]. 55.26/55.09 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(5725,a,5720,a)]. 55.26/55.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5725,a,5721,a)]. 55.26/55.09 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5725,a,5722,a)]. 55.26/55.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,uminus_uminus(real),A))). [resolve(5725,a,5723,a)]. 55.26/55.09 5726 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_798_diff__eq__diff__less) # label(axiom). [clausify(2764)]. 55.26/55.09 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5726,a,5705,a)]. 55.26/55.09 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5726,a,5725,a)]. 55.26/55.09 5727 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_798_diff__eq__diff__less) # label(axiom). [clausify(2764)]. 55.26/55.09 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5727,a,5705,a)]. 55.26/55.09 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5727,a,5725,a)]. 55.26/55.09 5728 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 55.26/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5728,a,5706,a)]. 55.26/55.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5728,a,5707,a)]. 55.26/55.10 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(5728,a,5708,a)]. 55.26/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5728,a,5709,a)]. 55.29/55.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5728,a,5710,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f193(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,int,D,C) = zero_zero(int). [resolve(5728,a,5711,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f193(A,int,D,C,B)))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,int,C,D) = zero_zero(int). [resolve(5728,a,5712,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5728,a,5713,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(fun(nat,int),bool,monoseq(int),A)) | hBOOL(hAPP(fun(nat,int),bool,monoseq(int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),uminus_uminus(int)),A))). [resolve(5728,a,5714,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(5728,a,5715,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(5728,a,5717,a)]. 55.29/55.10 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(5728,a,5719,a)]. 55.29/55.10 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(5728,a,5720,a)]. 55.29/55.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5728,a,5721,a)]. 55.29/55.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5728,a,5722,a)]. 55.48/55.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(5728,a,5723,a)]. 55.48/55.36 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5728,a,5726,a)]. 55.48/55.36 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5728,a,5727,a)]. 55.48/55.36 5729 -ordered_ab_group_add(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom). [clausify(3087)]. 55.48/55.36 Derived: ord_gr676655987ssThan(rat) = ti(fun(rat,fun(rat,fun(rat,bool))),ord_gr676655987ssThan(rat)). [resolve(5729,a,5705,a)]. 55.48/55.36 Derived: ord_gr676655987ssThan(real) = ti(fun(real,fun(real,fun(real,bool))),ord_gr676655987ssThan(real)). [resolve(5729,a,5725,a)]. 55.48/55.36 Derived: ord_gr676655987ssThan(int) = ti(fun(int,fun(int,fun(int,bool))),ord_gr676655987ssThan(int)). [resolve(5729,a,5728,a)]. 55.48/55.36 5730 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f610(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) != E | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,F,D)),E)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(3429)]. 55.48/55.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,rat,C,D,E,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,E,C)),D)). [resolve(5730,a,5705,a)]. 55.48/55.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,real,C,D,E,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,E,C)),D)). [resolve(5730,a,5725,a)]. 55.48/55.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f610(A,int,C,D,E,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) != D | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,E,C)),D)). [resolve(5730,a,5728,a)]. 55.48/55.36 5731 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,D,f610(B,A,E,F,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != F | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,D,E)),F)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(3429)]. 55.48/55.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,C,f610(A,rat,D,E,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,C,D)),E)). [resolve(5731,a,5705,a)]. 55.79/55.68 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,C,f610(A,real,D,E,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,C,D)),E)). [resolve(5731,a,5725,a)]. 55.79/55.68 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,C,f610(A,int,D,E,C,B)))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) != E | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,C,D)),E)). [resolve(5731,a,5728,a)]. 55.79/55.68 5732 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom). [clausify(3610)]. 55.79/55.68 Derived: hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,rat),fun(fun(rat,bool),fun(rat,bool)),image(rat,rat),uminus_uminus(rat)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5732,a,5705,a)]. 55.79/55.68 Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(5732,a,5725,a)]. 55.79/55.68 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(5732,a,5728,a)]. 55.79/55.68 5733 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2016_neg__less__iff__less) # label(axiom). [clausify(3907)]. 55.79/55.68 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5733,a,5705,a)]. 55.79/55.68 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5733,a,5725,a)]. 55.79/55.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(5733,a,5728,a)]. 55.79/55.68 5734 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2016_neg__less__iff__less) # label(axiom). [clausify(3907)]. 56.09/55.96 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5734,a,5705,a)]. 56.09/55.96 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5734,a,5725,a)]. 56.09/55.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(5734,a,5728,a)]. 56.09/55.96 5735 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2057_neg__le__0__iff__le) # label(axiom). [clausify(4161)]. 56.09/55.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5735,a,5705,a)]. 56.09/55.96 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5735,a,5725,a)]. 56.09/55.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5735,a,5728,a)]. 56.09/55.96 5736 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2057_neg__le__0__iff__le) # label(axiom). [clausify(4161)]. 56.09/55.96 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5736,a,5705,a)]. 56.09/55.96 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5736,a,5725,a)]. 56.09/55.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5736,a,5728,a)]. 56.09/55.96 5737 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2061_neg__0__less__iff__less) # label(axiom). [clausify(4346)]. 56.09/55.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5737,a,5705,a)]. 56.09/55.96 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5737,a,5725,a)]. 56.09/55.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5737,a,5728,a)]. 56.09/55.96 5738 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2061_neg__0__less__iff__less) # label(axiom). [clausify(4346)]. 56.09/55.96 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5738,a,5705,a)]. 56.32/56.17 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5738,a,5725,a)]. 56.32/56.17 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5738,a,5728,a)]. 56.32/56.17 5739 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2028_neg__le__iff__le) # label(axiom). [clausify(4541)]. 56.32/56.17 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5739,a,5705,a)]. 56.32/56.17 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5739,a,5725,a)]. 56.32/56.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5739,a,5728,a)]. 56.32/56.17 5740 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2028_neg__le__iff__le) # label(axiom). [clausify(4541)]. 56.32/56.17 5741 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_826_less__iff__diff__less__0) # label(axiom). [clausify(4601)]. 56.32/56.17 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5741,a,5705,a)]. 56.32/56.17 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5741,a,5725,a)]. 56.32/56.17 5742 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_826_less__iff__diff__less__0) # label(axiom). [clausify(4601)]. 56.32/56.17 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5742,a,5705,a)]. 56.32/56.17 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5742,a,5725,a)]. 56.32/56.17 5743 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom). [clausify(4615)]. 56.32/56.17 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)). [resolve(5743,a,5705,a)]. 56.32/56.17 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)). [resolve(5743,a,5725,a)]. 58.69/58.50 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(5743,a,5728,a)]. 58.69/58.50 5744 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom). [clausify(4615)]. 58.69/58.50 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)). [resolve(5744,a,5705,a)]. 58.69/58.50 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)). [resolve(5744,a,5725,a)]. 58.69/58.50 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(5744,a,5728,a)]. 58.69/58.50 5745 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom). [clausify(4684)]. 58.69/58.50 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5745,a,5705,a)]. 58.69/58.50 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,uminus_uminus(real),A))). [resolve(5745,a,5725,a)]. 58.69/58.50 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(5745,a,5728,a)]. 58.69/58.50 5746 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom). [clausify(4684)]. 58.69/58.50 5747 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom). [assumption]. 58.69/58.50 5748 -semiring_0(A) | -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),zero_zero(A)))) | -hBOOL(hAPP(A,bool,D,C)) | hBOOL(hAPP(A,bool,D,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),f19(A,D,B)))) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(67)]. 58.69/58.50 5749 -semiring_0(A) | -dvd(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f20(A,C,B)),zero_zero(A)))) | -hBOOL(hAPP(A,bool,C,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(67)]. 58.69/58.50 5750 -semiring_0(A) | -dvd(A) | hBOOL(hAPP(A,bool,B,f20(A,B,C))) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(67)]. 58.69/58.50 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),zero_zero(int)))) | -hBOOL(hAPP(int,bool,C,B)) | hBOOL(hAPP(int,bool,C,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),f19(int,C,A)))). [resolve(5747,a,5748,a)]. 58.71/58.57 Derived: -dvd(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f20(int,B,A)),zero_zero(int)))) | -hBOOL(hAPP(int,bool,B,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5747,a,5749,a)]. 58.71/58.57 Derived: -dvd(int) | hBOOL(hAPP(int,bool,A,f20(int,A,B))) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(5747,a,5750,a)]. 58.71/58.57 5751 semiring_0(rat) # label(arity_Rat_Orat___Rings_Osemiring__0) # label(axiom). [assumption]. 58.71/58.57 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),zero_zero(rat)))) | -hBOOL(hAPP(rat,bool,C,B)) | hBOOL(hAPP(rat,bool,C,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),f19(rat,C,A)))). [resolve(5751,a,5748,a)]. 58.71/58.57 Derived: -dvd(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f20(rat,B,A)),zero_zero(rat)))) | -hBOOL(hAPP(rat,bool,B,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(5751,a,5749,a)]. 58.71/58.57 Derived: -dvd(rat) | hBOOL(hAPP(rat,bool,A,f20(rat,A,B))) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(5751,a,5750,a)]. 58.71/58.57 5752 semiring_0(complex) # label(arity_Complex_Ocomplex___Rings_Osemiring__0) # label(axiom). [assumption]. 58.71/58.57 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),zero_zero(complex)))) | -hBOOL(hAPP(complex,bool,C,B)) | hBOOL(hAPP(complex,bool,C,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),f19(complex,C,A)))). [resolve(5752,a,5748,a)]. 58.71/58.57 Derived: -dvd(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f20(complex,B,A)),zero_zero(complex)))) | -hBOOL(hAPP(complex,bool,B,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))). [resolve(5752,a,5749,a)]. 58.71/58.57 Derived: -dvd(complex) | hBOOL(hAPP(complex,bool,A,f20(complex,A,B))) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(5752,a,5750,a)]. 58.71/58.57 5753 -power(A) | -semiring_0(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(nat,nat,suc,B)) = zero_zero(A) # label(fact_1300_power__0__Suc) # label(axiom). [clausify(952)]. 58.71/58.57 Derived: -power(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(nat,nat,suc,A)) = zero_zero(int). [resolve(5753,b,5747,a)]. 58.71/58.57 Derived: -power(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(nat,nat,suc,A)) = zero_zero(rat). [resolve(5753,b,5751,a)]. 58.71/58.57 Derived: -power(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(nat,nat,suc,A)) = zero_zero(complex). [resolve(5753,b,5752,a)]. 58.71/58.57 5754 semiring_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Osemiring__0) # label(axiom). [assumption]. 58.71/58.57 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),zero_zero(quickcheck_code_int)))) | -hBOOL(hAPP(quickcheck_code_int,bool,C,B)) | hBOOL(hAPP(quickcheck_code_int,bool,C,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),f19(quickcheck_code_int,C,A)))). [resolve(5754,a,5748,a)]. 58.71/58.57 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),f20(quickcheck_code_int,B,A)),zero_zero(quickcheck_code_int)))) | -hBOOL(hAPP(quickcheck_code_int,bool,B,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))). [resolve(5754,a,5749,a)]. 59.19/59.05 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,A,f20(quickcheck_code_int,A,B))) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))). [resolve(5754,a,5750,a)]. 59.19/59.05 Derived: -power(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,nat,suc,A)) = zero_zero(quickcheck_code_int). [resolve(5754,a,5753,b)]. 59.19/59.05 5755 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom). [assumption]. 59.19/59.05 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),zero_zero(nat)))) | -hBOOL(hAPP(nat,bool,C,B)) | hBOOL(hAPP(nat,bool,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),f19(nat,C,A)))). [resolve(5755,a,5748,a)]. 59.19/59.05 Derived: -dvd(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f20(nat,B,A)),zero_zero(nat)))) | -hBOOL(hAPP(nat,bool,B,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))). [resolve(5755,a,5749,a)]. 59.19/59.05 Derived: -dvd(nat) | hBOOL(hAPP(nat,bool,A,f20(nat,A,B))) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(5755,a,5750,a)]. 59.19/59.05 Derived: -power(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(nat,nat,suc,A)) = zero_zero(nat). [resolve(5755,a,5753,b)]. 59.19/59.05 5756 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) # label(fact_262_power__0__left__number__of) # label(axiom). [clausify(2497)]. 59.19/59.05 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5756,b,5747,a)]. 59.19/59.05 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5756,b,5751,a)]. 59.19/59.05 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5756,b,5752,a)]. 59.19/59.05 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5756,b,5754,a)]. 59.19/59.05 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5756,b,5755,a)]. 59.19/59.05 5757 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_262_power__0__left__number__of) # label(axiom). [clausify(2497)]. 59.19/59.05 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(5757,b,5747,a)]. 60.11/59.96 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(5757,b,5751,a)]. 60.11/59.96 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(5757,b,5752,a)]. 60.11/59.96 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(quickcheck_code_int). [resolve(5757,b,5754,a)]. 60.11/59.96 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(nat). [resolve(5757,b,5755,a)]. 60.11/59.96 5758 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4210_setsum__left__distrib) # label(axiom). [clausify(3812)]. 60.11/59.96 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),C). [resolve(5758,a,5747,a)]. 60.11/59.96 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),C). [resolve(5758,a,5751,a)]. 60.11/59.96 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),C). [resolve(5758,a,5754,a)]. 60.11/59.96 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),C). [resolve(5758,a,5755,a)]. 60.55/60.42 5759 semiring_0(real) # label(arity_RealDef_Oreal___Rings_Osemiring__0) # label(axiom). [assumption]. 60.55/60.42 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),zero_zero(real)))) | -hBOOL(hAPP(real,bool,C,B)) | hBOOL(hAPP(real,bool,C,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),f19(real,C,A)))). [resolve(5759,a,5748,a)]. 60.55/60.42 Derived: -dvd(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f20(real,B,A)),zero_zero(real)))) | -hBOOL(hAPP(real,bool,B,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5759,a,5749,a)]. 60.55/60.42 Derived: -dvd(real) | hBOOL(hAPP(real,bool,A,f20(real,A,B))) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5759,a,5750,a)]. 60.55/60.42 Derived: -power(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(nat,nat,suc,A)) = zero_zero(real). [resolve(5759,a,5753,b)]. 60.55/60.42 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5759,a,5756,b)]. 60.55/60.42 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(5759,a,5757,b)]. 60.55/60.42 5760 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4211_setsum__right__distrib) # label(axiom). [clausify(4344)]. 60.55/60.42 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),hAPP(int,fun(int,int),times_times(int),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(5760,a,5747,a)]. 60.55/60.42 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),hAPP(rat,fun(rat,rat),times_times(rat),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(5760,a,5751,a)]. 60.55/60.42 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combb(quickcheck_code_int,quickcheck_code_int,A),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D)). [resolve(5760,a,5754,a)]. 60.55/60.42 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),hAPP(nat,fun(nat,nat),times_times(nat),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)). [resolve(5760,a,5755,a)]. 60.75/60.61 5761 -semiring_0(A) | -power(A) | zero_zero(nat) = B | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) = zero_zero(A) # label(fact_446_power__0__left) # label(axiom). [clausify(4531)]. 60.75/60.61 Derived: -power(int) | zero_zero(nat) = A | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A) = zero_zero(int). [resolve(5761,a,5747,a)]. 60.75/60.61 Derived: -power(rat) | zero_zero(nat) = A | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(5761,a,5751,a)]. 60.75/60.61 Derived: -power(complex) | zero_zero(nat) = A | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5761,a,5752,a)]. 60.75/60.61 Derived: -power(quickcheck_code_int) | zero_zero(nat) = A | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5761,a,5754,a)]. 60.75/60.61 Derived: -power(nat) | zero_zero(nat) = A | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5761,a,5755,a)]. 60.75/60.61 Derived: -power(real) | zero_zero(nat) = A | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A) = zero_zero(real). [resolve(5761,a,5759,a)]. 60.75/60.61 5762 -semiring_0(A) | -power(A) | zero_zero(nat) != B | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) # label(fact_446_power__0__left) # label(axiom). [clausify(4531)]. 60.75/60.61 Derived: -power(int) | zero_zero(nat) != A | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A). [resolve(5762,a,5747,a)]. 60.75/60.61 Derived: -power(rat) | zero_zero(nat) != A | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A). [resolve(5762,a,5751,a)]. 60.75/60.61 Derived: -power(complex) | zero_zero(nat) != A | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A). [resolve(5762,a,5752,a)]. 60.75/60.61 Derived: -power(quickcheck_code_int) | zero_zero(nat) != A | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(5762,a,5754,a)]. 60.75/60.61 Derived: -power(nat) | zero_zero(nat) != A | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A). [resolve(5762,a,5755,a)]. 60.75/60.61 Derived: -power(real) | zero_zero(nat) != A | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A). [resolve(5762,a,5759,a)]. 60.75/60.61 5763 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,A),fun(B,fun(C,A)),hAPP(fun(B,fun(fun(C,A),fun(C,A))),fun(fun(C,A),fun(B,fun(C,A))),combc(B,fun(C,A),fun(C,A)),hAPP(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A))),hAPP(fun(fun(A,A),fun(fun(C,A),fun(C,A))),fun(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A)))),combb(fun(A,A),fun(fun(C,A),fun(C,A)),B),combb(A,A,C)),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D))),E))),F)),V6) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),V6)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F)) # label(fact_4209_setsum__product) # label(axiom). [clausify(4560)]. 60.75/60.61 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,int),fun(A,fun(B,int)),hAPP(fun(A,fun(fun(B,int),fun(B,int))),fun(fun(B,int),fun(A,fun(B,int))),combc(A,fun(B,int),fun(B,int)),hAPP(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int))),hAPP(fun(fun(int,int),fun(fun(B,int),fun(B,int))),fun(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int)))),combb(fun(int,int),fun(fun(B,int),fun(B,int)),A),combb(int,int,B)),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C))),D))),E)),F) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),F)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E)). [resolve(5763,a,5747,a)]. 60.75/60.62 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(B,bool),fun(A,rat),hAPP(fun(A,fun(fun(B,bool),rat)),fun(fun(B,bool),fun(A,rat)),combc(A,fun(B,bool),rat),hAPP(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat)),hAPP(fun(fun(B,rat),fun(fun(B,bool),rat)),fun(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat))),combb(fun(B,rat),fun(fun(B,bool),rat),A),big_co1399186613setsum(B,rat)),hAPP(fun(B,rat),fun(A,fun(B,rat)),hAPP(fun(A,fun(fun(B,rat),fun(B,rat))),fun(fun(B,rat),fun(A,fun(B,rat))),combc(A,fun(B,rat),fun(B,rat)),hAPP(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat))),hAPP(fun(fun(rat,rat),fun(fun(B,rat),fun(B,rat))),fun(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat)))),combb(fun(rat,rat),fun(fun(B,rat),fun(B,rat)),A),combb(rat,rat,B)),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),C))),D))),E)),F) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),F)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E)). [resolve(5763,a,5751,a)]. 60.75/60.62 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(B,bool),fun(A,complex),hAPP(fun(A,fun(fun(B,bool),complex)),fun(fun(B,bool),fun(A,complex)),combc(A,fun(B,bool),complex),hAPP(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex)),hAPP(fun(fun(B,complex),fun(fun(B,bool),complex)),fun(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex))),combb(fun(B,complex),fun(fun(B,bool),complex),A),big_co1399186613setsum(B,complex)),hAPP(fun(B,complex),fun(A,fun(B,complex)),hAPP(fun(A,fun(fun(B,complex),fun(B,complex))),fun(fun(B,complex),fun(A,fun(B,complex))),combc(A,fun(B,complex),fun(B,complex)),hAPP(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex))),hAPP(fun(fun(complex,complex),fun(fun(B,complex),fun(B,complex))),fun(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex)))),combb(fun(complex,complex),fun(fun(B,complex),fun(B,complex)),A),combb(complex,complex,B)),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),C))),D))),E)),F) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),F)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E)). [resolve(5763,a,5752,a)]. 60.75/60.62 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(B,bool),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(B,bool),quickcheck_code_int)),fun(fun(B,bool),fun(A,quickcheck_code_int)),combc(A,fun(B,bool),quickcheck_code_int),hAPP(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int)),hAPP(fun(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int)),fun(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int))),combb(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),A),big_co1399186613setsum(B,quickcheck_code_int)),hAPP(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int)),hAPP(fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int))),combc(A,fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),hAPP(fun(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)))),combb(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),A),combb(quickcheck_code_int,quickcheck_code_int,B)),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),C))),D))),E)),F) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),F)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E)). [resolve(5763,a,5754,a)]. 60.75/60.62 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,nat),fun(A,fun(B,nat)),hAPP(fun(A,fun(fun(B,nat),fun(B,nat))),fun(fun(B,nat),fun(A,fun(B,nat))),combc(A,fun(B,nat),fun(B,nat)),hAPP(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat))),hAPP(fun(fun(nat,nat),fun(fun(B,nat),fun(B,nat))),fun(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat)))),combb(fun(nat,nat),fun(fun(B,nat),fun(B,nat)),A),combb(nat,nat,B)),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C))),D))),E)),F) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),F)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E)). [resolve(5763,a,5755,a)]. 60.75/60.62 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(B,bool),fun(A,real),hAPP(fun(A,fun(fun(B,bool),real)),fun(fun(B,bool),fun(A,real)),combc(A,fun(B,bool),real),hAPP(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real)),hAPP(fun(fun(B,real),fun(fun(B,bool),real)),fun(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real))),combb(fun(B,real),fun(fun(B,bool),real),A),big_co1399186613setsum(B,real)),hAPP(fun(B,real),fun(A,fun(B,real)),hAPP(fun(A,fun(fun(B,real),fun(B,real))),fun(fun(B,real),fun(A,fun(B,real))),combc(A,fun(B,real),fun(B,real)),hAPP(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real))),hAPP(fun(fun(real,real),fun(fun(B,real),fun(B,real))),fun(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real)))),combb(fun(real,real),fun(fun(B,real),fun(B,real)),A),combb(real,real,B)),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),C))),D))),E)),F) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),F)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E)). [resolve(5763,a,5759,a)]. 60.87/60.69 5764 semiring_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Osemiring__0) # label(axiom). [assumption]. 60.87/60.69 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),zero_zero(code_code_numeral)))) | -hBOOL(hAPP(code_code_numeral,bool,C,B)) | hBOOL(hAPP(code_code_numeral,bool,C,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),f19(code_code_numeral,C,A)))). [resolve(5764,a,5748,a)]. 60.87/60.69 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),f20(code_code_numeral,B,A)),zero_zero(code_code_numeral)))) | -hBOOL(hAPP(code_code_numeral,bool,B,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))). [resolve(5764,a,5749,a)]. 60.87/60.69 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,A,f20(code_code_numeral,A,B))) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))). [resolve(5764,a,5750,a)]. 60.87/60.69 Derived: -power(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,nat,suc,A)) = zero_zero(code_code_numeral). [resolve(5764,a,5753,b)]. 60.87/60.69 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5764,a,5756,b)]. 60.87/60.69 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(code_code_numeral). [resolve(5764,a,5757,b)]. 60.87/60.69 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),C). [resolve(5764,a,5758,a)]. 60.87/60.69 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combb(code_code_numeral,code_code_numeral,A),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D)). [resolve(5764,a,5760,a)]. 63.39/63.23 Derived: -power(code_code_numeral) | zero_zero(nat) = A | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5764,a,5761,a)]. 63.39/63.23 Derived: -power(code_code_numeral) | zero_zero(nat) != A | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(5764,a,5762,a)]. 63.39/63.23 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(B,bool),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(B,bool),code_code_numeral)),fun(fun(B,bool),fun(A,code_code_numeral)),combc(A,fun(B,bool),code_code_numeral),hAPP(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral)),hAPP(fun(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral)),fun(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral))),combb(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),A),big_co1399186613setsum(B,code_code_numeral)),hAPP(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral)),hAPP(fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral))),combc(A,fun(B,code_code_numeral),fun(B,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),hAPP(fun(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral)))),combb(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral)),A),combb(code_code_numeral,code_code_numeral,B)),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),C))),D))),E)),F) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),F)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E)). [resolve(5764,a,5763,a)]. 63.39/63.23 5765 divisi14063676e_zero(complex) # label(arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 63.39/63.23 5766 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),C) # label(fact_2518_power__inverse) # label(axiom). [clausify(72)]. 63.39/63.23 5767 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2536_inverse__minus__eq) # label(axiom). [clausify(1102)]. 63.39/63.23 Derived: hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),B). [resolve(5765,a,5766,a)]. 64.44/64.26 Derived: hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5765,a,5767,a)]. 64.44/64.26 5768 -divisi14063676e_zero(A) | ti(A,B) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2521_inverse__inverse__eq) # label(axiom). [clausify(1534)]. 64.44/64.26 Derived: ti(complex,A) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5768,a,5765,a)]. 64.44/64.26 5769 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | ti(A,B) = ti(A,C) # label(fact_2523_inverse__eq__imp__eq) # label(axiom). [clausify(2239)]. 64.44/64.26 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != hAPP(complex,complex,inverse_inverse(complex),B) | ti(complex,A) = ti(complex,B). [resolve(5769,a,5765,a)]. 64.44/64.26 5770 divisi14063676e_zero(real) # label(arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 64.44/64.26 Derived: hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),B). [resolve(5770,a,5766,a)]. 64.44/64.26 Derived: hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5770,a,5767,a)]. 64.44/64.26 Derived: ti(real,A) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5770,a,5768,a)]. 64.44/64.26 Derived: hAPP(real,real,inverse_inverse(real),A) != hAPP(real,real,inverse_inverse(real),B) | ti(real,A) = ti(real,B). [resolve(5770,a,5769,a)]. 64.44/64.26 5771 -divisi14063676e_zero(A) | -real_div_algebra(A) | hAPP(A,A,inverse_inverse(A),hAPP(real,A,of_real(A),B)) = hAPP(real,A,of_real(A),hAPP(real,real,inverse_inverse(real),B)) # label(fact_2798_of__real__inverse) # label(axiom). [clausify(2663)]. 64.44/64.26 Derived: -real_div_algebra(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,of_real(complex),A)) = hAPP(real,complex,of_real(complex),hAPP(real,real,inverse_inverse(real),A)). [resolve(5771,a,5765,a)]. 64.44/64.26 Derived: -real_div_algebra(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,of_real(real),A)) = hAPP(real,real,of_real(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5771,a,5770,a)]. 64.44/64.26 5772 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_2527_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(2863)]. 64.44/64.26 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != zero_zero(complex) | ti(complex,A) = zero_zero(complex). [resolve(5772,a,5765,a)]. 64.44/64.26 Derived: hAPP(real,real,inverse_inverse(real),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(5772,a,5770,a)]. 64.44/64.26 5773 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_2527_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(2863)]. 64.44/64.26 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = zero_zero(complex) | ti(complex,A) != zero_zero(complex). [resolve(5773,a,5765,a)]. 64.44/64.26 Derived: hAPP(real,real,inverse_inverse(real),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(5773,a,5770,a)]. 64.44/64.26 5774 divisi14063676e_zero(rat) # label(arity_Rat_Orat___Fields_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 64.44/64.26 Derived: hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,inverse_inverse(rat),A)),B). [resolve(5774,a,5766,a)]. 64.44/64.26 Derived: hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5774,a,5767,a)]. 64.44/64.26 Derived: ti(rat,A) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5774,a,5768,a)]. 64.69/64.55 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != hAPP(rat,rat,inverse_inverse(rat),B) | ti(rat,A) = ti(rat,B). [resolve(5774,a,5769,a)]. 64.69/64.55 Derived: -real_div_algebra(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(real,rat,of_real(rat),A)) = hAPP(real,rat,of_real(rat),hAPP(real,real,inverse_inverse(real),A)). [resolve(5774,a,5771,a)]. 64.69/64.55 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(5774,a,5772,a)]. 64.69/64.55 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(5774,a,5773,a)]. 64.69/64.55 5775 -divisi14063676e_zero(A) | -real_n1866405975lgebra(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) # label(fact_2510_norm__inverse) # label(axiom). [clausify(3529)]. 64.69/64.55 Derived: -real_n1866405975lgebra(complex) | hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)) = hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)). [resolve(5775,a,5765,a)]. 64.69/64.55 Derived: -real_n1866405975lgebra(real) | hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)). [resolve(5775,a,5770,a)]. 64.69/64.55 Derived: -real_n1866405975lgebra(rat) | hAPP(rat,real,norm_norm(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(real,real,inverse_inverse(real),hAPP(rat,real,norm_norm(rat),A)). [resolve(5775,a,5774,a)]. 64.69/64.55 5776 -real_div_algebra(A) | -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_4684_inverse__scaleR__distrib) # label(axiom). [clausify(3869)]. 64.69/64.55 Derived: -real_div_algebra(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5776,b,5765,a)]. 64.69/64.55 Derived: -real_div_algebra(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(5776,b,5770,a)]. 64.69/64.55 Derived: -real_div_algebra(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,hAPP(real,fun(rat,rat),scaleR_scaleR(rat),A),B)) = hAPP(rat,rat,hAPP(real,fun(rat,rat),scaleR_scaleR(rat),hAPP(real,real,inverse_inverse(real),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5776,b,5774,a)]. 64.69/64.55 5777 -divisi14063676e_zero(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) # label(fact_1694_divide__self__if) # label(axiom). [clausify(3945)]. 64.69/64.55 Derived: ti(complex,A) = zero_zero(complex) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A). [resolve(5777,a,5765,a)]. 64.69/64.55 Derived: ti(real,A) = zero_zero(real) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A). [resolve(5777,a,5770,a)]. 64.69/64.55 Derived: ti(rat,A) = zero_zero(rat) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A). [resolve(5777,a,5774,a)]. 64.69/64.55 5778 -divisi14063676e_zero(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) = zero_zero(A) # label(fact_1694_divide__self__if) # label(axiom). [clausify(3945)]. 64.69/64.55 Derived: ti(complex,A) != zero_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A) = zero_zero(complex). [resolve(5778,a,5765,a)]. 64.69/64.55 Derived: ti(real,A) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A) = zero_zero(real). [resolve(5778,a,5770,a)]. 64.69/64.55 Derived: ti(rat,A) != zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A) = zero_zero(rat). [resolve(5778,a,5774,a)]. 67.83/67.67 5779 -divisi14063676e_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),zero_zero(A)) = zero_zero(A) # label(fact_1657_divide__zero) # label(axiom). [clausify(4336)]. 67.83/67.67 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5779,a,5765,a)]. 67.83/67.67 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),zero_zero(real)) = zero_zero(real). [resolve(5779,a,5770,a)]. 67.83/67.67 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),zero_zero(rat)) = zero_zero(rat). [resolve(5779,a,5774,a)]. 67.83/67.67 5780 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | ti(A,B) = ti(A,C) # label(fact_2522_inverse__eq__iff__eq) # label(axiom). [clausify(4456)]. 67.83/67.67 5781 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,inverse_inverse(A),C) | ti(A,B) != ti(A,C) # label(fact_2522_inverse__eq__iff__eq) # label(axiom). [clausify(4456)]. 67.83/67.67 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,inverse_inverse(complex),B) | ti(complex,A) != ti(complex,B). [resolve(5781,a,5765,a)]. 67.83/67.67 Derived: hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,inverse_inverse(real),B) | ti(real,A) != ti(real,B). [resolve(5781,a,5770,a)]. 67.83/67.67 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,inverse_inverse(rat),B) | ti(rat,A) != ti(rat,B). [resolve(5781,a,5774,a)]. 67.83/67.67 5782 -divisi14063676e_zero(A) | hAPP(A,A,inverse_inverse(A),zero_zero(A)) = zero_zero(A) # label(fact_2526_inverse__zero) # label(axiom). [clausify(4900)]. 67.83/67.67 Derived: hAPP(complex,complex,inverse_inverse(complex),zero_zero(complex)) = zero_zero(complex). [resolve(5782,a,5765,a)]. 67.83/67.67 Derived: hAPP(real,real,inverse_inverse(real),zero_zero(real)) = zero_zero(real). [resolve(5782,a,5770,a)]. 67.83/67.67 Derived: hAPP(rat,rat,inverse_inverse(rat),zero_zero(rat)) = zero_zero(rat). [resolve(5782,a,5774,a)]. 67.83/67.67 5783 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom). [assumption]. 67.83/67.67 5784 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1679_divide__pos__pos) # label(axiom). [clausify(75)]. 67.83/67.67 5785 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))),C)) # label(fact_1731_gt__half__sum) # label(axiom). [clausify(229)]. 67.83/67.67 5786 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom). [clausify(291)]. 67.83/67.67 5787 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1711_pos__divide__less__eq) # label(axiom). [clausify(412)]. 67.83/67.67 5788 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1711_pos__divide__less__eq) # label(axiom). [clausify(412)]. 67.83/67.67 5789 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f87(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom). [clausify(425)]. 67.83/67.68 5790 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),f87(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom). [clausify(425)]. 67.83/67.68 5791 -linordered_field(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2559_nonzero__abs__inverse) # label(axiom). [clausify(628)]. 67.83/67.68 5792 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom). [clausify(702)]. 67.83/67.68 5793 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom). [clausify(1007)]. 67.83/67.68 5794 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom). [clausify(1045)]. 67.83/67.68 5795 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom). [clausify(1164)]. 67.83/67.68 5796 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom). [clausify(1231)]. 67.83/67.68 5797 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom). [clausify(1253)]. 67.83/67.68 5798 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom). [clausify(1253)]. 67.83/67.68 5799 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1712_mult__imp__div__pos__less) # label(axiom). [clausify(1437)]. 67.83/67.68 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(5783,a,5784,a)]. 67.83/67.68 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))),B)). [resolve(5783,a,5785,a)]. 67.83/67.71 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,inverse_inverse(real),A)),zero_zero(real))). [resolve(5783,a,5786,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)). [resolve(5783,a,5787,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)). [resolve(5783,a,5788,a)]. 67.83/67.71 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f87(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5783,a,5789,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),f87(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5783,a,5790,a)]. 67.83/67.71 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5783,a,5791,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5783,a,5792,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5783,a,5793,a)]. 67.83/67.71 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(5783,a,5794,a)]. 67.83/67.71 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(5783,a,5795,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5783,a,5796,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5783,a,5797,a)]. 67.83/67.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5783,a,5798,a)]. 67.83/67.71 5800 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2546_less__imp__inverse__less) # label(axiom). [clausify(1554)]. 68.24/68.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5800,a,5783,a)]. 68.24/68.08 5801 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom). [clausify(1610)]. 68.24/68.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5801,a,5783,a)]. 68.24/68.08 5802 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2610_one__le__inverse) # label(axiom). [clausify(1668)]. 68.24/68.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5802,a,5783,a)]. 68.24/68.08 5803 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom). [clausify(2249)]. 68.24/68.08 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),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))). [resolve(5803,a,5783,a)]. 68.24/68.08 5804 -linordered_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D)) # label(fact_3948_abs__setprod) # label(axiom). [clausify(2275)]. 68.24/68.08 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C) = hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C)). [resolve(5804,a,5783,a)]. 68.24/68.08 5805 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom). [clausify(2335)]. 68.24/68.08 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),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(5805,a,5783,a)]. 68.59/68.43 5806 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2576_one__less__inverse) # label(axiom). [clausify(2503)]. 68.59/68.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5806,a,5783,a)]. 68.59/68.43 5807 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1743_divide__left__mono) # label(axiom). [clausify(2542)]. 68.59/68.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5807,a,5783,a)]. 68.59/68.43 5808 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) # label(fact_1710_pos__less__divide__eq) # label(axiom). [clausify(2785)]. 68.59/68.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)). [resolve(5808,a,5783,a)]. 68.59/68.43 5809 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) # label(fact_1710_pos__less__divide__eq) # label(axiom). [clausify(2785)]. 68.59/68.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)). [resolve(5809,a,5783,a)]. 68.59/68.43 5810 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1705_frac__le) # label(axiom). [clausify(2841)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5810,a,5783,a)]. 68.72/68.57 5811 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2549_inverse__less__imp__less) # label(axiom). [clausify(2909)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5811,a,5783,a)]. 68.72/68.57 5812 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2570_le__imp__inverse__le) # label(axiom). [clausify(2982)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5812,a,5783,a)]. 68.72/68.57 5813 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2572_inverse__le__imp__le) # label(axiom). [clausify(3054)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5813,a,5783,a)]. 68.72/68.57 5814 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom). [clausify(3089)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5814,a,5783,a)]. 68.72/68.57 5815 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom). [clausify(3089)]. 68.72/68.57 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5815,a,5783,a)]. 68.91/68.82 5816 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1739_mult__imp__div__pos__le) # label(axiom). [clausify(3148)]. 68.91/68.82 5817 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2548_inverse__negative__imp__negative) # label(axiom). [clausify(3173)]. 68.91/68.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5817,a,5783,a)]. 68.91/68.82 5818 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1716_divide__strict__left__mono) # label(axiom). [clausify(3206)]. 68.91/68.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5818,a,5783,a)]. 68.91/68.82 5819 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom). [clausify(3226)]. 68.91/68.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5819,a,5783,a)]. 68.91/68.82 5820 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom). [clausify(3226)]. 68.91/68.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5820,a,5783,a)]. 68.91/68.82 5821 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1704_frac__less) # label(axiom). [clausify(3393)]. 69.21/69.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5821,a,5783,a)]. 69.21/69.09 5822 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1737_pos__le__divide__eq) # label(axiom). [clausify(3531)]. 69.21/69.09 5823 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1737_pos__le__divide__eq) # label(axiom). [clausify(3531)]. 69.21/69.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5823,a,5783,a)]. 69.21/69.09 5824 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom). [clausify(3602)]. 69.21/69.09 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,inverse_inverse(real),A))). [resolve(5824,a,5783,a)]. 69.21/69.09 5825 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1707_divide__nonpos__neg) # label(axiom). [clausify(3640)]. 69.21/69.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(5825,a,5783,a)]. 69.21/69.09 5826 -linordered_field(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),B)) # label(fact_1871_nonzero__abs__divide) # label(axiom). [clausify(3692)]. 69.21/69.09 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),A)). [resolve(5826,a,5783,a)]. 69.21/69.09 5827 linordered_field(rat) # label(arity_Rat_Orat___Fields_Olinordered__field) # label(axiom). [assumption]. 69.21/69.09 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5827,a,5784,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat)))),B)). [resolve(5827,a,5785,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))). [resolve(5827,a,5786,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)). [resolve(5827,a,5787,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)). [resolve(5827,a,5788,a)]. 69.21/69.10 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f87(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5827,a,5789,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),f87(rat,A,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5827,a,5790,a)]. 69.21/69.10 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5827,a,5791,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5792,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5827,a,5793,a)]. 69.21/69.10 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(5827,a,5794,a)]. 69.21/69.10 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A))))). [resolve(5827,a,5795,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5827,a,5796,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5827,a,5797,a)]. 69.21/69.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5827,a,5798,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5800,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5827,a,5801,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5802,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))). [resolve(5827,a,5803,a)]. 69.21/69.11 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C)). [resolve(5827,a,5804,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(5827,a,5805,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5806,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5827,a,5807,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)). [resolve(5827,a,5808,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)). [resolve(5827,a,5809,a)]. 69.21/69.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5827,a,5810,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5827,a,5811,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5812,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5827,a,5813,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5827,a,5814,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5827,a,5815,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5827,a,5817,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5827,a,5818,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5827,a,5819,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5827,a,5820,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5827,a,5821,a)]. 69.21/69.12 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5827,a,5823,a)]. 69.38/69.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5827,a,5824,a)]. 69.38/69.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5827,a,5825,a)]. 69.38/69.24 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5827,a,5826,a)]. 69.38/69.24 5828 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1680_divide__pos__neg) # label(axiom). [clausify(3790)]. 69.38/69.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(5828,a,5783,a)]. 69.38/69.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(5828,a,5827,a)]. 69.38/69.24 5829 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))))) # label(fact_1730_less__half__sum) # label(axiom). [clausify(3857)]. 69.38/69.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))))). [resolve(5829,a,5783,a)]. 69.38/69.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))))). [resolve(5829,a,5827,a)]. 69.38/69.24 5830 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2544_inverse__positive__imp__positive) # label(axiom). [clausify(3868)]. 69.38/69.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5830,a,5783,a)]. 69.38/69.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5830,a,5827,a)]. 69.38/69.24 5831 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1701_divide__nonneg__pos) # label(axiom). [clausify(3886)]. 69.60/69.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(5831,a,5783,a)]. 69.60/69.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5831,a,5827,a)]. 69.60/69.47 5832 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom). [clausify(3955)]. 69.60/69.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5832,a,5783,a)]. 69.60/69.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5832,a,5827,a)]. 69.60/69.47 5833 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1682_divide__neg__neg) # label(axiom). [clausify(4128)]. 69.60/69.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(5833,a,5783,a)]. 69.60/69.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5833,a,5827,a)]. 69.60/69.47 5834 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1683_divide__strict__right__mono) # label(axiom). [clausify(4169)]. 69.60/69.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5834,a,5783,a)]. 69.60/69.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5834,a,5827,a)]. 69.88/69.72 5835 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1702_divide__nonneg__neg) # label(axiom). [clausify(4179)]. 69.88/69.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(5835,a,5783,a)]. 69.88/69.72 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(5835,a,5827,a)]. 69.88/69.72 5836 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom). [clausify(4306)]. 69.88/69.72 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,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(5836,a,5783,a)]. 69.88/69.72 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(5836,a,5827,a)]. 69.88/69.72 5837 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom). [clausify(4306)]. 69.88/69.72 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,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(5837,a,5783,a)]. 69.88/69.72 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(5837,a,5827,a)]. 69.88/69.72 5838 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1706_divide__nonpos__pos) # label(axiom). [clausify(4451)]. 69.88/69.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(5838,a,5783,a)]. 69.93/69.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(5838,a,5827,a)]. 69.93/69.77 5839 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1681_divide__neg__pos) # label(axiom). [clausify(4484)]. 69.93/69.77 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),inverse_divide(real),A),B)),zero_zero(real))). [resolve(5839,a,5783,a)]. 69.93/69.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(5839,a,5827,a)]. 69.93/69.77 5840 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom). [clausify(4505)]. 69.93/69.77 5841 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom). [clausify(4513)]. 69.93/69.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(5841,a,5783,a)]. 69.93/69.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(5841,a,5827,a)]. 69.93/69.77 5842 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom). [clausify(4513)]. 69.93/69.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),B)). [resolve(5842,a,5783,a)]. 69.93/69.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),B)). [resolve(5842,a,5827,a)]. 72.62/72.49 5843 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1703_frac__less2) # label(axiom). [clausify(4863)]. 72.62/72.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5843,a,5783,a)]. 72.62/72.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5843,a,5827,a)]. 72.62/72.49 5844 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)),C) # label(fact_4716_scaleR__left_Odiff) # label(axiom). [clausify(97)]. 72.62/72.49 5845 real_vector(real) # label(arity_RealDef_Oreal___RealVector_Oreal__vector) # label(axiom). [assumption]. 72.62/72.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B). [resolve(5844,a,5845,a)]. 72.62/72.49 5846 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(real,fun(A,A),scaleR_scaleR(A),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4730_scaleR__right_Osetsum) # label(axiom). [clausify(125)]. 72.62/72.49 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),scaleR_scaleR(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5846,a,5845,a)]. 72.62/72.49 5847 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_4718_scaleR__right_Oadd) # label(axiom). [clausify(671)]. 72.62/72.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(5847,a,5845,a)]. 72.62/72.49 5848 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),zero_zero(real)),B) = zero_zero(A) # label(fact_4709_scaleR__left_Ozero) # label(axiom). [clausify(701)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),zero_zero(real)),A) = zero_zero(real). [resolve(5848,a,5845,a)]. 72.87/72.71 5849 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4688_scaleR__minus__right) # label(axiom). [clausify(711)]. 72.87/72.71 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5849,a,5845,a)]. 72.87/72.71 5850 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) | zero_zero(real) = B # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(1048)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) = ti(real,C) | zero_zero(real) = A. [resolve(5850,a,5845,a)]. 72.87/72.71 5851 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) != ti(A,D) # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(1048)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) != ti(real,C). [resolve(5851,a,5845,a)]. 72.87/72.71 5852 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) != B # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(1048)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) != A. [resolve(5852,a,5845,a)]. 72.87/72.71 5853 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != zero_zero(A) | zero_zero(real) = B | ti(A,C) = zero_zero(A) # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(1297)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != zero_zero(real) | zero_zero(real) = A | ti(real,B) = zero_zero(real). [resolve(5853,a,5845,a)]. 72.87/72.71 5854 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = zero_zero(A) | zero_zero(real) != B # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(1297)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = zero_zero(real) | zero_zero(real) != A. [resolve(5854,a,5845,a)]. 72.87/72.71 5855 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = zero_zero(A) | ti(A,C) != zero_zero(A) # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(1297)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = zero_zero(real) | ti(real,B) != zero_zero(real). [resolve(5855,a,5845,a)]. 72.87/72.71 5856 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),C) # label(fact_4713_scaleR__left_Oadd) # label(axiom). [clausify(1501)]. 72.87/72.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5856,a,5845,a)]. 72.87/72.71 5857 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),C) # label(fact_4711_real__vector_Oscale__left__distrib) # label(axiom). [clausify(1840)]. 73.63/73.49 5858 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4672_real__vector_Oscale__scale) # label(axiom). [clausify(2166)]. 73.63/73.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(5858,a,5845,a)]. 73.63/73.49 5859 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4687_scaleR__left_Ominus) # label(axiom). [clausify(2247)]. 73.63/73.49 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5859,a,5845,a)]. 73.63/73.49 5860 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),zero_zero(A)) = zero_zero(A) # label(fact_4702_scaleR__right_Ozero) # label(axiom). [clausify(2318)]. 73.63/73.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),zero_zero(real)) = zero_zero(real). [resolve(5860,a,5845,a)]. 73.63/73.49 5861 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4694_scaleR__left__commute) # label(axiom). [clausify(2595)]. 73.63/73.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(5861,a,5845,a)]. 73.63/73.49 5862 -real_vector(A) | scaleR_scaleR(A) = ti(fun(real,fun(A,A)),scaleR_scaleR(A)) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom). [clausify(3104)]. 73.63/73.49 Derived: scaleR_scaleR(real) = ti(fun(real,fun(real,real)),scaleR_scaleR(real)). [resolve(5862,a,5845,a)]. 73.63/73.49 5863 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)),C) # label(fact_4714_scaleR__left__diff__distrib) # label(axiom). [clausify(3131)]. 73.63/73.49 5864 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4686_scaleR__minus__left) # label(axiom). [clausify(3202)]. 73.63/73.49 5865 -real_vector(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(int,real,number_number_of(real),min_1)),B) # label(fact_4724_scaleR__minus1__left) # label(axiom). [clausify(3242)]. 73.63/73.49 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5865,a,5845,a)]. 73.63/73.49 5866 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,real),fun(B,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(B,real),fun(B,fun(A,A))),combb(real,fun(A,A),B),scaleR_scaleR(A)),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),D) # label(fact_4731_scaleR__left_Osetsum) # label(axiom). [clausify(3296)]. 73.63/73.49 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),scaleR_scaleR(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5866,a,5845,a)]. 74.55/74.36 5867 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | ti(A,C) = zero_zero(A) | B = D # label(fact_4704_scaleR__cancel__right) # label(axiom). [clausify(3464)]. 74.55/74.36 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | ti(real,B) = zero_zero(real) | A = C. [resolve(5867,a,5845,a)]. 74.55/74.36 5868 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | ti(A,C) != zero_zero(A) # label(fact_4704_scaleR__cancel__right) # label(axiom). [clausify(3464)]. 74.55/74.36 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | ti(real,B) != zero_zero(real). [resolve(5868,a,5845,a)]. 74.55/74.36 5869 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) | B != D # label(fact_4704_scaleR__cancel__right) # label(axiom). [clausify(3464)]. 74.55/74.36 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B) | A != C. [resolve(5869,a,5845,a)]. 74.55/74.36 5870 -real_vector(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) | C = D # label(fact_4705_scaleR__right__imp__eq) # label(axiom). [clausify(3770)]. 74.55/74.36 5871 -real_vector(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_4720_scaleR__right_Odiff) # label(axiom). [clausify(4168)]. 74.55/74.36 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)). [resolve(5871,a,5845,a)]. 74.55/74.36 5872 -real_vector(A) | zero_zero(real) = B | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) # label(fact_4701_scaleR__left__imp__eq) # label(axiom). [clausify(4609)]. 74.55/74.36 5873 real_vector(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__vector) # label(axiom). [assumption]. 74.55/74.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B). [resolve(5873,a,5844,a)]. 74.55/74.36 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5873,a,5846,a)]. 74.55/74.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)). [resolve(5873,a,5847,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),zero_zero(real)),A) = zero_zero(complex). [resolve(5873,a,5848,a)]. 74.55/74.37 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5873,a,5849,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) = ti(complex,C) | zero_zero(real) = A. [resolve(5873,a,5850,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(5873,a,5851,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) != A. [resolve(5873,a,5852,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != zero_zero(complex) | zero_zero(real) = A | ti(complex,B) = zero_zero(complex). [resolve(5873,a,5853,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = zero_zero(complex) | zero_zero(real) != A. [resolve(5873,a,5854,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = zero_zero(complex) | ti(complex,B) != zero_zero(complex). [resolve(5873,a,5855,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5873,a,5856,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(5873,a,5858,a)]. 74.55/74.37 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5873,a,5859,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5873,a,5860,a)]. 74.55/74.37 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(5873,a,5861,a)]. 74.55/74.37 Derived: scaleR_scaleR(complex) = ti(fun(real,fun(complex,complex)),scaleR_scaleR(complex)). [resolve(5873,a,5862,a)]. 74.55/74.37 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(5873,a,5865,a)]. 74.55/74.37 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,real),fun(A,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(A,real),fun(A,fun(complex,complex))),combb(real,fun(complex,complex),A),scaleR_scaleR(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5873,a,5866,a)]. 77.65/77.47 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | ti(complex,B) = zero_zero(complex) | A = C. [resolve(5873,a,5867,a)]. 77.65/77.47 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | ti(complex,B) != zero_zero(complex). [resolve(5873,a,5868,a)]. 77.65/77.47 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B) | A != C. [resolve(5873,a,5869,a)]. 77.65/77.47 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)). [resolve(5873,a,5871,a)]. 77.65/77.47 5874 -real_vector(A) | ti(A,B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),one_one(real)),B) # label(fact_4706_real__vector_Oscale__one) # label(axiom). [clausify(4757)]. 77.65/77.47 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),one_one(real)),A). [resolve(5874,a,5845,a)]. 77.65/77.47 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),one_one(real)),A). [resolve(5874,a,5873,a)]. 77.65/77.47 5875 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 77.65/77.47 5876 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_766_add__right__imp__eq) # label(axiom). [clausify(81)]. 77.65/77.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(5875,a,5876,a)]. 77.65/77.47 5877 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_769_add__right__cancel) # label(axiom). [clausify(659)]. 77.65/77.47 5878 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) != ti(A,D) # label(fact_769_add__right__cancel) # label(axiom). [clausify(659)]. 77.65/77.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) != ti(int,C). [resolve(5878,a,5875,a)]. 77.65/77.47 5879 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 77.65/77.47 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(5879,a,5876,a)]. 77.65/77.47 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C). [resolve(5879,a,5878,a)]. 77.65/77.47 5880 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_3_res) # label(axiom). [clausify(2352)]. 77.65/77.47 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(5880,a,5875,a)]. 77.65/77.47 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(5880,a,5879,a)]. 77.65/77.47 5881 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_768_add__left__imp__eq) # label(axiom). [clausify(2483)]. 77.65/77.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(5881,a,5875,a)]. 78.84/78.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(5881,a,5879,a)]. 78.84/78.69 5882 cancel_semigroup_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 78.84/78.69 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(5882,a,5876,a)]. 78.84/78.69 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B) | ti(code_code_numeral,A) != ti(code_code_numeral,C). [resolve(5882,a,5878,a)]. 78.84/78.69 Derived: plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)). [resolve(5882,a,5880,a)]. 78.84/78.69 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) = ti(code_code_numeral,C). [resolve(5882,a,5881,a)]. 78.84/78.69 5883 cancel_semigroup_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 78.84/78.69 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),B) | ti(complex,A) = ti(complex,C). [resolve(5883,a,5876,a)]. 78.84/78.69 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),B) | ti(complex,A) != ti(complex,C). [resolve(5883,a,5878,a)]. 78.84/78.69 Derived: plus_plus(complex) = ti(fun(complex,fun(complex,complex)),plus_plus(complex)). [resolve(5883,a,5880,a)]. 78.84/78.69 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) = ti(complex,C). [resolve(5883,a,5881,a)]. 78.84/78.69 5884 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_770_add__left__cancel) # label(axiom). [clausify(3542)]. 78.84/78.69 5885 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_770_add__left__cancel) # label(axiom). [clausify(3542)]. 78.84/78.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(5885,a,5875,a)]. 78.84/78.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(5885,a,5879,a)]. 78.84/78.69 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) != ti(code_code_numeral,C). [resolve(5885,a,5882,a)]. 78.84/78.69 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(5885,a,5883,a)]. 78.84/78.69 5886 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 83.01/82.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) = ti(real,C). [resolve(5886,a,5876,a)]. 83.01/82.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) != ti(real,C). [resolve(5886,a,5878,a)]. 83.01/82.88 Derived: plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(5886,a,5880,a)]. 83.01/82.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) = ti(real,C). [resolve(5886,a,5881,a)]. 83.01/82.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) != ti(real,C). [resolve(5886,a,5885,a)]. 83.01/82.88 5887 cancel_semigroup_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 83.01/82.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(5887,a,5876,a)]. 83.01/82.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,C). [resolve(5887,a,5878,a)]. 83.01/82.88 Derived: plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)). [resolve(5887,a,5880,a)]. 83.01/82.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,C). [resolve(5887,a,5881,a)]. 83.01/82.88 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,C). [resolve(5887,a,5885,a)]. 83.01/82.88 5888 cancel_semigroup_add(rat) # label(arity_Rat_Orat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 83.01/82.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B) | ti(rat,A) = ti(rat,C). [resolve(5888,a,5876,a)]. 83.01/82.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B) | ti(rat,A) != ti(rat,C). [resolve(5888,a,5878,a)]. 83.01/82.88 Derived: plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)). [resolve(5888,a,5880,a)]. 83.01/82.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) = ti(rat,C). [resolve(5888,a,5881,a)]. 83.01/82.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) != ti(rat,C). [resolve(5888,a,5885,a)]. 83.01/82.88 5889 t2_space(complex) # label(arity_Complex_Ocomplex___RealVector_Ot2__space) # label(axiom). [assumption]. 83.01/82.88 5890 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,A),A,suminf(A),B)),sequentially)) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom). [clausify(82)]. 83.01/82.88 5891 -t2_space(A) | -comm_monoid_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f125(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))) # label(fact_4291_series__zero) # label(axiom). [clausify(733)]. 83.01/82.88 5892 -t2_space(A) | -comm_monoid_add(A) | hAPP(nat,A,B,f125(A,B,C)) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)))) # label(fact_4291_series__zero) # label(axiom). [clausify(733)]. 83.01/82.88 5893 -t2_space(A) | hBOOL(hAPP(filter(B),bool,trivial_limit(B),C)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),E),C)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),F),C)) | ti(A,F) = ti(A,E) # label(fact_4767_tendsto__unique) # label(axiom). [clausify(1215)]. 83.01/82.88 5894 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4093_sums__iff) # label(axiom). [clausify(1344)]. 83.01/82.88 5895 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | ti(A,C) = hAPP(fun(nat,A),A,suminf(A),B) # label(fact_4093_sums__iff) # label(axiom). [clausify(1344)]. 83.01/82.88 5896 -comm_monoid_add(A) | -t2_space(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | ti(A,C) != hAPP(fun(nat,A),A,suminf(A),B) # label(fact_4093_sums__iff) # label(axiom). [clausify(1344)]. 83.01/82.88 5897 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | ti(A,C) = hAPP(fun(nat,A),A,suminf(A),B) # label(fact_4089_sums__unique) # label(axiom). [clausify(3014)]. 83.01/82.88 5898 -comm_monoid_add(A) | -t2_space(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))) = zero_zero(A) # label(fact_3968_suminf__zero) # label(axiom). [clausify(3493)]. 83.01/82.88 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,complex),complex,suminf(complex),A)),sequentially)). [resolve(5889,a,5890,a)]. 83.01/82.88 Derived: -comm_monoid_add(complex) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f125(complex,B,A))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5889,a,5891,a)]. 83.01/82.88 Derived: -comm_monoid_add(complex) | hAPP(nat,complex,A,f125(complex,A,B)) != zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5889,a,5892,a)]. 83.19/82.99 Derived: hBOOL(hAPP(filter(A),bool,trivial_limit(A),B)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),C),D),B)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),C),E),B)) | ti(complex,E) = ti(complex,D). [resolve(5889,a,5893,a)]. 83.19/82.99 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5889,a,5894,b)]. 83.19/82.99 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | ti(complex,B) = hAPP(fun(nat,complex),complex,suminf(complex),A). [resolve(5889,a,5895,b)]. 83.19/82.99 Derived: -comm_monoid_add(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | ti(complex,B) != hAPP(fun(nat,complex),complex,suminf(complex),A). [resolve(5889,a,5896,b)]. 83.19/82.99 Derived: -comm_monoid_add(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))) = zero_zero(complex). [resolve(5889,a,5898,b)]. 83.19/82.99 5899 t2_space(real) # label(arity_RealDef_Oreal___RealVector_Ot2__space) # label(axiom). [assumption]. 83.19/82.99 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,real),real,suminf(real),A)),sequentially)). [resolve(5899,a,5890,a)]. 83.19/82.99 Derived: -comm_monoid_add(real) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f125(real,B,A))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A)))). [resolve(5899,a,5891,a)]. 83.19/82.99 Derived: -comm_monoid_add(real) | hAPP(nat,real,A,f125(real,A,B)) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5899,a,5892,a)]. 83.19/82.99 Derived: hBOOL(hAPP(filter(A),bool,trivial_limit(A),B)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),C),D),B)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),C),E),B)) | ti(real,E) = ti(real,D). [resolve(5899,a,5893,a)]. 83.19/82.99 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5899,a,5894,b)]. 83.19/82.99 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | ti(real,B) = hAPP(fun(nat,real),real,suminf(real),A). [resolve(5899,a,5895,b)]. 83.19/82.99 Derived: -comm_monoid_add(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | ti(real,B) != hAPP(fun(nat,real),real,suminf(real),A). [resolve(5899,a,5896,b)]. 83.19/82.99 Derived: -comm_monoid_add(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))) = zero_zero(real). [resolve(5899,a,5898,b)]. 86.49/86.30 5900 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4092_summable__sums) # label(axiom). [clausify(4403)]. 86.49/86.30 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,complex),complex,suminf(complex),A))). [resolve(5900,b,5889,a)]. 86.49/86.30 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,real),real,suminf(real),A))). [resolve(5900,b,5899,a)]. 86.49/86.30 5901 semiring_div(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Divides_Osemiring__div) # label(axiom). [assumption]. 86.49/86.30 5902 -semiring_div(A) | div_mod(A) = ti(fun(A,fun(A,A)),div_mod(A)) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom). [clausify(93)]. 86.49/86.30 5903 -semiring_div(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = zero_zero(A) # label(fact_998_div__mult__mult1__if) # label(axiom). [clausify(152)]. 86.49/86.30 5904 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_998_div__mult__mult1__if) # label(axiom). [clausify(152)]. 86.49/86.30 5905 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_915_mod__div__equality) # label(axiom). [clausify(182)]. 86.49/86.30 5906 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_942_mod__add__self2) # label(axiom). [clausify(256)]. 86.49/86.30 5907 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),D)) # label(fact_1000_div__mult__div__if__dvd) # label(axiom). [clausify(264)]. 86.49/86.30 5908 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_978_mod__mult__self2) # label(axiom). [clausify(342)]. 86.49/86.30 5909 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) = zero_zero(A) # label(fact_979_dvd__imp__mod__0) # label(axiom). [clausify(361)]. 86.49/86.30 5910 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom). [clausify(367)]. 86.49/86.30 5911 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom). [clausify(367)]. 86.49/86.30 5912 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),C) # label(fact_934_mod__mult__cong) # label(axiom). [clausify(379)]. 86.49/86.30 5913 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_939_mod__add__left__eq) # label(axiom). [clausify(397)]. 86.49/86.31 5914 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1041_div__add__self1) # label(axiom). [clausify(461)]. 86.49/86.31 5915 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) # label(fact_1006_div__power) # label(axiom). [clausify(725)]. 86.49/86.31 5916 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_930_mod__mult__eq) # label(axiom). [clausify(754)]. 86.49/86.31 5917 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F)),C) # label(fact_935_mod__add__cong) # label(axiom). [clausify(801)]. 86.49/86.31 5918 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) # label(fact_917_div__mod__equality) # label(axiom). [clausify(931)]. 86.49/86.31 5919 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1004_dvd__mult__div__cancel) # label(axiom). [clausify(1028)]. 86.49/86.31 5920 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D)),C) # label(fact_932_mod__mult__mult2) # label(axiom). [clausify(1050)]. 86.49/86.31 Derived: div_mod(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_mod(code_code_numeral)). [resolve(5901,a,5902,a)]. 86.49/86.31 Derived: ti(code_code_numeral,A) != zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = zero_zero(code_code_numeral). [resolve(5901,a,5903,a)]. 86.49/86.31 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(5901,a,5904,a)]. 86.49/86.31 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)). [resolve(5901,a,5905,a)]. 86.49/86.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5901,a,5906,a)]. 86.49/86.32 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),C),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),C)). [resolve(5901,a,5907,a)]. 86.49/86.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5901,a,5908,a)]. 86.49/86.32 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A) = zero_zero(code_code_numeral). [resolve(5901,a,5909,a)]. 86.49/86.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != zero_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),A)). [resolve(5901,a,5910,a)]. 86.49/86.32 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),E)),B). [resolve(5901,a,5912,a)]. 86.49/86.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5901,a,5913,a)]. 86.49/86.33 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(5901,a,5914,a)]. 86.49/86.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),C)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C). [resolve(5901,a,5915,a)]. 86.49/86.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5901,a,5916,a)]. 86.49/86.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),E),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),D)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),E)),B). [resolve(5901,a,5917,a)]. 86.49/86.36 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C). [resolve(5901,a,5918,a)]. 86.49/86.36 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(5901,a,5919,a)]. 86.49/86.36 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),C)),B). [resolve(5901,a,5920,a)]. 86.49/86.36 5921 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) = zero_zero(A) # label(fact_974_mod__mult__self2__is__0) # label(axiom). [clausify(1224)]. 86.49/86.36 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(5921,a,5901,a)]. 86.49/86.36 5922 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_994_div__mult__mult1) # label(axiom). [clausify(1234)]. 86.49/86.36 5923 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_940_mod__add__right__eq) # label(axiom). [clausify(1321)]. 86.49/86.36 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),C). [resolve(5923,a,5901,a)]. 86.61/86.41 5924 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) # label(fact_996_div__mult__self1__is__id) # label(axiom). [clausify(1374)]. 86.61/86.41 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A). [resolve(5924,a,5901,a)]. 86.61/86.41 5925 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_928_mod__mult__right__eq) # label(axiom). [clausify(1425)]. 86.61/86.41 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),C). [resolve(5925,a,5901,a)]. 86.61/86.41 5926 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) # label(fact_1001_dvd__div__mult) # label(axiom). [clausify(1456)]. 86.61/86.41 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),C). [resolve(5926,a,5901,a)]. 86.61/86.41 5927 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom). [clausify(1495)]. 86.61/86.41 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B). [resolve(5927,a,5901,a)]. 86.71/86.52 5928 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom). [clausify(1495)]. 86.71/86.52 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),D) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B). [resolve(5928,a,5901,a)]. 86.71/86.52 5929 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_936_zmod__simps_I1_J) # label(axiom). [clausify(1502)]. 86.71/86.52 5930 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),zero_zero(A)),B) = zero_zero(A) # label(fact_926_mod__0) # label(axiom). [clausify(1717)]. 86.71/86.52 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5930,a,5901,a)]. 86.71/86.52 5931 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),B) = zero_zero(A) # label(fact_924_mod__self) # label(axiom). [clausify(1760)]. 86.71/86.52 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),A) = zero_zero(code_code_numeral). [resolve(5931,a,5901,a)]. 86.71/86.52 5932 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1042_div__add__self2) # label(axiom). [clausify(1808)]. 86.71/86.52 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(5932,a,5901,a)]. 86.71/86.52 5933 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) = zero_zero(A) # label(fact_973_mod__mult__self1__is__0) # label(axiom). [clausify(1857)]. 86.71/86.52 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A) = zero_zero(code_code_numeral). [resolve(5933,a,5901,a)]. 86.79/86.65 5934 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_914_mod__div__equality2) # label(axiom). [clausify(1869)]. 86.79/86.65 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)). [resolve(5934,a,5901,a)]. 86.79/86.65 5935 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_938_mod__add__eq) # label(axiom). [clausify(1931)]. 86.79/86.65 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5935,a,5901,a)]. 86.79/86.65 5936 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),one_one(A)) # label(fact_966_div__by__1) # label(axiom). [clausify(1963)]. 86.79/86.65 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),one_one(code_code_numeral)). [resolve(5936,a,5901,a)]. 86.79/86.65 5937 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),zero_zero(A)) = zero_zero(A) # label(fact_964_div__by__0) # label(axiom). [clausify(2037)]. 86.79/86.65 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5937,a,5901,a)]. 86.79/86.65 5938 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1039_div__mult__self1) # label(axiom). [clausify(2213)]. 86.79/86.65 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(5938,a,5901,a)]. 87.32/87.16 5939 -semiring_div(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) = zero_zero(A) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(2473)]. 87.32/87.16 5940 -semiring_div(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B)) != zero_zero(A) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(2473)]. 87.32/87.16 5941 -semiring_div(A) | div_div(A) = ti(fun(A,fun(A,A)),div_div(A)) # label(tsy_c_Divides_Odiv__class_Odiv_res) # label(axiom). [clausify(2548)]. 87.32/87.16 Derived: div_div(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_div(code_code_numeral)). [resolve(5941,a,5901,a)]. 87.32/87.16 5942 semiring_div(int) # label(arity_Int_Oint___Divides_Osemiring__div) # label(axiom). [assumption]. 87.32/87.16 Derived: div_mod(int) = ti(fun(int,fun(int,int)),div_mod(int)). [resolve(5942,a,5902,a)]. 87.32/87.16 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = zero_zero(int). [resolve(5942,a,5903,a)]. 87.32/87.16 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(5942,a,5904,a)]. 87.32/87.16 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)). [resolve(5942,a,5905,a)]. 87.32/87.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5942,a,5906,a)]. 87.32/87.16 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),C),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),C)). [resolve(5942,a,5907,a)]. 87.32/87.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5942,a,5908,a)]. 87.32/87.16 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A) = zero_zero(int). [resolve(5942,a,5909,a)]. 87.32/87.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). [resolve(5942,a,5910,a)]. 87.32/87.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),E)),B). [resolve(5942,a,5912,a)]. 87.32/87.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5942,a,5913,a)]. 87.32/87.17 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(5942,a,5914,a)]. 87.32/87.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C). [resolve(5942,a,5915,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5942,a,5916,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),E)),B). [resolve(5942,a,5917,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C). [resolve(5942,a,5918,a)]. 87.32/87.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(5942,a,5919,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),C)),B). [resolve(5942,a,5920,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B) = zero_zero(int). [resolve(5942,a,5921,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C). [resolve(5942,a,5923,a)]. 87.32/87.17 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A). [resolve(5942,a,5924,a)]. 87.32/87.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C). [resolve(5942,a,5925,a)]. 87.32/87.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),C). [resolve(5942,a,5926,a)]. 87.32/87.17 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B). [resolve(5942,a,5927,a)]. 87.39/87.24 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B). [resolve(5942,a,5928,a)]. 87.39/87.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),A) = zero_zero(int). [resolve(5942,a,5930,a)]. 87.39/87.24 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(5942,a,5932,a)]. 87.39/87.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A) = zero_zero(int). [resolve(5942,a,5933,a)]. 87.39/87.24 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)). [resolve(5942,a,5934,a)]. 87.39/87.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5942,a,5935,a)]. 87.39/87.24 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),one_one(int)). [resolve(5942,a,5936,a)]. 87.39/87.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),zero_zero(int)) = zero_zero(int). [resolve(5942,a,5937,a)]. 87.39/87.24 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(5942,a,5938,a)]. 87.39/87.24 Derived: div_div(int) = ti(fun(int,fun(int,int)),div_div(int)). [resolve(5942,a,5941,a)]. 87.39/87.24 5943 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B) # label(fact_997_div__mult__self2__is__id) # label(axiom). [clausify(2867)]. 87.39/87.24 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),A). [resolve(5943,a,5901,a)]. 87.39/87.24 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A). [resolve(5943,a,5942,a)]. 87.39/87.24 5944 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) # label(fact_947_dvd__mod__iff) # label(axiom). [clausify(2980)]. 87.39/87.24 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))). [resolve(5944,a,5901,a)]. 87.92/87.74 5945 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) # label(fact_947_dvd__mod__iff) # label(axiom). [clausify(2980)]. 87.92/87.74 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B))). [resolve(5945,a,5901,a)]. 87.92/87.74 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))). [resolve(5945,a,5942,a)]. 87.92/87.74 5946 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_950_dvd__mod__imp__dvd) # label(axiom). [clausify(3386)]. 87.92/87.74 5947 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_1074_mod__div__decomp) # label(axiom). [clausify(3397)]. 87.92/87.74 5948 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_906_mod__mod__trivial) # label(axiom). [clausify(3467)]. 87.92/87.74 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B). [resolve(5948,a,5901,a)]. 87.92/87.74 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B). [resolve(5948,a,5942,a)]. 87.92/87.74 5949 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_933_zmod__simps_I4_J) # label(axiom). [clausify(3566)]. 87.92/87.74 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),C)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),B). [resolve(5949,a,5901,a)]. 87.92/87.74 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(5949,a,5942,a)]. 87.92/87.74 5950 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D) # label(fact_977_mod__mult__self1) # label(axiom). [clausify(3636)]. 88.09/87.90 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),C). [resolve(5950,a,5901,a)]. 88.09/87.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),C). [resolve(5950,a,5942,a)]. 88.09/87.90 5951 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),one_one(A)) = zero_zero(A) # label(fact_975_mod__by__1) # label(axiom). [clausify(3721)]. 88.09/87.90 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),one_one(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(5951,a,5901,a)]. 88.09/87.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),one_one(int)) = zero_zero(int). [resolve(5951,a,5942,a)]. 88.09/87.90 5952 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_941_mod__add__self1) # label(axiom). [clausify(3756)]. 88.09/87.90 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A). [resolve(5952,a,5901,a)]. 88.09/87.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A). [resolve(5952,a,5942,a)]. 88.09/87.90 5953 semiring_div(nat) # label(arity_Nat_Onat___Divides_Osemiring__div) # label(axiom). [assumption]. 88.09/87.90 Derived: div_mod(nat) = ti(fun(nat,fun(nat,nat)),div_mod(nat)). [resolve(5953,a,5902,a)]. 88.09/87.90 Derived: ti(nat,A) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = zero_zero(nat). [resolve(5953,a,5903,a)]. 88.09/87.90 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(5953,a,5904,a)]. 88.09/87.90 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)). [resolve(5953,a,5905,a)]. 88.09/87.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5953,a,5906,a)]. 88.09/87.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),C)). [resolve(5953,a,5907,a)]. 88.09/87.90 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5953,a,5908,a)]. 88.09/87.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A) = zero_zero(nat). [resolve(5953,a,5909,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A)). [resolve(5953,a,5910,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),E)),B). [resolve(5953,a,5912,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5953,a,5913,a)]. 88.09/87.91 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(5953,a,5914,a)]. 88.09/87.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C). [resolve(5953,a,5915,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5953,a,5916,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),E),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)),B). [resolve(5953,a,5917,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C). [resolve(5953,a,5918,a)]. 88.09/87.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(5953,a,5919,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),C)),B). [resolve(5953,a,5920,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B) = zero_zero(nat). [resolve(5953,a,5921,a)]. 88.09/87.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C). [resolve(5953,a,5923,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A). [resolve(5953,a,5924,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C). [resolve(5953,a,5925,a)]. 88.09/87.92 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),C). [resolve(5953,a,5926,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B). [resolve(5953,a,5927,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B). [resolve(5953,a,5928,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5953,a,5930,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),A) = zero_zero(nat). [resolve(5953,a,5931,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(5953,a,5932,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A) = zero_zero(nat). [resolve(5953,a,5933,a)]. 88.09/87.92 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)). [resolve(5953,a,5934,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5953,a,5935,a)]. 88.09/87.92 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),one_one(nat)). [resolve(5953,a,5936,a)]. 88.09/87.92 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(5953,a,5937,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(5953,a,5938,a)]. 88.09/87.92 Derived: div_div(nat) = ti(fun(nat,fun(nat,nat)),div_div(nat)). [resolve(5953,a,5941,a)]. 88.09/87.92 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),A). [resolve(5953,a,5943,a)]. 88.09/87.92 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))). [resolve(5953,a,5944,a)]. 88.26/88.10 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B))). [resolve(5953,a,5945,a)]. 88.26/88.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B). [resolve(5953,a,5948,a)]. 88.26/88.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(5953,a,5949,a)]. 88.26/88.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),C). [resolve(5953,a,5950,a)]. 88.26/88.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),one_one(nat)) = zero_zero(nat). [resolve(5953,a,5951,a)]. 88.26/88.10 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A). [resolve(5953,a,5952,a)]. 88.26/88.10 5954 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_995_div__mult__mult2) # label(axiom). [clausify(3923)]. 88.26/88.10 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(5954,a,5901,a)]. 88.26/88.10 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(5954,a,5942,a)]. 88.26/88.10 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(5954,a,5953,a)]. 88.26/88.10 5955 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(4037)]. 88.26/88.10 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),B)),B)). [resolve(5955,a,5901,a)]. 88.26/88.10 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)). [resolve(5955,a,5942,a)]. 88.39/88.21 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),B)),B)). [resolve(5955,a,5953,a)]. 88.39/88.21 5956 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) # label(fact_949_dvd__mod) # label(axiom). [clausify(4110)]. 88.39/88.21 5957 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1040_div__mult__self2) # label(axiom). [clausify(4138)]. 88.39/88.21 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(5957,a,5901,a)]. 88.39/88.21 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(5957,a,5942,a)]. 88.39/88.21 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(5957,a,5953,a)]. 88.39/88.21 5958 -semiring_div(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),B) # label(fact_999_div__self) # label(axiom). [clausify(4151)]. 88.39/88.21 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | one_one(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),A). [resolve(5958,a,5901,a)]. 88.39/88.21 Derived: ti(int,A) = zero_zero(int) | one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),A). [resolve(5958,a,5942,a)]. 88.39/88.21 Derived: ti(nat,A) = zero_zero(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),A). [resolve(5958,a,5953,a)]. 88.39/88.21 5959 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = zero_zero(A) # label(fact_909_mod__div__trivial) # label(axiom). [clausify(4158)]. 88.39/88.21 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(5959,a,5901,a)]. 88.39/88.21 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = zero_zero(int). [resolve(5959,a,5942,a)]. 88.39/88.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = zero_zero(nat). [resolve(5959,a,5953,a)]. 88.39/88.24 5960 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_929_mod__mult__left__eq) # label(axiom). [clausify(4160)]. 88.39/88.24 5961 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_916_div__mod__equality2) # label(axiom). [clausify(4176)]. 88.39/88.24 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A))),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C). [resolve(5961,a,5901,a)]. 88.39/88.24 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A))),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C). [resolve(5961,a,5953,a)]. 88.39/88.24 5962 -semiring_div(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) # label(fact_1044_dvd__div__eq__mult) # label(axiom). [clausify(4195)]. 88.39/88.24 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,C) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A). [resolve(5962,a,5901,a)]. 88.39/88.24 Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | ti(int,C) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A). [resolve(5962,a,5942,a)]. 88.39/88.24 Derived: ti(nat,A) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | ti(nat,C) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A). [resolve(5962,a,5953,a)]. 88.39/88.24 5963 -semiring_div(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) # label(fact_1044_dvd__div__eq__mult) # label(axiom). [clausify(4195)]. 88.39/88.24 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A) | ti(code_code_numeral,B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A). [resolve(5963,a,5901,a)]. 88.71/88.51 Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | ti(int,C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A). [resolve(5963,a,5942,a)]. 88.71/88.51 Derived: ti(nat,A) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | ti(nat,C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A). [resolve(5963,a,5953,a)]. 88.71/88.51 5964 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),zero_zero(A)) # label(fact_925_mod__by__0) # label(axiom). [clausify(4238)]. 88.71/88.51 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),zero_zero(code_code_numeral)). [resolve(5964,a,5901,a)]. 88.71/88.51 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),zero_zero(int)). [resolve(5964,a,5942,a)]. 88.71/88.51 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),zero_zero(nat)). [resolve(5964,a,5953,a)]. 88.71/88.51 5965 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1003_div__mult__swap) # label(axiom). [clausify(4411)]. 88.71/88.51 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(5965,a,5901,a)]. 88.71/88.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(5965,a,5942,a)]. 88.71/88.51 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(5965,a,5953,a)]. 88.71/88.51 5966 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom). [clausify(4506)]. 88.71/88.51 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(5966,a,5901,a)]. 88.71/88.51 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5966,a,5942,a)]. 88.83/88.64 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(5966,a,5953,a)]. 88.83/88.64 5967 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom). [clausify(4506)]. 88.83/88.64 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(5967,a,5901,a)]. 88.83/88.64 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(5967,a,5942,a)]. 88.83/88.64 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(5967,a,5953,a)]. 88.83/88.64 5968 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D)) # label(fact_931_mod__mult__mult1) # label(axiom). [clausify(4645)]. 88.83/88.64 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C)). [resolve(5968,a,5901,a)]. 88.83/88.64 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C)). [resolve(5968,a,5942,a)]. 88.89/88.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C)). [resolve(5968,a,5953,a)]. 88.89/88.69 5969 semiring_div(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Divides_Osemiring__div) # label(axiom). [assumption]. 88.89/88.69 Derived: div_mod(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_mod(quickcheck_code_int)). [resolve(5969,a,5902,a)]. 88.89/88.69 Derived: ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = zero_zero(quickcheck_code_int). [resolve(5969,a,5903,a)]. 88.89/88.69 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(5969,a,5904,a)]. 88.89/88.69 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)). [resolve(5969,a,5905,a)]. 88.89/88.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5969,a,5906,a)]. 88.89/88.69 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),C)). [resolve(5969,a,5907,a)]. 88.89/88.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5969,a,5908,a)]. 88.89/88.69 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A) = zero_zero(quickcheck_code_int). [resolve(5969,a,5909,a)]. 88.89/88.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),A)). [resolve(5969,a,5910,a)]. 88.89/88.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),E)),B). [resolve(5969,a,5912,a)]. 88.89/88.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5969,a,5913,a)]. 88.89/88.69 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(5969,a,5914,a)]. 88.89/88.70 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),C)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C). [resolve(5969,a,5915,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5969,a,5916,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),E),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),D)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),E)),B). [resolve(5969,a,5917,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C). [resolve(5969,a,5918,a)]. 88.89/88.70 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(5969,a,5919,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),C)),B). [resolve(5969,a,5920,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(5969,a,5921,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),C). [resolve(5969,a,5923,a)]. 88.89/88.70 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A). [resolve(5969,a,5924,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),C). [resolve(5969,a,5925,a)]. 88.89/88.70 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C). [resolve(5969,a,5926,a)]. 88.89/88.70 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B). [resolve(5969,a,5927,a)]. 88.89/88.70 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),D) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B). [resolve(5969,a,5928,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5969,a,5930,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),A) = zero_zero(quickcheck_code_int). [resolve(5969,a,5931,a)]. 88.89/88.70 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(5969,a,5932,a)]. 88.89/88.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A) = zero_zero(quickcheck_code_int). [resolve(5969,a,5933,a)]. 88.89/88.71 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)). [resolve(5969,a,5934,a)]. 88.89/88.71 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5969,a,5935,a)]. 88.89/88.71 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),one_one(quickcheck_code_int)). [resolve(5969,a,5936,a)]. 88.89/88.71 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5969,a,5937,a)]. 88.89/88.71 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(5969,a,5938,a)]. 88.89/88.71 Derived: div_div(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_div(quickcheck_code_int)). [resolve(5969,a,5941,a)]. 88.89/88.71 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),A). [resolve(5969,a,5943,a)]. 88.89/88.71 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))). [resolve(5969,a,5944,a)]. 88.89/88.72 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B))). [resolve(5969,a,5945,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B). [resolve(5969,a,5948,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),C)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),B). [resolve(5969,a,5949,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),C). [resolve(5969,a,5950,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),one_one(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(5969,a,5951,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A). [resolve(5969,a,5952,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(5969,a,5954,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),B)),B)). [resolve(5969,a,5955,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(5969,a,5957,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | one_one(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),A). [resolve(5969,a,5958,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(5969,a,5959,a)]. 88.89/88.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A))),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C). [resolve(5969,a,5961,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,C) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A). [resolve(5969,a,5962,a)]. 88.89/88.72 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A) | ti(quickcheck_code_int,B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A). [resolve(5969,a,5963,a)]. 88.96/88.80 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),zero_zero(quickcheck_code_int)). [resolve(5969,a,5964,a)]. 88.96/88.80 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(5969,a,5965,a)]. 88.96/88.80 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(5969,a,5966,a)]. 88.96/88.80 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(5969,a,5967,a)]. 88.96/88.80 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C)). [resolve(5969,a,5968,a)]. 88.96/88.80 5970 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),zero_zero(A)),B) = zero_zero(A) # label(fact_965_div__0) # label(axiom). [clausify(4796)]. 88.96/88.80 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(5970,a,5901,a)]. 88.96/88.80 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),A) = zero_zero(int). [resolve(5970,a,5942,a)]. 88.96/88.80 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(5970,a,5953,a)]. 89.04/88.92 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(5970,a,5969,a)]. 89.04/88.92 5971 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),B) # label(fact_948_mod__mod__cancel) # label(axiom). [clausify(4817)]. 89.04/88.92 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),C),A). [resolve(5971,a,5901,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),A). [resolve(5971,a,5942,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),C),A). [resolve(5971,a,5953,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),C),A). [resolve(5971,a,5969,a)]. 89.04/88.92 5972 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_937_zmod__simps_I2_J) # label(axiom). [clausify(4901)]. 89.04/88.92 5973 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),B) # label(fact_1002_dvd__div__mult__self) # label(axiom). [clausify(4902)]. 89.04/88.92 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),A). [resolve(5973,a,5901,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),A). [resolve(5973,a,5942,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),A). [resolve(5973,a,5953,a)]. 89.04/88.92 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),A). [resolve(5973,a,5969,a)]. 91.84/91.66 5974 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) # label(fact_1005_div__add) # label(axiom). [clausify(4924)]. 91.84/91.66 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A)). [resolve(5974,a,5901,a)]. 91.84/91.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A)). [resolve(5974,a,5942,a)]. 91.84/91.66 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A)). [resolve(5974,a,5953,a)]. 91.84/91.66 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A)). [resolve(5974,a,5969,a)]. 91.84/91.66 5975 -comm_ring(A) | -monoid_mult(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(A,fun(nat,A),power_power(A),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) # label(fact_4226_lemma__termdiff1) # label(axiom). [clausify(1207)]. 92.07/91.87 5976 comm_ring(int) # label(arity_Int_Oint___Rings_Ocomm__ring) # label(axiom). [assumption]. 92.07/91.87 Derived: -monoid_mult(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(int,fun(nat,int),power_power(int),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5975,a,5976,a)]. 92.07/91.87 5977 comm_ring(real) # label(arity_RealDef_Oreal___Rings_Ocomm__ring) # label(axiom). [assumption]. 92.07/91.87 Derived: -monoid_mult(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(real,fun(nat,real),power_power(real),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5977,a,5975,a)]. 92.52/92.39 5978 -comm_ring(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom). [clausify(3043)]. 92.52/92.39 Derived: -monoid_mult(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5978,a,5976,a)]. 92.72/92.58 Derived: -monoid_mult(real) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5978,a,5977,a)]. 92.72/92.58 5979 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),C))),E))) # label(fact_488_inf__period_I4_J) # label(axiom). [clausify(3306)]. 92.72/92.58 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),B))),D))). [resolve(5979,b,5976,a)]. 92.72/92.58 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),B))),D))). [resolve(5979,b,5977,a)]. 92.72/92.58 5980 -dvd(A) | -comm_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),C))),E))) # label(fact_488_inf__period_I4_J) # label(axiom). [clausify(3306)]. 92.72/92.58 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),B))),D))). [resolve(5980,b,5976,a)]. 92.72/92.58 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),B))),D))). [resolve(5980,b,5977,a)]. 92.89/92.72 5981 comm_ring(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__ring) # label(axiom). [assumption]. 92.89/92.72 Derived: -monoid_mult(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(complex,fun(nat,complex),power_power(complex),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5981,a,5975,a)]. 92.89/92.72 Derived: -monoid_mult(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,suc,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5981,a,5978,a)]. 93.12/92.93 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),B))),D))). [resolve(5981,a,5979,b)]. 93.12/92.93 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),B))),D))). [resolve(5981,a,5980,b)]. 93.12/92.93 5982 comm_ring(rat) # label(arity_Rat_Orat___Rings_Ocomm__ring) # label(axiom). [assumption]. 93.12/92.93 Derived: -monoid_mult(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(rat,fun(nat,rat),power_power(rat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5982,a,5975,a)]. 93.12/92.93 Derived: -monoid_mult(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5982,a,5978,a)]. 96.29/96.13 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),E),B))),D))). [resolve(5982,a,5979,b)]. 96.29/96.13 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),E),B))),D))). [resolve(5982,a,5980,b)]. 96.29/96.13 5983 -comm_ring(A) | -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C))),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_487_inf__period_I3_J) # label(axiom). [clausify(4075)]. 96.29/96.13 5984 -comm_ring(A) | -dvd(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C))),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_487_inf__period_I3_J) # label(axiom). [clausify(4075)]. 96.29/96.13 5985 number(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Int_Onumber) # label(axiom). [assumption]. 96.29/96.13 5986 -number(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) # label(fact_3872_power__number__of__even__number__of) # label(axiom). [clausify(114)]. 96.29/96.13 5987 -ring(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(int,A,number_number_of(A),C)) # label(fact_492_left__diff__distrib__number__of) # label(axiom). [clausify(145)]. 96.29/96.13 Derived: -ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)). [resolve(5985,a,5987,b)]. 96.40/96.21 5988 number(real) # label(arity_RealDef_Oreal___Int_Onumber) # label(axiom). [assumption]. 96.40/96.21 Derived: -monoid_mult(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5988,a,5986,a)]. 96.40/96.21 5989 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B))),D)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.40/96.21 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)). [resolve(5989,a,5985,a)]. 96.40/96.21 5990 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -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(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.40/96.21 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(5990,a,5985,a)]. 96.41/96.22 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(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(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)). [resolve(5990,a,5988,a)]. 96.41/96.22 5991 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -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),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.22 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(5991,a,5985,a)]. 96.41/96.22 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(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),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)). [resolve(5991,a,5988,a)]. 96.41/96.22 5992 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.22 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(5992,a,5985,a)]. 96.41/96.23 5993 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.23 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(5993,a,5985,a)]. 96.41/96.23 5994 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.23 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(5994,a,5985,a)]. 96.41/96.24 Derived: -linord1117847801e_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),hAPP(int,real,number_number_of(real),B))),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),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B))),A)). [resolve(5994,a,5988,a)]. 96.41/96.24 5995 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.24 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(5995,a,5985,a)]. 96.41/96.24 Derived: -linord1117847801e_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),hAPP(int,real,number_number_of(real),B))),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_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B))),A)). [resolve(5995,a,5988,a)]. 96.41/96.24 5996 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.24 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(5996,a,5985,a)]. 96.41/96.24 5997 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.24 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(5997,a,5985,a)]. 96.41/96.24 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)). [resolve(5997,a,5988,a)]. 96.41/96.24 5998 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B))),D)) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(1038)]. 96.41/96.26 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)). [resolve(5998,a,5985,a)]. 96.41/96.26 5999 number(rat) # label(arity_Rat_Orat___Int_Onumber) # label(axiom). [assumption]. 96.41/96.26 Derived: -monoid_mult(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5999,a,5986,a)]. 96.41/96.26 Derived: -ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(int,rat,number_number_of(rat),B)). [resolve(5999,a,5987,b)]. 96.41/96.26 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)). [resolve(5999,a,5990,a)]. 96.41/96.26 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)). [resolve(5999,a,5991,a)]. 96.41/96.26 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(5999,a,5994,a)]. 96.41/96.28 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(5999,a,5995,a)]. 96.41/96.28 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)). [resolve(5999,a,5997,a)]. 96.41/96.28 6000 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.28 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6000,b,5985,a)]. 96.41/96.28 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6000,b,5988,a)]. 96.41/96.28 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6000,b,5999,a)]. 96.41/96.28 6001 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.29 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6001,b,5985,a)]. 96.41/96.29 6002 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.29 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6002,b,5985,a)]. 96.41/96.29 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6002,b,5988,a)]. 96.41/96.29 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6002,b,5999,a)]. 96.41/96.30 6003 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.30 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6003,b,5985,a)]. 96.41/96.30 6004 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.30 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6004,b,5985,a)]. 96.41/96.30 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(int,real,number_number_of(real),B))). [resolve(6004,b,5988,a)]. 96.41/96.31 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6004,b,5999,a)]. 96.41/96.31 6005 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.31 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6005,b,5985,a)]. 96.41/96.31 6006 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.31 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6006,b,5985,a)]. 96.41/96.32 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),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),hAPP(int,real,number_number_of(real),B)),C)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(int,real,number_number_of(real),B))). [resolve(6006,b,5988,a)]. 96.41/96.32 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6006,b,5999,a)]. 96.41/96.32 6007 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(int,A,number_number_of(A),D))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.32 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C))). [resolve(6007,b,5985,a)]. 96.41/96.32 6008 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.41/96.32 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6008,b,5985,a)]. 96.60/96.41 6009 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(1053)]. 96.60/96.41 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6009,b,5985,a)]. 96.60/96.41 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6009,b,5988,a)]. 96.60/96.41 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6009,b,5999,a)]. 96.60/96.41 6010 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.41 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6010,a,5985,a)]. 96.60/96.42 6011 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.42 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6011,a,5985,a)]. 96.60/96.42 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(6011,a,5988,a)]. 96.60/96.42 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6011,a,5999,a)]. 96.60/96.42 6012 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.42 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6012,a,5985,a)]. 96.60/96.42 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(6012,a,5988,a)]. 96.60/96.42 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6012,a,5999,a)]. 96.60/96.42 6013 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.42 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6013,a,5985,a)]. 96.60/96.44 6014 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.44 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6014,a,5985,a)]. 96.60/96.44 6015 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.44 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6015,a,5985,a)]. 96.60/96.44 Derived: -linord1117847801e_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),hAPP(int,real,number_number_of(real),B))),C)) | -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),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B)))). [resolve(6015,a,5988,a)]. 96.60/96.44 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B)))). [resolve(6015,a,5999,a)]. 96.60/96.44 6016 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.44 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6016,a,5985,a)]. 96.60/96.44 Derived: -linord1117847801e_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),hAPP(int,real,number_number_of(real),B))),C)) | -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),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B)))). [resolve(6016,a,5988,a)]. 96.60/96.44 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B)))). [resolve(6016,a,5999,a)]. 96.60/96.45 6017 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.45 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6017,a,5985,a)]. 96.60/96.45 6018 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.60/96.45 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6018,a,5985,a)]. 96.60/96.45 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(6018,a,5988,a)]. 96.60/96.45 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6018,a,5999,a)]. 96.79/96.61 6019 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(1457)]. 96.79/96.61 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6019,a,5985,a)]. 96.79/96.61 6020 number(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Int_Onumber) # label(axiom). [assumption]. 96.79/96.61 Derived: -monoid_mult(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(6020,a,5986,a)]. 96.79/96.61 Derived: -ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)). [resolve(6020,a,5987,b)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)). [resolve(6020,a,5989,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6020,a,5990,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6020,a,5991,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6020,a,5992,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6020,a,5993,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6020,a,5994,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6020,a,5995,a)]. 96.79/96.62 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6020,a,5996,a)]. 96.79/96.63 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6020,a,5997,a)]. 96.79/96.63 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)). [resolve(6020,a,5998,a)]. 96.79/96.63 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6000,b)]. 96.79/96.63 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6001,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6002,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6003,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6004,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6005,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6006,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C))). [resolve(6020,a,6007,b)]. 96.79/96.64 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6008,b)]. 96.79/96.65 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6020,a,6009,b)]. 96.79/96.65 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6010,a)]. 96.79/96.65 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6011,a)]. 96.79/96.65 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6012,a)]. 96.79/96.66 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6020,a,6013,a)]. 96.79/96.66 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6020,a,6014,a)]. 96.79/96.66 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6020,a,6015,a)]. 96.79/96.66 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6020,a,6016,a)]. 96.79/96.67 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6017,a)]. 96.79/96.67 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6018,a)]. 96.79/96.67 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6020,a,6019,a)]. 96.79/96.67 6021 -number(A) | number_number_of(A) = ti(fun(int,A),number_number_of(A)) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom). [clausify(2075)]. 96.79/96.67 Derived: number_number_of(quickcheck_code_int) = ti(fun(int,quickcheck_code_int),number_number_of(quickcheck_code_int)). [resolve(6021,a,5985,a)]. 96.90/96.72 Derived: number_number_of(real) = ti(fun(int,real),number_number_of(real)). [resolve(6021,a,5988,a)]. 96.90/96.72 Derived: number_number_of(rat) = ti(fun(int,rat),number_number_of(rat)). [resolve(6021,a,5999,a)]. 96.90/96.72 Derived: number_number_of(code_code_numeral) = ti(fun(int,code_code_numeral),number_number_of(code_code_numeral)). [resolve(6021,a,6020,a)]. 96.90/96.72 6022 -semiring(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(int,A,number_number_of(A),C)) # label(fact_95_left__distrib__number__of) # label(axiom). [clausify(2098)]. 96.90/96.72 6023 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.72 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C)),B)). [resolve(6023,a,5985,a)]. 96.90/96.72 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C)),B)). [resolve(6023,a,6020,a)]. 96.90/96.72 6024 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.72 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))). [resolve(6024,a,5985,a)]. 96.90/96.73 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(6024,a,5988,a)]. 96.90/96.73 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(6024,a,5999,a)]. 96.90/96.73 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))). [resolve(6024,a,6020,a)]. 96.90/96.73 6025 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.73 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C))). [resolve(6025,a,5985,a)]. 96.90/96.73 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C))). [resolve(6025,a,6020,a)]. 96.90/96.74 6026 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.74 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C))). [resolve(6026,a,5985,a)]. 96.90/96.74 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C))). [resolve(6026,a,6020,a)]. 96.90/96.74 6027 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.75 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))). [resolve(6027,a,5985,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6027,a,5988,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6027,a,5999,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))). [resolve(6027,a,6020,a)]. 96.90/96.75 6028 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.75 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C))). [resolve(6028,a,5985,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C))). [resolve(6028,a,5988,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C))). [resolve(6028,a,5999,a)]. 96.90/96.75 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C))). [resolve(6028,a,6020,a)]. 96.90/96.75 6029 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.75 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)). [resolve(6029,a,5985,a)]. 96.90/96.77 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)). [resolve(6029,a,6020,a)]. 96.90/96.77 6030 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.77 6031 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 96.90/96.77 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))). [resolve(6031,a,5985,a)]. 96.90/96.77 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))). [resolve(6031,a,5988,a)]. 97.09/96.93 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))). [resolve(6031,a,5999,a)]. 97.09/96.93 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))). [resolve(6031,a,6020,a)]. 97.09/96.93 6032 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(2173)]. 97.09/96.93 6033 -number(A) | -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_96_right__distrib__number__of) # label(axiom). [clausify(2283)]. 97.09/96.93 6034 -number(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_168_power2__eq__square__number__of) # label(axiom). [clausify(2407)]. 97.09/96.93 6035 -number(A) | -ord(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),B) # label(fact_4989_max__number__of) # label(axiom). [clausify(2446)]. 97.09/96.93 Derived: -ord(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A). [resolve(6035,a,5985,a)]. 97.32/97.18 Derived: -ord(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),A). [resolve(6035,a,5988,a)]. 97.32/97.18 Derived: -ord(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),A). [resolve(6035,a,5999,a)]. 97.32/97.18 Derived: -ord(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A). [resolve(6035,a,6020,a)]. 97.32/97.18 6036 -number(A) | -ord(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),C) # label(fact_4989_max__number__of) # label(axiom). [clausify(2446)]. 97.32/97.18 Derived: -ord(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B). [resolve(6036,a,5985,a)]. 97.32/97.18 Derived: -ord(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),B). [resolve(6036,a,5988,a)]. 97.32/97.18 Derived: -ord(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),B). [resolve(6036,a,5999,a)]. 97.32/97.18 Derived: -ord(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B). [resolve(6036,a,6020,a)]. 97.32/97.18 6037 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom). [clausify(2819)]. 97.32/97.19 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)) | ti(quickcheck_code_int,C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)). [resolve(6037,b,5985,a)]. 97.32/97.19 Derived: -field_inverse_zero(real) | hAPP(int,real,number_number_of(real),A) = zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(int,real,number_number_of(real),A)) | ti(real,C) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(int,real,number_number_of(real),A)). [resolve(6037,b,5988,a)]. 97.32/97.19 Derived: -field_inverse_zero(rat) | hAPP(int,rat,number_number_of(rat),A) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),A)) | ti(rat,C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),A)). [resolve(6037,b,5999,a)]. 97.32/97.19 Derived: -field_inverse_zero(code_code_numeral) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)) | ti(code_code_numeral,C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)). [resolve(6037,b,6020,a)]. 97.32/97.19 6038 -field_inverse_zero(A) | -number(A) | ti(A,B) != zero_zero(A) | hAPP(int,A,number_number_of(A),C) != zero_zero(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom). [clausify(2819)]. 97.32/97.19 Derived: -field_inverse_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)). [resolve(6038,b,5985,a)]. 97.32/97.19 Derived: -field_inverse_zero(real) | ti(real,A) != zero_zero(real) | hAPP(int,real,number_number_of(real),B) != zero_zero(real) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B)). [resolve(6038,b,5988,a)]. 97.32/97.19 Derived: -field_inverse_zero(rat) | ti(rat,A) != zero_zero(rat) | hAPP(int,rat,number_number_of(rat),B) != zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B)). [resolve(6038,b,5999,a)]. 97.32/97.19 Derived: -field_inverse_zero(code_code_numeral) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B) != zero_zero(code_code_numeral) | ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)). [resolve(6038,b,6020,a)]. 97.32/97.20 6039 -field_inverse_zero(A) | -number(A) | ti(A,B) != zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom). [clausify(2819)]. 97.32/97.20 Derived: -field_inverse_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)) | ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)). [resolve(6039,b,5985,a)]. 97.32/97.20 Derived: -field_inverse_zero(real) | ti(real,A) != zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C)) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(int,real,number_number_of(real),C)). [resolve(6039,b,5988,a)]. 97.32/97.20 Derived: -field_inverse_zero(rat) | ti(rat,A) != zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),C)) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),C)). [resolve(6039,b,5999,a)]. 97.32/97.20 Derived: -field_inverse_zero(code_code_numeral) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | ti(code_code_numeral,B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)) | ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)). [resolve(6039,b,6020,a)]. 97.32/97.20 6040 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) != zero_zero(A) | ti(A,C) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom). [clausify(2819)]. 97.32/97.20 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)). [resolve(6040,b,5985,a)]. 97.32/97.20 Derived: -field_inverse_zero(real) | hAPP(int,real,number_number_of(real),A) != zero_zero(real) | ti(real,B) = zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)). [resolve(6040,b,5988,a)]. 97.32/97.20 Derived: -field_inverse_zero(rat) | hAPP(int,rat,number_number_of(rat),A) != zero_zero(rat) | ti(rat,B) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)). [resolve(6040,b,5999,a)]. 97.32/97.20 Derived: -field_inverse_zero(code_code_numeral) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A) != zero_zero(code_code_numeral) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)). [resolve(6040,b,6020,a)]. 97.32/97.20 6041 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom). [clausify(2819)]. 97.42/97.26 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)) | ti(quickcheck_code_int,C) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)). [resolve(6041,b,5985,a)]. 97.42/97.26 Derived: -field_inverse_zero(real) | hAPP(int,real,number_number_of(real),A) = zero_zero(real) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(int,real,number_number_of(real),A)) | ti(real,C) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(int,real,number_number_of(real),A)). [resolve(6041,b,5988,a)]. 97.42/97.26 Derived: -field_inverse_zero(rat) | hAPP(int,rat,number_number_of(rat),A) = zero_zero(rat) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),A)) | ti(rat,C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),A)). [resolve(6041,b,5999,a)]. 97.42/97.26 Derived: -field_inverse_zero(code_code_numeral) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)) | ti(code_code_numeral,C) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)). [resolve(6041,b,6020,a)]. 97.42/97.26 6042 -ring(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_491_right__diff__distrib__number__of) # label(axiom). [clausify(2898)]. 97.42/97.26 Derived: -ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),B),C)). [resolve(6042,b,5985,a)]. 97.42/97.26 Derived: -ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)). [resolve(6042,b,5999,a)]. 97.57/97.41 Derived: -ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),B),C)). [resolve(6042,b,6020,a)]. 97.57/97.41 6043 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | ti(A,C) != zero_zero(A) | hAPP(int,A,number_number_of(A),D) = zero_zero(A) # label(fact_1724_eq__divide__eq__number__of) # label(axiom). [clausify(3143)]. 97.57/97.41 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),B) != hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) | ti(quickcheck_code_int,B) != zero_zero(quickcheck_code_int) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) = zero_zero(quickcheck_code_int). [resolve(6043,a,5985,a)]. 97.57/97.41 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) != hAPP(int,real,number_number_of(real),C) | ti(real,B) != zero_zero(real) | hAPP(int,real,number_number_of(real),C) = zero_zero(real). [resolve(6043,a,5988,a)]. 97.57/97.41 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) != hAPP(int,rat,number_number_of(rat),C) | ti(rat,B) != zero_zero(rat) | hAPP(int,rat,number_number_of(rat),C) = zero_zero(rat). [resolve(6043,a,5999,a)]. 97.57/97.41 Derived: -field_inverse_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),B) != hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) | ti(code_code_numeral,B) != zero_zero(code_code_numeral) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) = zero_zero(code_code_numeral). [resolve(6043,a,6020,a)]. 97.57/97.41 6044 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | ti(A,C) = zero_zero(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1724_eq__divide__eq__number__of) # label(axiom). [clausify(3143)]. 97.57/97.41 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),B) != hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),B). [resolve(6044,a,5985,a)]. 97.57/97.41 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) != hAPP(int,real,number_number_of(real),C) | ti(real,B) = zero_zero(real) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B). [resolve(6044,a,5988,a)]. 97.57/97.42 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) != hAPP(int,rat,number_number_of(rat),C) | ti(rat,B) = zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B). [resolve(6044,a,5999,a)]. 97.57/97.42 Derived: -field_inverse_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),B) != hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),B). [resolve(6044,a,6020,a)]. 97.57/97.42 6045 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | ti(A,C) = zero_zero(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1724_eq__divide__eq__number__of) # label(axiom). [clausify(3143)]. 97.57/97.42 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),B) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),B). [resolve(6045,a,5985,a)]. 97.57/97.42 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) = hAPP(int,real,number_number_of(real),C) | ti(real,B) = zero_zero(real) | ti(real,A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B). [resolve(6045,a,5988,a)]. 97.57/97.42 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) = hAPP(int,rat,number_number_of(rat),C) | ti(rat,B) = zero_zero(rat) | ti(rat,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B). [resolve(6045,a,5999,a)]. 97.57/97.42 Derived: -field_inverse_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),B) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | ti(code_code_numeral,A) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),B). [resolve(6045,a,6020,a)]. 97.57/97.42 6046 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | hAPP(int,A,number_number_of(A),D) != zero_zero(A) | ti(A,C) != zero_zero(A) # label(fact_1724_eq__divide__eq__number__of) # label(axiom). [clausify(3143)]. 97.57/97.42 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),B) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) != zero_zero(quickcheck_code_int). [resolve(6046,a,5985,a)]. 97.57/97.42 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) = hAPP(int,real,number_number_of(real),C) | hAPP(int,real,number_number_of(real),C) != zero_zero(real) | ti(real,B) != zero_zero(real). [resolve(6046,a,5988,a)]. 97.57/97.46 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) = hAPP(int,rat,number_number_of(rat),C) | hAPP(int,rat,number_number_of(rat),C) != zero_zero(rat) | ti(rat,B) != zero_zero(rat). [resolve(6046,a,5999,a)]. 97.57/97.46 Derived: -field_inverse_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),B) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) != zero_zero(code_code_numeral) | ti(code_code_numeral,B) != zero_zero(code_code_numeral). [resolve(6046,a,6020,a)]. 97.57/97.46 6047 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | hAPP(int,A,number_number_of(A),D) != zero_zero(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1724_eq__divide__eq__number__of) # label(axiom). [clausify(3143)]. 97.57/97.46 Derived: -field_inverse_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),B) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) | hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),B). [resolve(6047,a,5985,a)]. 97.57/97.46 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) = hAPP(int,real,number_number_of(real),C) | hAPP(int,real,number_number_of(real),C) != zero_zero(real) | ti(real,A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B). [resolve(6047,a,5988,a)]. 97.57/97.46 Derived: -field_inverse_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) = hAPP(int,rat,number_number_of(rat),C) | hAPP(int,rat,number_number_of(rat),C) != zero_zero(rat) | ti(rat,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B). [resolve(6047,a,5999,a)]. 97.57/97.46 Derived: -field_inverse_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),B) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) | hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C) != zero_zero(code_code_numeral) | ti(code_code_numeral,A) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),B). [resolve(6047,a,6020,a)]. 97.57/97.46 6048 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.57/97.46 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6048,a,5985,a)]. 97.67/97.47 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6048,a,6020,a)]. 97.67/97.47 6049 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.67/97.47 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6049,a,5985,a)]. 97.67/97.47 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6049,a,5988,a)]. 97.67/97.47 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6049,a,5999,a)]. 97.67/97.48 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6049,a,6020,a)]. 97.67/97.48 6050 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.67/97.48 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6050,a,5985,a)]. 97.67/97.48 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6050,a,5988,a)]. 97.67/97.48 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6050,a,5999,a)]. 97.67/97.48 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6050,a,6020,a)]. 97.67/97.49 6051 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.67/97.49 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6051,a,5985,a)]. 97.67/97.49 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6051,a,6020,a)]. 97.67/97.49 6052 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.67/97.49 6053 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.67/97.49 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),A),C)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6053,a,5985,a)]. 97.67/97.49 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(int,real,number_number_of(real),B))). [resolve(6053,a,5988,a)]. 97.67/97.49 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6053,a,5999,a)]. 97.67/97.49 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),A),C)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6053,a,6020,a)]. 97.67/97.49 6054 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.69/97.51 6055 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(int,A,number_number_of(A),D))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.69/97.51 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C))). [resolve(6055,a,5985,a)]. 97.69/97.51 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C))). [resolve(6055,a,6020,a)]. 97.69/97.51 6056 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.69/97.51 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6056,a,5985,a)]. 97.69/97.51 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(6056,a,5988,a)]. 97.69/97.51 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(6056,a,5999,a)]. 97.69/97.51 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6056,a,6020,a)]. 97.69/97.51 6057 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(3196)]. 97.69/97.51 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(6057,a,5985,a)]. 97.69/97.51 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(6057,a,6020,a)]. 97.89/97.71 6058 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom). [assumption]. 97.89/97.71 Derived: -monoid_mult(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(6058,a,5986,a)]. 97.89/97.71 Derived: -ring(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),C)),hAPP(int,nat,number_number_of(nat),B)). [resolve(6058,a,5987,b)]. 97.89/97.71 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)). [resolve(6058,a,5989,a)]. 97.89/97.71 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6058,a,5990,a)]. 97.89/97.71 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6058,a,5991,a)]. 97.89/97.71 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6058,a,5992,a)]. 97.89/97.71 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6058,a,5993,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),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)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6058,a,5994,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),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_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6058,a,5995,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6058,a,5996,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6058,a,5997,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)). [resolve(6058,a,5998,a)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6000,b)]. 97.89/97.72 Derived: -linord1117847801e_zero(nat) | 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6001,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6002,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6003,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6004,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6005,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6006,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),A)),hAPP(int,nat,number_number_of(nat),C))). [resolve(6058,a,6007,b)]. 97.89/97.73 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6008,b)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6009,b)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6010,a)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6011,a)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6012,a)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6058,a,6013,a)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6058,a,6014,a)]. 97.89/97.74 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6058,a,6015,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -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),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6058,a,6016,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6017,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(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),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6018,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6058,a,6019,a)]. 97.89/97.75 Derived: number_number_of(nat) = ti(fun(int,nat),number_number_of(nat)). [resolve(6058,a,6021,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C)),B)). [resolve(6058,a,6023,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))). [resolve(6058,a,6024,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C))). [resolve(6058,a,6025,a)]. 97.89/97.75 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C))). [resolve(6058,a,6026,a)]. 97.89/97.76 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))). [resolve(6058,a,6027,a)]. 97.89/97.76 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C))). [resolve(6058,a,6028,a)]. 97.89/97.76 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)). [resolve(6058,a,6029,a)]. 97.89/97.76 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))). [resolve(6058,a,6031,a)]. 97.89/97.76 Derived: -ord(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),A). [resolve(6058,a,6035,a)]. 97.89/97.76 Derived: -ord(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),B). [resolve(6058,a,6036,a)]. 97.89/97.76 Derived: -field_inverse_zero(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)) | ti(nat,C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)). [resolve(6058,a,6037,b)]. 97.89/97.76 Derived: -field_inverse_zero(nat) | ti(nat,A) != zero_zero(nat) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)). [resolve(6058,a,6038,b)]. 97.89/97.76 Derived: -field_inverse_zero(nat) | ti(nat,A) != zero_zero(nat) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),C)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),C)). [resolve(6058,a,6039,b)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | ti(nat,B) = zero_zero(nat) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)). [resolve(6058,a,6040,b)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)) | ti(nat,C) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)). [resolve(6058,a,6041,b)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),B) != hAPP(int,nat,number_number_of(nat),C) | ti(nat,B) != zero_zero(nat) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat). [resolve(6058,a,6043,a)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),B) != hAPP(int,nat,number_number_of(nat),C) | ti(nat,B) = zero_zero(nat) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B). [resolve(6058,a,6044,a)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),B) = hAPP(int,nat,number_number_of(nat),C) | ti(nat,B) = zero_zero(nat) | ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B). [resolve(6058,a,6045,a)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),B) = hAPP(int,nat,number_number_of(nat),C) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) | ti(nat,B) != zero_zero(nat). [resolve(6058,a,6046,a)]. 97.89/97.77 Derived: -field_inverse_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),B) = hAPP(int,nat,number_number_of(nat),C) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) | ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B). [resolve(6058,a,6047,a)]. 97.89/97.77 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6048,a)]. 97.89/97.77 Derived: -linord1117847801e_zero(nat) | 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(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6049,a)]. 97.89/97.77 Derived: -linord1117847801e_zero(nat) | 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(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6050,a)]. 97.89/97.77 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6051,a)]. 98.08/97.90 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),A),C)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6053,a)]. 98.08/97.90 Derived: -linord1117847801e_zero(nat) | -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),A)),hAPP(int,nat,number_number_of(nat),C))). [resolve(6058,a,6055,a)]. 98.08/97.90 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6056,a)]. 98.08/97.90 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A)),hAPP(int,nat,number_number_of(nat),B))). [resolve(6058,a,6057,a)]. 98.08/97.90 6059 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | ti(A,C) != zero_zero(A) | hAPP(int,A,number_number_of(A),D) = zero_zero(A) # label(fact_1725_divide__eq__eq__number__of) # label(axiom). [clausify(3514)]. 98.08/97.90 6060 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | ti(A,C) = zero_zero(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1725_divide__eq__eq__number__of) # label(axiom). [clausify(3514)]. 98.08/97.90 6061 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | ti(A,C) = zero_zero(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1725_divide__eq__eq__number__of) # label(axiom). [clausify(3514)]. 98.08/97.90 6062 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | hAPP(int,A,number_number_of(A),D) != zero_zero(A) | ti(A,C) != zero_zero(A) # label(fact_1725_divide__eq__eq__number__of) # label(axiom). [clausify(3514)]. 98.08/97.90 6063 -number(A) | -field_inverse_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | hAPP(int,A,number_number_of(A),D) != zero_zero(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) # label(fact_1725_divide__eq__eq__number__of) # label(axiom). [clausify(3514)]. 98.08/97.90 6064 number(complex) # label(arity_Complex_Ocomplex___Int_Onumber) # label(axiom). [assumption]. 98.08/97.90 Derived: -monoid_mult(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(6064,a,5986,a)]. 98.08/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)). [resolve(6064,a,5989,a)]. 98.08/97.91 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6064,a,5990,a)]. 98.08/97.91 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6064,a,5991,a)]. 98.08/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6064,a,5992,a)]. 98.08/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6064,a,5993,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6064,a,5994,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6064,a,5995,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6064,a,5996,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6064,a,5997,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)). [resolve(6064,a,5998,a)]. 98.11/97.91 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6000,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6001,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6002,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6003,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6004,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6005,b)]. 98.11/97.92 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6006,b)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(int,complex,number_number_of(complex),C))). [resolve(6064,a,6007,b)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6008,b)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6009,b)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6010,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6011,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6012,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6064,a,6013,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6064,a,6014,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6064,a,6015,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6064,a,6016,a)]. 98.11/97.93 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6017,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6018,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6064,a,6019,a)]. 98.14/97.94 Derived: number_number_of(complex) = ti(fun(int,complex),number_number_of(complex)). [resolve(6064,a,6021,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)),B)). [resolve(6064,a,6023,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))). [resolve(6064,a,6024,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C))). [resolve(6064,a,6025,a)]. 98.14/97.94 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C))). [resolve(6064,a,6026,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))). [resolve(6064,a,6027,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C))). [resolve(6064,a,6028,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)). [resolve(6064,a,6029,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C))). [resolve(6064,a,6030,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))). [resolve(6064,a,6031,a)]. 98.14/97.95 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),C))). [resolve(6064,a,6032,a)]. 98.14/97.96 Derived: -ord(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),ord_max(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),A). [resolve(6064,a,6035,a)]. 98.14/97.96 Derived: -ord(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),ord_max(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),B). [resolve(6064,a,6036,a)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(int,complex,number_number_of(complex),A) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)) | ti(complex,C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)). [resolve(6064,a,6037,b)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | ti(complex,A) != zero_zero(complex) | hAPP(int,complex,number_number_of(complex),B) != zero_zero(complex) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)). [resolve(6064,a,6038,b)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | ti(complex,A) != zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),C)) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),C)). [resolve(6064,a,6039,b)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(int,complex,number_number_of(complex),A) != zero_zero(complex) | ti(complex,B) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)). [resolve(6064,a,6040,b)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(int,complex,number_number_of(complex),A) = zero_zero(complex) | ti(complex,B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)) | ti(complex,C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)). [resolve(6064,a,6041,b)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B) != hAPP(int,complex,number_number_of(complex),C) | ti(complex,B) != zero_zero(complex) | hAPP(int,complex,number_number_of(complex),C) = zero_zero(complex). [resolve(6064,a,6043,a)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B) != hAPP(int,complex,number_number_of(complex),C) | ti(complex,B) = zero_zero(complex) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B). [resolve(6064,a,6044,a)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B) = hAPP(int,complex,number_number_of(complex),C) | ti(complex,B) = zero_zero(complex) | ti(complex,A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B). [resolve(6064,a,6045,a)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B) = hAPP(int,complex,number_number_of(complex),C) | hAPP(int,complex,number_number_of(complex),C) != zero_zero(complex) | ti(complex,B) != zero_zero(complex). [resolve(6064,a,6046,a)]. 98.14/97.96 Derived: -field_inverse_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B) = hAPP(int,complex,number_number_of(complex),C) | hAPP(int,complex,number_number_of(complex),C) != zero_zero(complex) | ti(complex,A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B). [resolve(6064,a,6047,a)]. 98.14/97.96 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6048,a)]. 98.14/97.96 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6049,a)]. 98.14/97.96 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6050,a)]. 98.14/97.96 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6051,a)]. 98.14/97.96 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6052,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6053,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),C)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6054,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(int,complex,number_number_of(complex),C))). [resolve(6064,a,6055,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6056,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(int,complex,number_number_of(complex),B))). [resolve(6064,a,6057,a)]. 98.28/98.13 6065 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.28/98.13 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6065,a,5985,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(6065,a,5988,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6065,a,5999,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6065,a,6020,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6065,a,6058,a)]. 98.28/98.13 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6065,a,6064,a)]. 98.28/98.14 6066 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.28/98.14 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6066,a,5985,a)]. 98.28/98.14 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6066,a,6020,a)]. 98.28/98.14 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6066,a,6058,a)]. 98.28/98.14 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6066,a,6064,a)]. 98.28/98.15 6067 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.28/98.15 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6067,a,5985,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(int,real,number_number_of(real),A)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(int,real,number_number_of(real),A)))). [resolve(6067,a,5988,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),A)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6067,a,5999,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6067,a,6020,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6067,a,6058,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6067,a,6064,a)]. 98.28/98.15 6068 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.28/98.15 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6068,a,5985,a)]. 98.28/98.15 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6068,a,6020,a)]. 98.35/98.16 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6068,a,6058,a)]. 98.35/98.16 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6068,a,6064,a)]. 98.35/98.16 6069 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.35/98.16 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(6069,a,5985,a)]. 98.35/98.16 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B)))). [resolve(6069,a,5988,a)]. 98.35/98.16 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B)))). [resolve(6069,a,5999,a)]. 98.35/98.17 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(6069,a,6020,a)]. 98.35/98.17 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(6069,a,6058,a)]. 98.35/98.17 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6069,a,6064,a)]. 98.35/98.17 6070 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.35/98.17 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6070,a,6064,a)]. 98.35/98.17 6071 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.37/98.18 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(6071,a,6064,a)]. 98.37/98.18 6072 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.37/98.18 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6072,a,5985,a)]. 98.37/98.18 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6072,a,6020,a)]. 98.37/98.18 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6072,a,6058,a)]. 98.37/98.18 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6072,a,6064,a)]. 98.37/98.18 6073 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.37/98.18 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6073,a,5985,a)]. 98.37/98.18 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6073,a,6020,a)]. 98.37/98.18 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6073,a,6058,a)]. 98.37/98.19 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6073,a,6064,a)]. 98.37/98.19 6074 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(3896)]. 98.37/98.19 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(6074,a,5985,a)]. 98.37/98.19 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(6074,a,5988,a)]. 98.37/98.19 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(6074,a,5999,a)]. 98.37/98.19 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(6074,a,6020,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)))). [resolve(6074,a,6058,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(6074,a,6064,a)]. 98.44/98.27 6075 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom). [assumption]. 98.44/98.27 Derived: -monoid_mult(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(6075,a,5986,a)]. 98.44/98.27 Derived: -ring(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(int,int,number_number_of(int),B)). [resolve(6075,a,5987,b)]. 98.44/98.27 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A))),C)). [resolve(6075,a,5989,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6075,a,5990,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6075,a,5991,a)]. 98.44/98.27 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6075,a,5992,a)]. 98.44/98.27 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6075,a,5993,a)]. 98.44/98.27 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),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),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6075,a,5994,a)]. 98.44/98.27 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),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_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6075,a,5995,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(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),B),hAPP(int,int,number_number_of(int),A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6075,a,5996,a)]. 98.44/98.27 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6075,a,5997,a)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A))),C)). [resolve(6075,a,5998,a)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6000,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6001,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6002,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6003,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C))) | 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_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6004,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(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),hAPP(int,int,number_number_of(int),B)),C)),A)) | -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_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6005,b)]. 98.44/98.28 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(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),hAPP(int,int,number_number_of(int),B)),C)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6006,b)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | -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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),A)),hAPP(int,int,number_number_of(int),C))). [resolve(6075,a,6007,b)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6008,b)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6009,b)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6010,a)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6011,a)]. 98.44/98.29 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6012,a)]. 98.44/98.29 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6013,a)]. 98.44/98.30 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6014,a)]. 98.44/98.30 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -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),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6015,a)]. 98.44/98.30 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -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),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6016,a)]. 98.44/98.30 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6017,a)]. 98.44/98.30 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(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),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6018,a)]. 98.44/98.30 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6019,a)]. 98.44/98.30 Derived: number_number_of(int) = ti(fun(int,int),number_number_of(int)). [resolve(6075,a,6021,a)]. 98.44/98.30 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)),B)). [resolve(6075,a,6023,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(6075,a,6024,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C))). [resolve(6075,a,6025,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C))). [resolve(6075,a,6026,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))). [resolve(6075,a,6027,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C))). [resolve(6075,a,6028,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(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),hAPP(int,int,number_number_of(int),A)),C)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)). [resolve(6075,a,6029,a)]. 98.44/98.31 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(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),hAPP(int,int,number_number_of(int),A)),C)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))). [resolve(6075,a,6031,a)]. 98.44/98.31 Derived: -ord(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),A). [resolve(6075,a,6035,a)]. 98.44/98.32 Derived: -ord(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),B). [resolve(6075,a,6036,a)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,number_number_of(int),A) = zero_zero(int) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)) | ti(int,C) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)). [resolve(6075,a,6037,b)]. 98.44/98.32 Derived: -field_inverse_zero(int) | ti(int,A) != zero_zero(int) | hAPP(int,int,number_number_of(int),B) != zero_zero(int) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)). [resolve(6075,a,6038,b)]. 98.44/98.32 Derived: -field_inverse_zero(int) | ti(int,A) != zero_zero(int) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),C)). [resolve(6075,a,6039,b)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,number_number_of(int),A) != zero_zero(int) | ti(int,B) = zero_zero(int) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)). [resolve(6075,a,6040,b)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,number_number_of(int),A) = zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)) | ti(int,C) != hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)). [resolve(6075,a,6041,b)]. 98.44/98.32 Derived: -ring(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)). [resolve(6075,a,6042,b)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),B) != hAPP(int,int,number_number_of(int),C) | ti(int,B) != zero_zero(int) | hAPP(int,int,number_number_of(int),C) = zero_zero(int). [resolve(6075,a,6043,a)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),B) != hAPP(int,int,number_number_of(int),C) | ti(int,B) = zero_zero(int) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B). [resolve(6075,a,6044,a)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),B) = hAPP(int,int,number_number_of(int),C) | ti(int,B) = zero_zero(int) | ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B). [resolve(6075,a,6045,a)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),B) = hAPP(int,int,number_number_of(int),C) | hAPP(int,int,number_number_of(int),C) != zero_zero(int) | ti(int,B) != zero_zero(int). [resolve(6075,a,6046,a)]. 98.44/98.32 Derived: -field_inverse_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),B) = hAPP(int,int,number_number_of(int),C) | hAPP(int,int,number_number_of(int),C) != zero_zero(int) | ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B). [resolve(6075,a,6047,a)]. 98.44/98.32 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6048,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | 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,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6049,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | 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,number_number_of(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),hAPP(int,int,number_number_of(int),B)),A)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6050,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6051,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),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),inverse_divide(int),A),C)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6053,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | -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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),A)),hAPP(int,int,number_number_of(int),C))). [resolve(6075,a,6055,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6056,a)]. 98.52/98.33 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A)),hAPP(int,int,number_number_of(int),B))). [resolve(6075,a,6057,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(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),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6065,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6066,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -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),C),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6067,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6068,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -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),A),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(6075,a,6069,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6072,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6073,a)]. 98.52/98.34 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(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),B),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)))). [resolve(6075,a,6074,a)]. 98.74/98.58 6076 -division_ring(A) | -number(A) | hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom). [clausify(4057)]. 98.74/98.58 Derived: -division_ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,inverse_inverse(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),one_one(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)). [resolve(6076,b,5985,a)]. 98.74/98.58 Derived: -division_ring(real) | hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),A)). [resolve(6076,b,5988,a)]. 98.74/98.58 Derived: -division_ring(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)). [resolve(6076,b,5999,a)]. 98.74/98.58 Derived: -division_ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,inverse_inverse(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),one_one(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)). [resolve(6076,b,6020,a)]. 98.74/98.58 Derived: -division_ring(nat) | hAPP(nat,nat,inverse_inverse(nat),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6076,b,6058,a)]. 98.74/98.58 Derived: -division_ring(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)). [resolve(6076,b,6064,a)]. 98.74/98.58 Derived: -division_ring(int) | hAPP(int,int,inverse_inverse(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),one_one(int)),hAPP(int,int,number_number_of(int),A)). [resolve(6076,b,6075,a)]. 98.74/98.58 6077 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) != zero_zero(A) | ti(A,C) != zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom). [clausify(4312)]. 98.74/98.58 6078 -field_inverse_zero(A) | -number(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)) | hAPP(int,A,number_number_of(A),D) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D)) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom). [clausify(4312)]. 98.74/98.58 6079 -field_inverse_zero(A) | -number(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)) | ti(A,C) != zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D)) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom). [clausify(4312)]. 98.74/98.58 6080 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom). [clausify(4312)]. 98.80/98.62 6081 -field_inverse_zero(A) | -number(A) | hAPP(int,A,number_number_of(A),B) != zero_zero(A) | ti(A,C) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom). [clausify(4312)]. 98.80/98.62 6082 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B))),D)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.62 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)). [resolve(6082,b,5985,a)]. 98.80/98.62 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)). [resolve(6082,b,6020,a)]. 98.80/98.62 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)). [resolve(6082,b,6058,a)]. 98.80/98.62 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)). [resolve(6082,b,6064,a)]. 98.80/98.62 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A))),C)). [resolve(6082,b,6075,a)]. 98.80/98.63 6083 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.63 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(6083,b,5985,a)]. 98.80/98.63 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6083,b,6020,a)]. 98.80/98.63 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6083,b,6058,a)]. 98.80/98.63 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6083,b,6064,a)]. 98.80/98.63 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6083,b,6075,a)]. 98.80/98.63 6084 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.63 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6084,b,6064,a)]. 98.80/98.63 6085 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.63 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(6085,b,5985,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B))),A)). [resolve(6085,b,5988,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(6085,b,5999,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6085,b,6020,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6085,b,6058,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6085,b,6064,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6085,b,6075,a)]. 98.80/98.64 6086 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.64 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(6086,b,5985,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B))),A)). [resolve(6086,b,5988,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(6086,b,5999,a)]. 98.80/98.64 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6086,b,6020,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6086,b,6058,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6086,b,6064,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6086,b,6075,a)]. 98.80/98.65 6087 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.80/98.65 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))),A)). [resolve(6087,b,5985,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B))),A)). [resolve(6087,b,5988,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(6087,b,5999,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))),A)). [resolve(6087,b,6020,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(nat) | -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),B))),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)). [resolve(6087,b,6058,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6087,b,6064,a)]. 98.80/98.65 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(6087,b,6075,a)]. 98.80/98.65 6088 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.86/98.66 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(6088,b,6064,a)]. 98.86/98.66 6089 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.86/98.66 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(6089,b,5985,a)]. 98.86/98.66 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A))),B)). [resolve(6089,b,5988,a)]. 98.86/98.66 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A))),B)). [resolve(6089,b,5999,a)]. 98.86/98.66 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6089,b,6020,a)]. 98.86/98.67 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6089,b,6058,a)]. 98.86/98.67 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6089,b,6064,a)]. 98.86/98.67 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(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),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6089,b,6075,a)]. 98.86/98.67 6090 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B))),C)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.86/98.67 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),B)). [resolve(6090,b,5985,a)]. 98.86/98.68 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),B)). [resolve(6090,b,6020,a)]. 98.86/98.68 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A))),B)). [resolve(6090,b,6058,a)]. 98.86/98.68 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A))),B)). [resolve(6090,b,6064,a)]. 98.86/98.68 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A))),B)). [resolve(6090,b,6075,a)]. 98.86/98.68 6091 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B))),D)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(4353)]. 98.86/98.68 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A))),C)). [resolve(6091,b,5985,a)]. 98.86/98.71 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))),C)). [resolve(6091,b,6020,a)]. 98.86/98.71 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),A)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),hAPP(int,nat,number_number_of(nat),A))),C)). [resolve(6091,b,6058,a)]. 98.86/98.71 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),A)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(int,complex,number_number_of(complex),A))),C)). [resolve(6091,b,6064,a)]. 98.86/98.71 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),hAPP(int,int,number_number_of(int),A))),C)). [resolve(6091,b,6075,a)]. 98.86/98.71 6092 -number(A) | -monoid_mult(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom). [clausify(4389)]. 98.86/98.71 Derived: -monoid_mult(quickcheck_code_int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,5985,a)]. 98.86/98.71 Derived: -monoid_mult(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,5988,a)]. 98.86/98.71 Derived: -monoid_mult(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,5999,a)]. 98.86/98.71 Derived: -monoid_mult(code_code_numeral) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,6020,a)]. 98.86/98.71 Derived: -monoid_mult(nat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,6058,a)]. 98.86/98.71 Derived: -monoid_mult(complex) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,6064,a)]. 98.86/98.71 Derived: -monoid_mult(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6092,a,6075,a)]. 98.86/98.71 6093 -number(A) | -monoid_mult(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom). [clausify(4389)]. 98.86/98.71 Derived: -monoid_mult(quickcheck_code_int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,5985,a)]. 98.86/98.72 Derived: -monoid_mult(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,5988,a)]. 98.86/98.72 Derived: -monoid_mult(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,5999,a)]. 98.86/98.72 Derived: -monoid_mult(code_code_numeral) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,6020,a)]. 98.86/98.72 Derived: -monoid_mult(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,6058,a)]. 98.86/98.72 Derived: -monoid_mult(complex) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,6064,a)]. 99.18/99.01 Derived: -monoid_mult(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(6093,a,6075,a)]. 99.18/99.01 6094 -ord(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),C) # label(fact_4831_min__number__of) # label(axiom). [clausify(4775)]. 99.18/99.01 Derived: -ord(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B). [resolve(6094,b,5985,a)]. 99.18/99.01 Derived: -ord(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),B). [resolve(6094,b,5988,a)]. 99.18/99.01 Derived: -ord(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),B). [resolve(6094,b,5999,a)]. 99.18/99.01 Derived: -ord(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B). [resolve(6094,b,6020,a)]. 99.18/99.01 Derived: -ord(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),B). [resolve(6094,b,6058,a)]. 99.18/99.01 Derived: -ord(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),ord_min(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),B). [resolve(6094,b,6064,a)]. 99.18/99.02 Derived: -ord(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),B). [resolve(6094,b,6075,a)]. 99.18/99.02 6095 -ord(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) = hAPP(int,A,number_number_of(A),B) # label(fact_4831_min__number__of) # label(axiom). [clausify(4775)]. 99.18/99.02 Derived: -ord(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A). [resolve(6095,b,5985,a)]. 99.18/99.02 Derived: -ord(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)) = hAPP(int,real,number_number_of(real),A). [resolve(6095,b,5988,a)]. 99.18/99.02 Derived: -ord(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B)) = hAPP(int,rat,number_number_of(rat),A). [resolve(6095,b,5999,a)]. 99.18/99.02 Derived: -ord(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A). [resolve(6095,b,6020,a)]. 99.18/99.02 Derived: -ord(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),A). [resolve(6095,b,6058,a)]. 99.18/99.02 Derived: -ord(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),ord_min(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,complex,number_number_of(complex),B)) = hAPP(int,complex,number_number_of(complex),A). [resolve(6095,b,6064,a)]. 99.18/99.02 Derived: -ord(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(int,int,number_number_of(int),A). [resolve(6095,b,6075,a)]. 99.28/99.10 6096 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.28/99.10 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),A))). [resolve(6096,a,5985,a)]. 99.28/99.10 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),A))). [resolve(6096,a,6020,a)]. 99.28/99.10 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),A))). [resolve(6096,a,6058,a)]. 99.28/99.10 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A))). [resolve(6096,a,6064,a)]. 99.28/99.10 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),C)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),A))). [resolve(6096,a,6075,a)]. 99.31/99.11 6097 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.31/99.11 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A))). [resolve(6097,a,5985,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(6097,a,5988,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(6097,a,5999,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A))). [resolve(6097,a,6020,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(nat) | 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),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A))). [resolve(6097,a,6058,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A))). [resolve(6097,a,6064,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | 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,number_number_of(int),B)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A))). [resolve(6097,a,6075,a)]. 99.31/99.11 6098 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.31/99.11 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A))). [resolve(6098,a,5985,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(6098,a,5988,a)]. 99.31/99.11 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(6098,a,5999,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A))). [resolve(6098,a,6020,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(nat) | 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),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A))). [resolve(6098,a,6058,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A))). [resolve(6098,a,6064,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A))). [resolve(6098,a,6075,a)]. 99.31/99.12 6099 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.31/99.12 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),B))). [resolve(6099,a,5985,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B))). [resolve(6099,a,6020,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B)),C)) | -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),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),B))). [resolve(6099,a,6058,a)]. 99.31/99.12 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B))). [resolve(6099,a,6064,a)]. 99.31/99.12 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),A)),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),B))). [resolve(6099,a,6075,a)]. 99.31/99.12 6100 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.31/99.12 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),B))). [resolve(6100,a,5985,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B))). [resolve(6100,a,6020,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),B))). [resolve(6100,a,6058,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B))). [resolve(6100,a,6064,a)]. 99.31/99.13 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),A)),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),B))). [resolve(6100,a,6075,a)]. 99.31/99.13 6101 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.31/99.13 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),B))). [resolve(6101,a,5985,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(6101,a,5988,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(6101,a,5999,a)]. 99.31/99.13 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B))). [resolve(6101,a,6020,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),B))). [resolve(6101,a,6058,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B))). [resolve(6101,a,6064,a)]. 99.34/99.14 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),A)),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),B))). [resolve(6101,a,6075,a)]. 99.34/99.14 6102 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.34/99.14 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),B))). [resolve(6102,a,5985,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(6102,a,5988,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(6102,a,5999,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B))). [resolve(6102,a,6020,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),B))). [resolve(6102,a,6058,a)]. 99.34/99.14 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),A)),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),B))). [resolve(6102,a,6064,a)]. 99.34/99.15 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),A)),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),B))). [resolve(6102,a,6075,a)]. 99.34/99.15 6103 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.34/99.15 Derived: -linord1117847801e_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),A)),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A))). [resolve(6103,a,5985,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),A)),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A))). [resolve(6103,a,6020,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(nat) | -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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),A)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A))). [resolve(6103,a,6058,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),A)),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A))). [resolve(6103,a,6064,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),A)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A))). [resolve(6103,a,6075,a)]. 99.34/99.15 6104 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.34/99.15 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),C),A))). [resolve(6104,a,5985,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(6104,a,5988,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(6104,a,5999,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),A))). [resolve(6104,a,6020,a)]. 99.34/99.15 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),B)),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),A))). [resolve(6104,a,6058,a)]. 99.34/99.16 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A))). [resolve(6104,a,6064,a)]. 99.34/99.16 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),A))). [resolve(6104,a,6075,a)]. 99.34/99.16 6105 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4857)]. 99.34/99.16 Derived: -linord1117847801e_zero(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(quickcheck_code_int),B),A))). [resolve(6105,a,5985,a)]. 99.34/99.16 Derived: -linord1117847801e_zero(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),B),A))). [resolve(6105,a,6020,a)]. 102.67/102.49 Derived: -linord1117847801e_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),B),A))). [resolve(6105,a,6058,a)]. 102.67/102.49 Derived: -linord1117847801e_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),zero_zero(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),A))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),hAPP(int,complex,number_number_of(complex),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A))). [resolve(6105,a,6064,a)]. 102.67/102.49 Derived: -linord1117847801e_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),C)),hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),B),A))). [resolve(6105,a,6075,a)]. 102.67/102.49 6106 -zero(A) | -metric_space(A) | -real_n2089651433ebra_1(B) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),combk(A,B),C)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4562_LIM__not__zero) # label(axiom). [clausify(459)]. 102.67/102.49 6107 zero(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ozero) # label(axiom). [assumption]. 102.67/102.49 Derived: -metric_space(quickcheck_code_int) | -real_n2089651433ebra_1(A) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(filter(A),bool,hAPP(quickcheck_code_int,fun(filter(A),bool),hAPP(fun(A,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(A),bool)),tendsto(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),combk(quickcheck_code_int,A),B)),zero_zero(quickcheck_code_int)),hAPP(A,filter(A),at(A),C))). [resolve(6106,a,6107,a)]. 102.67/102.49 6108 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption]. 102.67/102.49 Derived: -metric_space(int) | -real_n2089651433ebra_1(A) | ti(int,B) = zero_zero(int) | -hBOOL(hAPP(filter(A),bool,hAPP(int,fun(filter(A),bool),hAPP(fun(A,int),fun(int,fun(filter(A),bool)),tendsto(A,int),hAPP(int,fun(A,int),combk(int,A),B)),zero_zero(int)),hAPP(A,filter(A),at(A),C))). [resolve(6108,a,6106,a)]. 102.67/102.49 6109 -zero(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(638)]. 102.67/102.49 Derived: ti(quickcheck_code_int,zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(6109,a,6107,a)]. 102.67/102.49 Derived: ti(int,zero_zero(int)) = zero_zero(int). [resolve(6109,a,6108,a)]. 102.67/102.49 6110 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption]. 102.67/102.49 Derived: -metric_space(nat) | -real_n2089651433ebra_1(A) | ti(nat,B) = zero_zero(nat) | -hBOOL(hAPP(filter(A),bool,hAPP(nat,fun(filter(A),bool),hAPP(fun(A,nat),fun(nat,fun(filter(A),bool)),tendsto(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),B)),zero_zero(nat)),hAPP(A,filter(A),at(A),C))). [resolve(6110,a,6106,a)]. 102.67/102.49 Derived: ti(nat,zero_zero(nat)) = zero_zero(nat). [resolve(6110,a,6109,a)]. 104.31/104.11 6111 zero(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ozero) # label(axiom). [assumption]. 104.31/104.11 Derived: -metric_space(code_code_numeral) | -real_n2089651433ebra_1(A) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(filter(A),bool,hAPP(code_code_numeral,fun(filter(A),bool),hAPP(fun(A,code_code_numeral),fun(code_code_numeral,fun(filter(A),bool)),tendsto(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),combk(code_code_numeral,A),B)),zero_zero(code_code_numeral)),hAPP(A,filter(A),at(A),C))). [resolve(6111,a,6106,a)]. 104.31/104.11 Derived: ti(code_code_numeral,zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(6111,a,6109,a)]. 104.31/104.11 6112 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom). [assumption]. 104.31/104.11 Derived: -metric_space(real) | -real_n2089651433ebra_1(A) | ti(real,B) = zero_zero(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),combk(real,A),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(6112,a,6106,a)]. 104.31/104.11 Derived: ti(real,zero_zero(real)) = zero_zero(real). [resolve(6112,a,6109,a)]. 104.31/104.11 6113 zero(complex) # label(arity_Complex_Ocomplex___Groups_Ozero) # label(axiom). [assumption]. 104.31/104.11 Derived: -metric_space(complex) | -real_n2089651433ebra_1(A) | ti(complex,B) = zero_zero(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),combk(complex,A),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(6113,a,6106,a)]. 104.31/104.11 Derived: ti(complex,zero_zero(complex)) = zero_zero(complex). [resolve(6113,a,6109,a)]. 104.31/104.11 6114 -zero(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(A,real,hAPP(nat,fun(A,real),C,zero_zero(nat)),zero_zero(A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(A,fun(nat,real),hAPP(fun(nat,fun(A,real)),fun(A,fun(nat,real)),combc(nat,A,real),C),zero_zero(A)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,hAPP(nat,fun(A,real),C,B),zero_zero(A))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),B))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom). [clausify(4561)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,zero_zero(nat)),zero_zero(quickcheck_code_int)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(quickcheck_code_int,fun(nat,real),hAPP(fun(nat,fun(quickcheck_code_int,real)),fun(quickcheck_code_int,fun(nat,real)),combc(nat,quickcheck_code_int,real),B),zero_zero(quickcheck_code_int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,A),zero_zero(quickcheck_code_int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6107,a)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(int,real,hAPP(nat,fun(int,real),B,zero_zero(nat)),zero_zero(int)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(int,fun(nat,real),hAPP(fun(nat,fun(int,real)),fun(int,fun(nat,real)),combc(nat,int,real),B),zero_zero(int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,hAPP(nat,fun(int,real),B,A),zero_zero(int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6108,a)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,real,hAPP(nat,fun(nat,real),B,zero_zero(nat)),zero_zero(nat)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),B),zero_zero(nat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(nat,fun(nat,real),B,A),zero_zero(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6110,a)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,zero_zero(nat)),zero_zero(code_code_numeral)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(code_code_numeral,fun(nat,real),hAPP(fun(nat,fun(code_code_numeral,real)),fun(code_code_numeral,fun(nat,real)),combc(nat,code_code_numeral,real),B),zero_zero(code_code_numeral)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,A),zero_zero(code_code_numeral))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6111,a)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(nat,fun(real,real),B,zero_zero(nat)),zero_zero(real)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),B),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),B,A),zero_zero(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6112,a)]. 104.31/104.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(complex,real,hAPP(nat,fun(complex,real),B,zero_zero(nat)),zero_zero(complex)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(complex,fun(nat,real),hAPP(fun(nat,fun(complex,real)),fun(complex,fun(nat,real)),combc(nat,complex,real),B),zero_zero(complex)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,hAPP(nat,fun(complex,real),B,A),zero_zero(complex))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6114,a,6113,a)]. 108.33/108.17 6115 zero(rat) # label(arity_Rat_Orat___Groups_Ozero) # label(axiom). [assumption]. 108.33/108.17 Derived: -metric_space(rat) | -real_n2089651433ebra_1(A) | ti(rat,B) = zero_zero(rat) | -hBOOL(hAPP(filter(A),bool,hAPP(rat,fun(filter(A),bool),hAPP(fun(A,rat),fun(rat,fun(filter(A),bool)),tendsto(A,rat),hAPP(rat,fun(A,rat),combk(rat,A),B)),zero_zero(rat)),hAPP(A,filter(A),at(A),C))). [resolve(6115,a,6106,a)]. 108.33/108.17 Derived: ti(rat,zero_zero(rat)) = zero_zero(rat). [resolve(6115,a,6109,a)]. 108.33/108.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(rat,real,hAPP(nat,fun(rat,real),B,zero_zero(nat)),zero_zero(rat)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(rat,fun(nat,real),hAPP(fun(nat,fun(rat,real)),fun(rat,fun(nat,real)),combc(nat,rat,real),B),zero_zero(rat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,hAPP(nat,fun(rat,real),B,A),zero_zero(rat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6115,a,6114,a)]. 108.33/108.17 6116 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_789_add__strict__left__mono) # label(axiom). [clausify(2753)]. 108.33/108.17 6117 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 108.33/108.17 6118 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 108.33/108.17 6119 ordere223160158up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 108.78/108.57 6120 ordere223160158up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 108.78/108.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(6116,a,6117,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(6116,a,6118,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))). [resolve(6116,a,6119,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))). [resolve(6116,a,6120,a)]. 108.78/108.57 6121 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_788_add__strict__mono) # label(axiom). [clausify(3036)]. 108.78/108.57 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6121,a,6117,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6121,a,6118,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6121,a,6119,a)]. 108.78/108.57 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6121,a,6120,a)]. 108.78/108.57 6122 ordere223160158up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__cancel__ab__semigroup_) # label(axiom). [assumption]. 108.78/108.57 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))). [resolve(6122,a,6116,a)]. 108.95/108.75 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6122,a,6121,a)]. 108.95/108.75 6123 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_824_add__less__le__mono) # label(axiom). [clausify(3335)]. 108.95/108.75 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6123,a,6117,a)]. 108.95/108.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6123,a,6118,a)]. 108.95/108.75 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6123,a,6119,a)]. 108.95/108.75 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6123,a,6120,a)]. 108.95/108.75 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6123,a,6122,a)]. 108.95/108.75 6124 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 108.95/108.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))). [resolve(6124,a,6116,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6124,a,6121,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6124,a,6123,a)]. 108.95/108.81 6125 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_823_add__le__less__mono) # label(axiom). [clausify(3563)]. 108.95/108.81 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6125,a,6117,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6125,a,6118,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(6125,a,6119,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),D))). [resolve(6125,a,6120,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),D))). [resolve(6125,a,6122,a)]. 108.95/108.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(6125,a,6124,a)]. 113.41/113.21 6126 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_790_add__strict__right__mono) # label(axiom). [clausify(4355)]. 113.41/113.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(6126,a,6117,a)]. 113.41/113.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(6126,a,6118,a)]. 113.41/113.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(6126,a,6119,a)]. 113.41/113.21 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C))). [resolve(6126,a,6120,a)]. 113.41/113.21 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C))). [resolve(6126,a,6122,a)]. 113.41/113.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(6126,a,6124,a)]. 113.41/113.21 6127 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 113.41/113.21 6128 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4944_minus__min__eq__max) # label(axiom). [clausify(123)]. 113.41/113.21 6129 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(727)]. 113.41/113.21 6130 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(727)]. 113.41/113.21 6131 -linord219039673up_add(A) | ti(A,B) != zero_zero(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2023_equal__neg__zero) # label(axiom). [clausify(872)]. 113.41/113.21 6132 -linord219039673up_add(A) | ti(A,B) = zero_zero(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2023_equal__neg__zero) # label(axiom). [clausify(872)]. 113.41/113.21 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6127,a,6128,a)]. 113.58/113.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6127,a,6129,a)]. 113.58/113.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6127,a,6130,a)]. 113.58/113.39 Derived: ti(real,A) != zero_zero(real) | ti(real,A) = hAPP(real,real,uminus_uminus(real),A). [resolve(6127,a,6131,a)]. 113.58/113.39 Derived: ti(real,A) = zero_zero(real) | ti(real,A) != hAPP(real,real,uminus_uminus(real),A). [resolve(6127,a,6132,a)]. 113.58/113.39 6133 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2056_minus__le__self__iff) # label(axiom). [clausify(1539)]. 113.58/113.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6133,a,6127,a)]. 113.58/113.39 6134 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2056_minus__le__self__iff) # label(axiom). [clausify(1539)]. 113.58/113.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6134,a,6127,a)]. 113.58/113.39 6135 linord219039673up_add(rat) # label(arity_Rat_Orat___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 113.58/113.39 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6135,a,6128,a)]. 113.58/113.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6135,a,6129,a)]. 113.58/113.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6135,a,6130,a)]. 113.58/113.39 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6135,a,6131,a)]. 113.58/113.39 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6135,a,6132,a)]. 113.58/113.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6135,a,6133,a)]. 113.58/113.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6135,a,6134,a)]. 113.58/113.39 6136 -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),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2063_neg__less__nonneg) # label(axiom). [clausify(2033)]. 113.58/113.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6136,a,6127,a)]. 113.58/113.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6136,a,6135,a)]. 113.74/113.59 6137 -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),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2063_neg__less__nonneg) # label(axiom). [clausify(2033)]. 113.74/113.59 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6137,a,6127,a)]. 113.74/113.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6137,a,6135,a)]. 113.74/113.59 6138 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 113.74/113.59 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6138,a,6128,a)]. 113.74/113.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6138,a,6129,a)]. 113.74/113.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6138,a,6130,a)]. 113.74/113.59 Derived: ti(int,A) != zero_zero(int) | ti(int,A) = hAPP(int,int,uminus_uminus(int),A). [resolve(6138,a,6131,a)]. 113.74/113.59 Derived: ti(int,A) = zero_zero(int) | ti(int,A) != hAPP(int,int,uminus_uminus(int),A). [resolve(6138,a,6132,a)]. 113.74/113.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6138,a,6133,a)]. 113.74/113.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6138,a,6134,a)]. 113.74/113.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6138,a,6136,a)]. 113.74/113.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6138,a,6137,a)]. 113.74/113.59 6139 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(2391)]. 113.74/113.59 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))). [resolve(6139,a,6127,a)]. 113.74/113.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))). [resolve(6139,a,6135,a)]. 113.74/113.59 6140 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(2391)]. 113.74/113.59 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))). [resolve(6140,a,6127,a)]. 114.23/114.06 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))). [resolve(6140,a,6135,a)]. 114.23/114.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))). [resolve(6140,a,6138,a)]. 114.23/114.06 6141 -linord219039673up_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),B) | ti(A,B) = zero_zero(A) # label(fact_2021_neg__equal__zero) # label(axiom). [clausify(2539)]. 114.23/114.06 6142 -linord219039673up_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),B) | ti(A,B) != zero_zero(A) # label(fact_2021_neg__equal__zero) # label(axiom). [clausify(2539)]. 114.23/114.06 6143 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4943_minus__max__eq__min) # label(axiom). [clausify(2765)]. 114.23/114.06 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6143,a,6127,a)]. 114.23/114.06 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6143,a,6135,a)]. 114.23/114.06 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6143,a,6138,a)]. 114.23/114.06 6144 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2058_le__minus__self__iff) # label(axiom). [clausify(2937)]. 114.23/114.06 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),A),hAPP(real,real,uminus_uminus(real),A))). [resolve(6144,a,6127,a)]. 114.23/114.06 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(6144,a,6135,a)]. 114.23/114.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))). [resolve(6144,a,6138,a)]. 114.23/114.06 6145 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2058_le__minus__self__iff) # label(axiom). [clausify(2937)]. 114.23/114.06 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),A),hAPP(real,real,uminus_uminus(real),A))). [resolve(6145,a,6127,a)]. 114.23/114.06 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(6145,a,6135,a)]. 114.23/114.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))). [resolve(6145,a,6138,a)]. 114.23/114.06 6146 -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,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(3201)]. 114.53/114.33 6147 -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,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(3201)]. 114.53/114.33 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,hAPP(real,fun(real,real),plus_plus(real),A),A))). [resolve(6147,a,6127,a)]. 114.53/114.33 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))). [resolve(6147,a,6135,a)]. 114.53/114.33 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,hAPP(int,fun(int,int),plus_plus(int),A),A))). [resolve(6147,a,6138,a)]. 114.53/114.33 6148 -linord219039673up_add(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) # label(fact_776_double__zero__sym) # label(axiom). [clausify(3312)]. 114.53/114.33 Derived: ti(real,A) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real). [resolve(6148,a,6127,a)]. 114.53/114.33 Derived: ti(rat,A) != zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = zero_zero(rat). [resolve(6148,a,6135,a)]. 114.53/114.33 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int). [resolve(6148,a,6138,a)]. 114.53/114.33 6149 -linord219039673up_add(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) # label(fact_776_double__zero__sym) # label(axiom). [clausify(3312)]. 114.53/114.33 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real). [resolve(6149,a,6127,a)]. 114.53/114.33 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) != zero_zero(rat). [resolve(6149,a,6135,a)]. 114.53/114.33 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int). [resolve(6149,a,6138,a)]. 114.53/114.33 6150 -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,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(3668)]. 114.53/114.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6150,a,6127,a)]. 114.53/114.33 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6150,a,6135,a)]. 114.53/114.33 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6150,a,6138,a)]. 114.53/114.33 6151 -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,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(3668)]. 114.53/114.33 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6151,a,6127,a)]. 118.84/118.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6151,a,6135,a)]. 118.84/118.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6151,a,6138,a)]. 118.84/118.69 6152 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_115_double__eq__0__iff) # label(axiom). [clausify(4094)]. 118.84/118.69 6153 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_115_double__eq__0__iff) # label(axiom). [clausify(4094)]. 118.84/118.69 6154 ring_div(int) # label(arity_Int_Oint___Divides_Oring__div) # label(axiom). [assumption]. 118.84/118.69 6155 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) # label(fact_946_mod__diff__right__eq) # label(axiom). [clausify(133)]. 118.84/118.69 6156 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_944_mod__diff__eq) # label(axiom). [clausify(653)]. 118.84/118.69 6157 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F)),C) # label(fact_943_mod__diff__cong) # label(axiom). [clausify(736)]. 118.84/118.69 6158 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2012_mod__minus__eq) # label(axiom). [clausify(761)]. 118.84/118.69 6159 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2086_dvd__div__neg) # label(axiom). [clausify(1016)]. 118.84/118.69 6160 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_2085_dvd__neg__div) # label(axiom). [clausify(1035)]. 118.84/118.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6154,a,6156,a)]. 118.84/118.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),E)),B). [resolve(6154,a,6157,a)]. 118.84/118.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,uminus_uminus(int),A)). [resolve(6154,a,6159,a)]. 118.84/118.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),B)),A). [resolve(6154,a,6160,a)]. 124.00/123.79 6161 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),D)),C) # label(fact_2011_mod__minus__cong) # label(axiom). [clausify(2905)]. 124.00/123.79 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),C)),B). [resolve(6161,a,6154,a)]. 124.00/123.79 6162 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_945_mod__diff__left__eq) # label(axiom). [clausify(4581)]. 124.00/123.79 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6162,a,6154,a)]. 124.00/123.79 6163 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom). [assumption]. 124.00/123.79 6164 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_323_mult__zero__left) # label(axiom). [clausify(164)]. 124.00/123.79 6165 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom). [assumption]. 124.00/123.79 6166 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1522)]. 124.00/123.79 Derived: -power(int) | -zero_neq_one(int) | -no_zero_divisors(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(6166,d,6163,a)]. 124.00/123.79 Derived: -power(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != zero_zero(nat) | ti(nat,A) = zero_zero(nat). [resolve(6166,d,6165,a)]. 124.00/123.79 6167 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) | zero_zero(nat) != C # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1522)]. 124.00/123.79 Derived: -power(int) | -zero_neq_one(int) | -no_zero_divisors(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int) | zero_zero(nat) != B. [resolve(6167,d,6163,a)]. 124.00/123.79 6168 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = zero_zero(A) | ti(A,B) != zero_zero(A) | zero_zero(nat) = C # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1522)]. 124.00/123.79 Derived: -power(int) | -zero_neq_one(int) | -no_zero_divisors(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = zero_zero(int) | ti(int,A) != zero_zero(int) | zero_zero(nat) = B. [resolve(6168,d,6163,a)]. 124.00/123.79 Derived: -power(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = zero_zero(nat) | ti(nat,A) != zero_zero(nat) | zero_zero(nat) = B. [resolve(6168,d,6165,a)]. 124.00/123.79 6169 -mult_zero(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom). [clausify(1707)]. 124.00/123.79 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(6169,a,6163,a)]. 124.00/123.79 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(6169,a,6165,a)]. 124.00/123.79 6170 mult_zero(real) # label(arity_RealDef_Oreal___Rings_Omult__zero) # label(axiom). [assumption]. 124.00/123.79 Derived: -power(real) | -zero_neq_one(real) | -no_zero_divisors(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(6170,a,6166,d)]. 124.31/124.13 Derived: -power(real) | -zero_neq_one(real) | -no_zero_divisors(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real) | zero_zero(nat) != B. [resolve(6170,a,6167,d)]. 124.31/124.13 Derived: -power(real) | -zero_neq_one(real) | -no_zero_divisors(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = zero_zero(real) | ti(real,A) != zero_zero(real) | zero_zero(nat) = B. [resolve(6170,a,6168,d)]. 124.31/124.13 Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)). [resolve(6170,a,6169,a)]. 124.31/124.13 6171 mult_zero(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Omult__zero) # label(axiom). [assumption]. 124.31/124.13 Derived: -power(code_code_numeral) | -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != zero_zero(code_code_numeral) | ti(code_code_numeral,A) = zero_zero(code_code_numeral). [resolve(6171,a,6166,d)]. 124.31/124.13 Derived: -power(code_code_numeral) | -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != zero_zero(code_code_numeral) | zero_zero(nat) != B. [resolve(6171,a,6167,d)]. 124.31/124.13 Derived: -power(code_code_numeral) | -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) = zero_zero(code_code_numeral) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | zero_zero(nat) = B. [resolve(6171,a,6168,d)]. 124.31/124.13 Derived: times_times(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),times_times(code_code_numeral)). [resolve(6171,a,6169,a)]. 124.31/124.13 6172 mult_zero(rat) # label(arity_Rat_Orat___Rings_Omult__zero) # label(axiom). [assumption]. 124.31/124.13 Derived: -power(rat) | -zero_neq_one(rat) | -no_zero_divisors(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(6172,a,6166,d)]. 124.31/124.13 Derived: -power(rat) | -zero_neq_one(rat) | -no_zero_divisors(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat) | zero_zero(nat) != B. [resolve(6172,a,6167,d)]. 124.31/124.13 Derived: -power(rat) | -zero_neq_one(rat) | -no_zero_divisors(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = zero_zero(rat) | ti(rat,A) != zero_zero(rat) | zero_zero(nat) = B. [resolve(6172,a,6168,d)]. 124.31/124.13 Derived: times_times(rat) = ti(fun(rat,fun(rat,rat)),times_times(rat)). [resolve(6172,a,6169,a)]. 124.31/124.13 6173 mult_zero(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Omult__zero) # label(axiom). [assumption]. 124.31/124.13 Derived: -power(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int). [resolve(6173,a,6166,d)]. 124.31/124.13 Derived: -power(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int) | zero_zero(nat) != B. [resolve(6173,a,6167,d)]. 124.31/124.13 Derived: -power(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | zero_zero(nat) = B. [resolve(6173,a,6168,d)]. 124.31/124.13 Derived: times_times(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),times_times(quickcheck_code_int)). [resolve(6173,a,6169,a)]. 125.22/125.02 6174 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_322_mult__zero__right) # label(axiom). [clausify(2797)]. 125.22/125.02 6175 mult_zero(complex) # label(arity_Complex_Ocomplex___Rings_Omult__zero) # label(axiom). [assumption]. 125.22/125.02 Derived: -power(complex) | -zero_neq_one(complex) | -no_zero_divisors(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex) | ti(complex,A) = zero_zero(complex). [resolve(6175,a,6166,d)]. 125.22/125.02 Derived: -power(complex) | -zero_neq_one(complex) | -no_zero_divisors(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex) | zero_zero(nat) != B. [resolve(6175,a,6167,d)]. 125.22/125.02 Derived: -power(complex) | -zero_neq_one(complex) | -no_zero_divisors(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) = zero_zero(complex) | ti(complex,A) != zero_zero(complex) | zero_zero(nat) = B. [resolve(6175,a,6168,d)]. 125.22/125.02 Derived: times_times(complex) = ti(fun(complex,fun(complex,complex)),times_times(complex)). [resolve(6175,a,6169,a)]. 125.22/125.02 6176 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_256_power__eq__0__iff__number__of) # label(axiom). [clausify(4077)]. 125.22/125.02 6177 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) != zero_zero(A) | hAPP(int,nat,number_number_of(nat),C) != zero_zero(nat) # label(fact_256_power__eq__0__iff__number__of) # label(axiom). [clausify(4077)]. 125.22/125.02 Derived: -no_zero_divisors(int) | -zero_neq_one(int) | -power(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(int) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6163,a)]. 125.22/125.02 Derived: -no_zero_divisors(nat) | -zero_neq_one(nat) | -power(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(nat) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6165,a)]. 125.22/125.02 Derived: -no_zero_divisors(real) | -zero_neq_one(real) | -power(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(real) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6170,a)]. 125.22/125.02 Derived: -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | -power(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(code_code_numeral) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6171,a)]. 125.22/125.02 Derived: -no_zero_divisors(rat) | -zero_neq_one(rat) | -power(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(rat) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6172,a)]. 125.22/125.02 Derived: -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | -power(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6173,a)]. 125.22/125.02 Derived: -no_zero_divisors(complex) | -zero_neq_one(complex) | -power(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B)) != zero_zero(complex) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat). [resolve(6177,a,6175,a)]. 125.22/125.02 6178 -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -power(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) = zero_zero(A) | ti(A,B) != zero_zero(A) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) # label(fact_256_power__eq__0__iff__number__of) # label(axiom). [clausify(4077)]. 134.62/134.42 Derived: -no_zero_divisors(int) | -zero_neq_one(int) | -power(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(int) | ti(int,A) != zero_zero(int) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6163,a)]. 134.62/134.42 Derived: -no_zero_divisors(nat) | -zero_neq_one(nat) | -power(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(nat) | ti(nat,A) != zero_zero(nat) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6165,a)]. 134.62/134.42 Derived: -no_zero_divisors(real) | -zero_neq_one(real) | -power(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(real) | ti(real,A) != zero_zero(real) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6170,a)]. 134.62/134.42 Derived: -no_zero_divisors(code_code_numeral) | -zero_neq_one(code_code_numeral) | -power(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(code_code_numeral) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6171,a)]. 134.62/134.42 Derived: -no_zero_divisors(rat) | -zero_neq_one(rat) | -power(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(rat) | ti(rat,A) != zero_zero(rat) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6172,a)]. 134.62/134.42 Derived: -no_zero_divisors(quickcheck_code_int) | -zero_neq_one(quickcheck_code_int) | -power(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6173,a)]. 134.62/134.42 Derived: -no_zero_divisors(complex) | -zero_neq_one(complex) | -power(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(complex) | ti(complex,A) != zero_zero(complex) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat). [resolve(6178,a,6175,a)]. 134.62/134.42 6179 -monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_778_add__0__left) # label(axiom). [clausify(778)]. 134.62/134.42 6180 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6181 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(1708)]. 134.62/134.42 6182 monoid_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6183 monoid_add(real) # label(arity_RealDef_Oreal___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6184 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6185 monoid_add(complex) # label(arity_Complex_Ocomplex___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6186 -monoid_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_775_add__0__right) # label(axiom). [clausify(3189)]. 134.62/134.42 6187 monoid_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6188 monoid_add(rat) # label(arity_Rat_Orat___Groups_Omonoid__add) # label(axiom). [assumption]. 134.62/134.42 6189 -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_1214_of__nat__eq__iff) # label(axiom). [clausify(688)]. 139.72/139.57 6190 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B. [resolve(6189,a,6190,a)]. 139.72/139.57 6191 -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_1214_of__nat__eq__iff) # label(axiom). [clausify(688)]. 139.72/139.57 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B. [resolve(6191,a,6190,a)]. 139.72/139.57 6192 semiring_char_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) != hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A = B. [resolve(6192,a,6189,a)]. 139.72/139.57 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A != B. [resolve(6192,a,6191,a)]. 139.72/139.57 6193 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)) != zero_zero(A) # label(fact_2486_of__nat__fact__not__zero) # label(axiom). [clausify(2556)]. 139.72/139.57 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(real). [resolve(6193,a,6190,a)]. 139.72/139.57 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(quickcheck_code_int). [resolve(6193,a,6192,a)]. 139.72/139.57 6194 semiring_char_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) != hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A = B. [resolve(6194,a,6189,a)]. 139.72/139.57 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A != B. [resolve(6194,a,6191,a)]. 139.72/139.57 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(code_code_numeral). [resolve(6194,a,6193,a)]. 139.72/139.57 6195 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(6195,a,6189,a)]. 139.72/139.57 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(6195,a,6191,a)]. 139.72/139.57 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(nat). [resolve(6195,a,6193,a)]. 139.72/139.57 6196 semiring_char_0(rat) # label(arity_Rat_Orat___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) != hAPP(nat,rat,semiring_1_of_nat(rat),B) | A = B. [resolve(6196,a,6189,a)]. 139.72/139.57 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(nat,rat,semiring_1_of_nat(rat),B) | A != B. [resolve(6196,a,6191,a)]. 139.72/139.57 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(rat). [resolve(6196,a,6193,a)]. 139.72/139.57 6197 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(int). [resolve(6197,a,6193,a)]. 139.72/139.57 6198 semiring_char_0(complex) # label(arity_Complex_Ocomplex___Nat_Osemiring__char__0) # label(axiom). [assumption]. 139.72/139.57 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) != hAPP(nat,complex,semiring_1_of_nat(complex),B) | A = B. [resolve(6198,a,6189,a)]. 139.72/139.57 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(nat,complex,semiring_1_of_nat(complex),B) | A != B. [resolve(6198,a,6191,a)]. 139.72/139.57 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(complex). [resolve(6198,a,6193,a)]. 139.72/139.57 6199 dist_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Odist__norm) # label(axiom). [assumption]. 139.72/139.57 6200 -dist_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom). [clausify(187)]. 146.53/146.31 Derived: norm_norm(complex) = ti(fun(complex,real),norm_norm(complex)). [resolve(6199,a,6200,a)]. 146.53/146.31 6201 -dist_norm(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,real,hAPP(A,fun(A,real),dist_dist(A),B),C) # label(fact_3503_dist__norm) # label(axiom). [clausify(3515)]. 146.53/146.31 6202 dist_norm(real) # label(arity_RealDef_Oreal___RealVector_Odist__norm) # label(axiom). [assumption]. 146.53/146.31 Derived: norm_norm(real) = ti(fun(real,real),norm_norm(real)). [resolve(6202,a,6200,a)]. 146.53/146.31 Derived: hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),A),B). [resolve(6202,a,6201,a)]. 146.53/146.31 6203 -dist_norm(A) | dist_dist(A) = ti(fun(A,fun(A,real)),dist_dist(A)) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom). [clausify(4557)]. 146.53/146.31 Derived: dist_dist(complex) = ti(fun(complex,fun(complex,real)),dist_dist(complex)). [resolve(6203,a,6199,a)]. 146.53/146.31 Derived: dist_dist(real) = ti(fun(real,fun(real,real)),dist_dist(real)). [resolve(6203,a,6202,a)]. 146.53/146.31 6204 dense_linorder(rat) # label(arity_Rat_Orat___Orderings_Odense__linorder) # label(axiom). [assumption]. 146.53/146.31 6205 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f51(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2825_dense__le) # label(axiom). [clausify(199)]. 146.53/146.31 6206 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f51(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2825_dense__le) # label(axiom). [clausify(199)]. 146.53/146.31 6207 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(1635)]. 146.53/146.31 6208 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(1635)]. 146.53/146.31 6209 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(1635)]. 146.53/146.31 6210 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(1635)]. 146.53/146.31 6211 -dense_linorder(A) | ord_gr676655987ssThan(A) = ti(fun(A,fun(A,fun(A,bool))),ord_gr676655987ssThan(A)) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom). [clausify(2946)]. 146.53/146.31 6212 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(2990)]. 146.53/146.31 6213 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(2990)]. 146.53/146.31 6214 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(2990)]. 146.53/146.31 6215 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(2990)]. 146.53/146.31 6216 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3287)]. 146.53/146.31 6217 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3287)]. 146.53/146.31 6218 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3287)]. 146.53/146.31 6219 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3287)]. 146.53/146.31 6220 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),E)) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(3476)]. 146.53/146.31 6221 -dense_linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(3476)]. 146.53/146.32 6222 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(3476)]. 146.53/146.32 6223 -dense_linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(3476)]. 146.53/146.32 6224 -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),f671(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom). [clausify(3820)]. 146.53/146.32 6225 -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),f671(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom). [clausify(3820)]. 146.53/146.32 6226 -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),f671(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2826_dense__le__bounded) # label(axiom). [clausify(3820)]. 146.53/146.32 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f51(rat,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6204,a,6205,a)]. 146.53/146.32 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f51(rat,A,B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6204,a,6206,a)]. 146.53/146.32 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6207,a)]. 146.53/146.32 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6204,a,6208,a)]. 146.53/146.32 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6204,a,6209,a)]. 146.53/146.32 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6204,a,6210,a)]. 146.53/146.33 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6204,a,6212,a)]. 146.53/146.33 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6213,a)]. 146.53/146.33 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6204,a,6214,a)]. 146.53/146.33 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_gr676655987ssThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6215,a)]. 146.53/146.33 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6204,a,6216,a)]. 146.53/146.33 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6217,a)]. 146.53/146.33 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6204,a,6218,a)]. 146.53/146.33 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6219,a)]. 146.53/146.33 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),D)). [resolve(6204,a,6220,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6221,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6204,a,6222,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastAtMost(rat),A),B)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(6204,a,6223,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f671(rat,C,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6204,a,6224,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f671(rat,C,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6204,a,6225,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f671(rat,C,A,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6204,a,6226,a)]. 146.72/146.51 6227 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom). [assumption]. 146.72/146.51 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f51(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6227,a,6205,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f51(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6227,a,6206,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6207,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6227,a,6208,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6227,a,6209,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6227,a,6210,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6227,a,6212,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6213,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6227,a,6214,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6215,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6227,a,6216,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6217,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6227,a,6218,a)]. 146.72/146.51 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6219,a)]. 146.72/146.51 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),D)). [resolve(6227,a,6220,a)]. 150.43/150.24 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6221,a)]. 150.43/150.24 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6227,a,6222,a)]. 150.43/150.24 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),A),B)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(6227,a,6223,a)]. 150.43/150.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f671(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6227,a,6224,a)]. 150.43/150.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f671(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6227,a,6225,a)]. 150.43/150.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f671(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6227,a,6226,a)]. 150.43/150.24 6228 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 150.43/150.24 6229 -semiri456707255roduct(A) | ti(A,B) = zero_zero(A) | ti(A,C) != ti(A,D) | ti(A,E) = ti(A,F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),F)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) # label(fact_252_add__scale__eq__noteq) # label(axiom). [clausify(202)]. 150.43/150.24 Derived: ti(int,A) = zero_zero(int) | ti(int,B) != ti(int,C) | ti(int,D) = ti(int,E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),E)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)). [resolve(6228,a,6229,a)]. 150.43/150.24 6230 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 150.43/150.24 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) != ti(nat,C) | ti(nat,D) = ti(nat,E) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),E)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)). [resolve(6230,a,6229,a)]. 150.43/150.24 6231 semiri456707255roduct(complex) # label(arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__cro) # label(axiom). [assumption]. 150.43/150.24 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) != ti(complex,C) | ti(complex,D) = ti(complex,E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),E)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)). [resolve(6231,a,6229,a)]. 152.44/152.27 6232 semiri456707255roduct(rat) # label(arity_Rat_Orat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 152.44/152.27 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) != ti(rat,C) | ti(rat,D) = ti(rat,E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),E)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)). [resolve(6232,a,6229,a)]. 152.44/152.27 6233 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom). [assumption]. 152.44/152.27 Derived: ti(real,A) = zero_zero(real) | ti(real,B) != ti(real,C) | ti(real,D) = ti(real,E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),E)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)). [resolve(6233,a,6229,a)]. 152.44/152.27 6234 -semiri456707255roduct(A) | ti(A,B) != zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_239_add__0__iff) # label(axiom). [clausify(4090)]. 152.44/152.27 Derived: ti(int,A) != zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(6234,a,6228,a)]. 152.44/152.27 Derived: ti(nat,A) != zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(6234,a,6230,a)]. 152.44/152.27 Derived: ti(complex,A) != zero_zero(complex) | ti(complex,B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(6234,a,6231,a)]. 152.44/152.27 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(6234,a,6232,a)]. 152.44/152.27 Derived: ti(real,A) != zero_zero(real) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(6234,a,6233,a)]. 152.44/152.27 6235 -semiri456707255roduct(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_239_add__0__iff) # label(axiom). [clausify(4090)]. 152.44/152.27 Derived: ti(int,A) = zero_zero(int) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(6235,a,6228,a)]. 152.44/152.27 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(6235,a,6230,a)]. 152.44/152.27 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(6235,a,6231,a)]. 152.44/152.27 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(6235,a,6232,a)]. 152.44/152.27 Derived: ti(real,A) = zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(6235,a,6233,a)]. 152.44/152.27 6236 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(4915)]. 152.44/152.27 Derived: ti(int,A) = ti(int,B) | ti(int,C) = ti(int,D) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(6236,a,6228,a)]. 152.44/152.27 Derived: ti(nat,A) = ti(nat,B) | ti(nat,C) = ti(nat,D) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6236,a,6230,a)]. 152.44/152.28 Derived: ti(complex,A) = ti(complex,B) | ti(complex,C) = ti(complex,D) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(6236,a,6231,a)]. 152.44/152.28 Derived: ti(rat,A) = ti(rat,B) | ti(rat,C) = ti(rat,D) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(6236,a,6232,a)]. 152.44/152.28 Derived: ti(real,A) = ti(real,B) | ti(real,C) = ti(real,D) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(6236,a,6233,a)]. 152.44/152.28 6237 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(4915)]. 152.44/152.28 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(6237,a,6228,a)]. 152.44/152.28 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6237,a,6230,a)]. 152.44/152.28 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(6237,a,6231,a)]. 152.44/152.28 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(6237,a,6232,a)]. 152.44/152.28 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(6237,a,6233,a)]. 157.23/157.02 6238 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(4915)]. 157.23/157.02 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)). [resolve(6238,a,6228,a)]. 157.23/157.02 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),A)). [resolve(6238,a,6230,a)]. 157.23/157.02 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),A)). [resolve(6238,a,6231,a)]. 157.23/157.02 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A)). [resolve(6238,a,6232,a)]. 157.23/157.02 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)). [resolve(6238,a,6233,a)]. 157.23/157.02 6239 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) = ti(A,E) | ti(A,B) = ti(A,D) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(4928)]. 157.23/157.02 6240 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(4928)]. 157.23/157.02 6241 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(4928)]. 157.23/157.02 6242 -ordere1490568538miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_371_comm__mult__left__mono) # label(axiom). [clausify(4080)]. 161.13/160.91 6243 ordere1490568538miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 6244 ordere1490568538miring(nat) # label(arity_Nat_Onat___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 6245 ordere1490568538miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 6246 ordere1490568538miring(rat) # label(arity_Rat_Orat___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 6247 ordere1490568538miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 6248 ordere1490568538miring(int) # label(arity_Int_Oint___Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 161.13/160.91 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_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(6242,a,6244,a)]. 161.13/160.91 6249 -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_428_mult__left__less__imp__less) # label(axiom). [clausify(1319)]. 161.13/160.91 6250 linordered_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring) # label(axiom). [assumption]. 161.13/160.91 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)). [resolve(6249,a,6250,a)]. 161.13/160.91 6251 linordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring) # label(axiom). [assumption]. 161.13/160.91 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(6251,a,6249,a)]. 161.13/160.91 6252 linordered_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring) # label(axiom). [assumption]. 161.13/160.91 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)). [resolve(6252,a,6249,a)]. 162.13/161.91 6253 -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_430_mult__right__less__imp__less) # label(axiom). [clausify(1828)]. 162.13/161.91 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6253,a,6250,a)]. 162.13/161.91 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(6253,a,6251,a)]. 162.13/161.91 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6253,a,6252,a)]. 162.13/161.91 6254 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom). [assumption]. 162.13/161.91 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(6254,a,6249,a)]. 162.13/161.91 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(6254,a,6253,a)]. 162.13/161.91 6255 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom). [assumption]. 162.13/161.91 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(6255,a,6249,a)]. 162.13/161.91 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(6255,a,6253,a)]. 162.13/161.91 6256 linordered_semiring(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring) # label(axiom). [assumption]. 166.69/166.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6256,a,6249,a)]. 166.69/166.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6256,a,6253,a)]. 166.69/166.49 6257 group_add(real) # label(arity_RealDef_Oreal___Groups_Ogroup__add) # label(axiom). [assumption]. 166.69/166.49 6258 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) = zero_zero(A) # label(fact_2064_add__eq__0__iff) # label(axiom). [clausify(239)]. 166.69/166.49 6259 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) != zero_zero(A) # label(fact_2064_add__eq__0__iff) # label(axiom). [clausify(239)]. 166.69/166.49 6260 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_795_diff__self) # label(axiom). [clausify(265)]. 166.69/166.49 6261 -group_add(A) | hAPP(A,A,uminus_uminus(A),zero_zero(A)) = zero_zero(A) # label(fact_2025_minus__zero) # label(axiom). [clausify(306)]. 166.69/166.49 6262 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) # label(fact_796_diff__0__right) # label(axiom). [clausify(463)]. 166.69/166.49 6263 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2069_minus__unique) # label(axiom). [clausify(471)]. 166.69/166.49 6264 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),B)) = zero_zero(A) # label(fact_2065_right__minus) # label(axiom). [clausify(612)]. 166.69/166.49 6265 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) # label(fact_808_add__diff__cancel) # label(axiom). [clausify(1671)]. 166.69/166.49 6266 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2050_minus__add) # label(axiom). [clausify(1901)]. 166.69/166.49 6267 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2043_minus__equation__iff) # label(axiom). [clausify(2035)]. 166.69/166.49 6268 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2043_minus__equation__iff) # label(axiom). [clausify(2035)]. 166.69/166.49 6269 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2049_add__minus__cancel) # label(axiom). [clausify(2187)]. 166.69/166.49 6270 -group_add(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom). [clausify(2289)]. 166.69/166.49 6271 -group_add(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom). [clausify(2289)]. 166.69/166.49 6272 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) # label(fact_809_diff__add__cancel) # label(axiom). [clausify(2373)]. 166.69/166.49 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A) = zero_zero(real). [resolve(6257,a,6258,a)]. 166.69/166.49 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A) != zero_zero(real). [resolve(6257,a,6259,a)]. 166.69/166.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),A) = zero_zero(real). [resolve(6257,a,6260,a)]. 166.69/166.49 Derived: hAPP(real,real,uminus_uminus(real),zero_zero(real)) = zero_zero(real). [resolve(6257,a,6261,a)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),zero_zero(real)). [resolve(6257,a,6262,a)]. 167.32/167.16 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),A)) = zero_zero(real). [resolve(6257,a,6264,a)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),B). [resolve(6257,a,6265,a)]. 167.32/167.16 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(6257,a,6266,a)]. 167.32/167.16 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A). [resolve(6257,a,6267,a)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(6257,a,6269,a)]. 167.32/167.16 Derived: ti(real,A) != zero_zero(real) | hAPP(real,real,uminus_uminus(real),A) = zero_zero(real). [resolve(6257,a,6270,a)]. 167.32/167.16 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),A) != zero_zero(real). [resolve(6257,a,6271,a)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),B). [resolve(6257,a,6272,a)]. 167.32/167.16 6273 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom). [clausify(2678)]. 167.32/167.16 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real). [resolve(6273,a,6257,a)]. 167.32/167.16 6274 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom). [clausify(2678)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real). [resolve(6274,a,6257,a)]. 167.32/167.16 6275 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_2074_diff__minus__eq__add) # label(axiom). [clausify(3194)]. 167.32/167.16 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B). [resolve(6275,a,6257,a)]. 167.32/167.16 6276 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_2048_minus__add__cancel) # label(axiom). [clausify(3336)]. 167.32/167.16 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)). [resolve(6276,a,6257,a)]. 167.32/167.16 6277 group_add(complex) # label(arity_Complex_Ocomplex___Groups_Ogroup__add) # label(axiom). [assumption]. 167.32/167.16 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A) = zero_zero(complex). [resolve(6277,a,6258,a)]. 167.32/167.16 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A) != zero_zero(complex). [resolve(6277,a,6259,a)]. 167.32/167.16 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),A) = zero_zero(complex). [resolve(6277,a,6260,a)]. 167.32/167.16 Derived: hAPP(complex,complex,uminus_uminus(complex),zero_zero(complex)) = zero_zero(complex). [resolve(6277,a,6261,a)]. 167.32/167.16 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),zero_zero(complex)). [resolve(6277,a,6262,a)]. 167.63/167.46 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),A)) = zero_zero(complex). [resolve(6277,a,6264,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),B). [resolve(6277,a,6265,a)]. 167.63/167.46 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(6277,a,6266,a)]. 167.63/167.46 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(6277,a,6267,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),B)),A)). [resolve(6277,a,6269,a)]. 167.63/167.46 Derived: ti(complex,A) != zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),A) = zero_zero(complex). [resolve(6277,a,6270,a)]. 167.63/167.46 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),A) != zero_zero(complex). [resolve(6277,a,6271,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),B). [resolve(6277,a,6272,a)]. 167.63/167.46 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = zero_zero(complex). [resolve(6277,a,6273,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != zero_zero(complex). [resolve(6277,a,6274,a)]. 167.63/167.46 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B). [resolve(6277,a,6275,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)). [resolve(6277,a,6276,a)]. 167.63/167.46 6278 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2041_minus__minus) # label(axiom). [clausify(3694)]. 167.63/167.46 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(6278,a,6257,a)]. 167.63/167.46 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(6278,a,6277,a)]. 167.63/167.46 6279 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2076_Groups_Odiff__def) # label(axiom). [clausify(3837)]. 167.63/167.46 6280 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom). [clausify(3930)]. 167.63/167.46 6281 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom). [clausify(3930)]. 167.63/167.46 6282 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_2067_left__minus) # label(axiom). [clausify(3982)]. 167.63/167.46 6283 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),zero_zero(A)),B) # label(fact_2070_diff__0) # label(axiom). [clausify(4115)]. 167.63/167.46 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),zero_zero(real)),A). [resolve(6283,a,6257,a)]. 167.63/167.46 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),zero_zero(complex)),A). [resolve(6283,a,6277,a)]. 167.73/167.55 6284 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption]. 167.73/167.55 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A) = zero_zero(int). [resolve(6284,a,6258,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A) != zero_zero(int). [resolve(6284,a,6259,a)]. 167.73/167.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(6284,a,6260,a)]. 167.73/167.55 Derived: hAPP(int,int,uminus_uminus(int),zero_zero(int)) = zero_zero(int). [resolve(6284,a,6261,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)). [resolve(6284,a,6262,a)]. 167.73/167.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),A)) = zero_zero(int). [resolve(6284,a,6264,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B). [resolve(6284,a,6265,a)]. 167.73/167.55 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(6284,a,6266,a)]. 167.73/167.55 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(6284,a,6267,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(6284,a,6269,a)]. 167.73/167.55 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,uminus_uminus(int),A) = zero_zero(int). [resolve(6284,a,6270,a)]. 167.73/167.55 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,uminus_uminus(int),A) != zero_zero(int). [resolve(6284,a,6271,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B). [resolve(6284,a,6272,a)]. 167.73/167.55 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int). [resolve(6284,a,6273,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int). [resolve(6284,a,6274,a)]. 167.73/167.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B). [resolve(6284,a,6275,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)). [resolve(6284,a,6276,a)]. 167.73/167.55 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(6284,a,6278,a)]. 167.73/167.55 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),A). [resolve(6284,a,6283,a)]. 167.73/167.55 6285 group_add(rat) # label(arity_Rat_Orat___Groups_Ogroup__add) # label(axiom). [assumption]. 167.73/167.55 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A) = zero_zero(rat). [resolve(6285,a,6258,a)]. 167.73/167.55 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A) != zero_zero(rat). [resolve(6285,a,6259,a)]. 167.73/167.55 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),A) = zero_zero(rat). [resolve(6285,a,6260,a)]. 167.73/167.55 Derived: hAPP(rat,rat,uminus_uminus(rat),zero_zero(rat)) = zero_zero(rat). [resolve(6285,a,6261,a)]. 167.73/167.55 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),zero_zero(rat)). [resolve(6285,a,6262,a)]. 167.73/167.55 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),A)) = zero_zero(rat). [resolve(6285,a,6264,a)]. 167.73/167.55 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),B). [resolve(6285,a,6265,a)]. 168.14/167.91 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6285,a,6266,a)]. 168.14/167.91 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6285,a,6267,a)]. 168.14/167.91 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A)). [resolve(6285,a,6269,a)]. 168.14/167.91 Derived: ti(rat,A) != zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),A) = zero_zero(rat). [resolve(6285,a,6270,a)]. 168.14/167.91 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),A) != zero_zero(rat). [resolve(6285,a,6271,a)]. 168.14/167.91 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),B). [resolve(6285,a,6272,a)]. 168.14/167.91 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat). [resolve(6285,a,6273,a)]. 168.14/167.91 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat). [resolve(6285,a,6274,a)]. 168.14/167.91 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B). [resolve(6285,a,6275,a)]. 168.14/167.91 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)). [resolve(6285,a,6276,a)]. 168.14/167.91 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6285,a,6278,a)]. 168.14/167.91 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),zero_zero(rat)),A). [resolve(6285,a,6283,a)]. 168.14/167.91 6286 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2042_equation__minus__iff) # label(axiom). [clausify(4638)]. 168.14/167.91 6287 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2042_equation__minus__iff) # label(axiom). [clausify(4638)]. 168.14/167.91 6288 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_2044_neg__equal__iff__equal) # label(axiom). [clausify(4688)]. 168.14/167.91 Derived: hAPP(real,real,uminus_uminus(real),A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,A) = ti(real,B). [resolve(6288,a,6257,a)]. 168.14/167.91 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) = ti(complex,B). [resolve(6288,a,6277,a)]. 168.14/167.91 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(6288,a,6284,a)]. 168.14/167.91 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) = ti(rat,B). [resolve(6288,a,6285,a)]. 168.14/167.91 6289 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) != ti(A,C) # label(fact_2044_neg__equal__iff__equal) # label(axiom). [clausify(4688)]. 168.14/167.91 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,uminus_uminus(real),B) | ti(real,A) != ti(real,B). [resolve(6289,a,6257,a)]. 168.14/167.91 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) != ti(complex,B). [resolve(6289,a,6277,a)]. 168.14/167.91 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(6289,a,6284,a)]. 168.14/167.91 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) != ti(rat,B). [resolve(6289,a,6285,a)]. 168.14/167.91 6290 -group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) # label(fact_793_right__minus__eq) # label(axiom). [clausify(4785)]. 168.14/167.91 6291 -group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) # label(fact_793_right__minus__eq) # label(axiom). [clausify(4785)]. 177.26/177.10 6292 -linord626643107strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),F)) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),F) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))),C)) # label(fact_277_convex__bound__lt) # label(axiom). [clausify(1379)]. 177.26/177.10 6293 linord626643107strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 177.26/177.10 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),E)) | one_one(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),D),E) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),E),C))),B)). [resolve(6292,a,6293,a)]. 177.26/177.10 6294 linord626643107strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 177.26/177.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),E)) | one_one(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),E) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),B)). [resolve(6294,a,6292,a)]. 177.26/177.10 6295 linord626643107strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 177.26/177.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),E)) | one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),E) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),C))),B)). [resolve(6295,a,6292,a)]. 177.26/177.10 6296 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 177.26/177.10 6297 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom). [clausify(243)]. 177.26/177.10 6298 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_2095_abs__of__nonpos) # label(axiom). [clausify(376)]. 177.26/177.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),abs_abs(int)),B)),C))). [resolve(6296,a,6297,a)]. 177.65/177.44 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(6296,a,6298,a)]. 177.65/177.44 6299 -ordere142940540dd_abs(A) | ti(A,B) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_1861_abs__le__zero__iff) # label(axiom). [clausify(781)]. 177.65/177.44 Derived: ti(int,A) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(6299,a,6296,a)]. 177.65/177.44 6300 -ordere142940540dd_abs(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_1861_abs__le__zero__iff) # label(axiom). [clausify(781)]. 177.65/177.44 Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(6300,a,6296,a)]. 177.65/177.44 6301 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,abs_abs(A),B))) # label(fact_1843_abs__ge__self) # label(axiom). [clausify(1119)]. 177.65/177.44 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(6301,a,6296,a)]. 177.65/177.44 6302 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,abs_abs(A),B))) # label(fact_2079_abs__ge__minus__self) # label(axiom). [clausify(1138)]. 177.65/177.44 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,abs_abs(int),A))). [resolve(6302,a,6296,a)]. 177.65/177.44 6303 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),zero_zero(A)) = zero_zero(A) # label(fact_1851_abs__zero) # label(axiom). [clausify(1264)]. 177.65/177.44 Derived: hAPP(int,int,abs_abs(int),zero_zero(int)) = zero_zero(int). [resolve(6303,a,6296,a)]. 177.65/177.44 6304 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_1863_abs__not__less__zero) # label(axiom). [clausify(1368)]. 177.65/177.44 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(6304,a,6296,a)]. 177.65/177.44 6305 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_1862_abs__ge__zero) # label(axiom). [clausify(2039)]. 177.65/177.44 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))). [resolve(6305,a,6296,a)]. 177.65/177.44 6306 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_1850_abs__eq__0) # label(axiom). [clausify(2215)]. 177.65/177.44 Derived: hAPP(int,int,abs_abs(int),A) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(6306,a,6296,a)]. 177.65/177.44 6307 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_1850_abs__eq__0) # label(axiom). [clausify(2215)]. 177.65/177.44 Derived: hAPP(int,int,abs_abs(int),A) = zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(6307,a,6296,a)]. 177.65/177.44 6308 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2082_abs__le__D2) # label(axiom). [clausify(2242)]. 177.65/177.44 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)). [resolve(6308,a,6296,a)]. 177.65/177.44 6309 -ordere142940540dd_abs(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D)) # label(fact_4212_abs__setsum__abs) # label(axiom). [clausify(2297)]. 178.25/178.08 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),abs_abs(int)),B)),C) = hAPP(int,int,abs_abs(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),abs_abs(int)),B)),C)). [resolve(6309,a,6296,a)]. 178.25/178.08 6310 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_1867_abs__triangle__ineq) # label(axiom). [clausify(2420)]. 178.25/178.08 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(6310,a,6296,a)]. 178.25/178.08 6311 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = hAPP(A,A,abs_abs(A),B) # label(fact_1860_abs__of__nonneg) # label(axiom). [clausify(2575)]. 178.25/178.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | ti(int,A) = hAPP(int,int,abs_abs(int),A). [resolve(6311,a,6296,a)]. 178.25/178.08 6312 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)))) # label(fact_1870_abs__triangle__ineq2__sym) # label(axiom). [clausify(2609)]. 178.25/178.08 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)))). [resolve(6312,a,6296,a)]. 178.25/178.08 6313 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_2099_abs__of__neg) # label(axiom). [clausify(3021)]. 178.25/178.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(6313,a,6296,a)]. 178.25/178.08 6314 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_1852_abs__idempotent) # label(axiom). [clausify(3030)]. 178.25/178.08 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(6314,a,6296,a)]. 178.25/178.08 6315 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_2010_abs__minus__cancel) # label(axiom). [clausify(3387)]. 178.25/178.08 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(6315,a,6296,a)]. 178.25/178.08 6316 ordere142940540dd_abs(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 178.25/178.08 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C))). [resolve(6316,a,6297,a)]. 178.25/178.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(6316,a,6298,a)]. 178.25/178.08 Derived: ti(real,A) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(6316,a,6299,a)]. 178.25/178.08 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(6316,a,6300,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,abs_abs(real),A))). [resolve(6316,a,6301,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,abs_abs(real),A))). [resolve(6316,a,6302,a)]. 178.45/178.27 Derived: hAPP(real,real,abs_abs(real),zero_zero(real)) = zero_zero(real). [resolve(6316,a,6303,a)]. 178.45/178.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(6316,a,6304,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))). [resolve(6316,a,6305,a)]. 178.45/178.27 Derived: hAPP(real,real,abs_abs(real),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(6316,a,6306,a)]. 178.45/178.27 Derived: hAPP(real,real,abs_abs(real),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(6316,a,6307,a)]. 178.45/178.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(6316,a,6308,a)]. 178.45/178.27 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C) = hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C)). [resolve(6316,a,6309,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(6316,a,6310,a)]. 178.45/178.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | ti(real,A) = hAPP(real,real,abs_abs(real),A). [resolve(6316,a,6311,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)))). [resolve(6316,a,6312,a)]. 178.45/178.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(6316,a,6313,a)]. 178.45/178.27 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(6316,a,6314,a)]. 178.45/178.27 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(6316,a,6315,a)]. 178.45/178.27 6317 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,abs_abs(A),B))),zero_zero(A))) # label(fact_2096_abs__minus__le__zero) # label(axiom). [clausify(3409)]. 178.45/178.27 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,abs_abs(int),A))),zero_zero(int))). [resolve(6317,a,6296,a)]. 178.45/178.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,abs_abs(real),A))),zero_zero(real))). [resolve(6317,a,6316,a)]. 178.45/178.27 6318 ordere142940540dd_abs(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 178.45/178.27 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C))). [resolve(6318,a,6297,a)]. 178.45/178.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6318,a,6298,a)]. 178.65/178.42 Derived: ti(rat,A) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(6318,a,6299,a)]. 178.65/178.42 Derived: ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(6318,a,6300,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6318,a,6301,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6318,a,6302,a)]. 178.65/178.42 Derived: hAPP(rat,rat,abs_abs(rat),zero_zero(rat)) = zero_zero(rat). [resolve(6318,a,6303,a)]. 178.65/178.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(6318,a,6304,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6318,a,6305,a)]. 178.65/178.42 Derived: hAPP(rat,rat,abs_abs(rat),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(6318,a,6306,a)]. 178.65/178.42 Derived: hAPP(rat,rat,abs_abs(rat),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(6318,a,6307,a)]. 178.65/178.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(6318,a,6308,a)]. 178.65/178.42 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C)). [resolve(6318,a,6309,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)))). [resolve(6318,a,6310,a)]. 178.65/178.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | ti(rat,A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6318,a,6311,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A)))). [resolve(6318,a,6312,a)]. 178.65/178.42 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6318,a,6314,a)]. 178.65/178.42 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6318,a,6315,a)]. 178.65/178.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,abs_abs(rat),A))),zero_zero(rat))). [resolve(6318,a,6317,a)]. 178.65/178.42 6319 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | ti(A,B) = hAPP(A,A,abs_abs(A),B) # label(fact_1865_abs__of__pos) # label(axiom). [clausify(3878)]. 178.65/178.42 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | ti(int,A) = hAPP(int,int,abs_abs(int),A). [resolve(6319,a,6296,a)]. 178.65/178.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | ti(real,A) = hAPP(real,real,abs_abs(real),A). [resolve(6319,a,6316,a)]. 178.65/178.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | ti(rat,A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6319,a,6318,a)]. 178.65/178.42 6320 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)) # label(fact_1858_abs__minus__commute) # label(axiom). [clausify(3946)]. 178.84/178.64 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)). [resolve(6320,a,6296,a)]. 178.84/178.64 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)). [resolve(6320,a,6316,a)]. 178.84/178.64 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A)). [resolve(6320,a,6318,a)]. 178.84/178.64 6321 -ordere142940540dd_abs(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom). [clausify(3990)]. 178.84/178.64 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(6321,a,6296,a)]. 178.84/178.64 Derived: abs_abs(real) = ti(fun(real,real),abs_abs(real)). [resolve(6321,a,6316,a)]. 178.84/178.64 Derived: abs_abs(rat) = ti(fun(rat,rat),abs_abs(rat)). [resolve(6321,a,6318,a)]. 178.84/178.64 6322 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(4185)]. 178.84/178.64 6323 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(4185)]. 178.84/178.64 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6323,a,6296,a)]. 178.84/178.64 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6323,a,6318,a)]. 178.84/178.64 6324 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(4185)]. 178.84/178.64 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(6324,a,6296,a)]. 178.84/178.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(6324,a,6316,a)]. 178.84/178.64 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(6324,a,6318,a)]. 178.84/178.64 6325 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1842_abs__le__D1) # label(axiom). [clausify(4222)]. 178.84/178.64 6326 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))))) # label(fact_1881_abs__diff__triangle__ineq) # label(axiom). [clausify(4296)]. 178.84/178.64 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D))))). [resolve(6326,a,6296,a)]. 178.93/178.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))))). [resolve(6326,a,6316,a)]. 178.93/178.74 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C))),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D))))). [resolve(6326,a,6318,a)]. 178.93/178.74 6327 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D))) # label(fact_4165_setsum__abs) # label(axiom). [clausify(4345)]. 178.93/178.74 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),abs_abs(int)),B)),C))). [resolve(6327,a,6296,a)]. 178.93/178.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),abs_abs(real)),B)),C))). [resolve(6327,a,6316,a)]. 178.93/178.74 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C))). [resolve(6327,a,6318,a)]. 178.93/178.74 6328 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_1882_abs__triangle__ineq4) # label(axiom). [clausify(4464)]. 178.93/178.74 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(6328,a,6296,a)]. 178.93/178.74 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(6328,a,6316,a)]. 179.04/178.89 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)))). [resolve(6328,a,6318,a)]. 179.04/178.89 6329 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | ti(A,B) != zero_zero(A) # label(fact_1864_zero__less__abs__iff) # label(axiom). [clausify(4529)]. 179.04/178.89 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | ti(int,A) != zero_zero(int). [resolve(6329,a,6296,a)]. 179.04/178.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | ti(real,A) != zero_zero(real). [resolve(6329,a,6316,a)]. 179.04/178.89 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | ti(rat,A) != zero_zero(rat). [resolve(6329,a,6318,a)]. 179.04/178.89 6330 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | ti(A,B) = zero_zero(A) # label(fact_1864_zero__less__abs__iff) # label(axiom). [clausify(4529)]. 179.04/178.89 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | ti(int,A) = zero_zero(int). [resolve(6330,a,6296,a)]. 179.04/178.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | ti(real,A) = zero_zero(real). [resolve(6330,a,6316,a)]. 179.04/178.89 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | ti(rat,A) = zero_zero(rat). [resolve(6330,a,6318,a)]. 179.04/178.89 6331 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1856_abs__add__abs) # label(axiom). [clausify(4610)]. 179.04/178.89 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)). [resolve(6331,a,6296,a)]. 179.04/178.89 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)). [resolve(6331,a,6316,a)]. 179.04/178.89 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)). [resolve(6331,a,6318,a)]. 179.04/178.89 6332 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_1869_abs__triangle__ineq2) # label(axiom). [clausify(4683)]. 179.04/178.89 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(6332,a,6296,a)]. 179.04/178.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)))). [resolve(6332,a,6316,a)]. 179.04/178.89 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,funCputime limit exceeded (core dumped) 180.07/179.84 EOF