0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n014.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 05:09:15 EDT 2022 0.13/0.34 % CPUTime : 7.41/7.40 ============================== Prover9 =============================== 7.41/7.40 Prover9 (32) version 2009-11A, November 2009. 7.41/7.40 Process 26659 was started by sandbox on n014.cluster.edu, 7.41/7.40 Tue Aug 9 05:09:22 2022 7.41/7.40 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_26506_n014.cluster.edu". 7.41/7.40 ============================== end of head =========================== 7.41/7.40 7.41/7.40 ============================== INPUT ================================= 7.41/7.40 7.41/7.40 % Reading from file /tmp/Prover9_26506_n014.cluster.edu 7.41/7.40 7.41/7.40 set(prolog_style_variables). 7.41/7.40 set(auto2). 7.41/7.40 % set(auto2) -> set(auto). 7.41/7.40 % set(auto) -> set(auto_inference). 7.41/7.40 % set(auto) -> set(auto_setup). 7.41/7.40 % set(auto_setup) -> set(predicate_elim). 7.41/7.40 % set(auto_setup) -> assign(eq_defs, unfold). 7.41/7.40 % set(auto) -> set(auto_limits). 7.41/7.40 % set(auto_limits) -> assign(max_weight, "100.000"). 7.41/7.40 % set(auto_limits) -> assign(sos_limit, 20000). 7.41/7.40 % set(auto) -> set(auto_denials). 7.41/7.40 % set(auto) -> set(auto_process). 7.41/7.40 % set(auto2) -> assign(new_constants, 1). 7.41/7.40 % set(auto2) -> assign(fold_denial_max, 3). 7.41/7.40 % set(auto2) -> assign(max_weight, "200.000"). 7.41/7.40 % set(auto2) -> assign(max_hours, 1). 7.41/7.40 % assign(max_hours, 1) -> assign(max_seconds, 3600). 7.41/7.40 % set(auto2) -> assign(max_seconds, 0). 7.41/7.40 % set(auto2) -> assign(max_minutes, 5). 7.41/7.40 % assign(max_minutes, 5) -> assign(max_seconds, 300). 7.41/7.40 % set(auto2) -> set(sort_initial_sos). 7.41/7.40 % set(auto2) -> assign(sos_limit, -1). 7.41/7.40 % set(auto2) -> assign(lrs_ticks, 3000). 7.41/7.40 % set(auto2) -> assign(max_megs, 400). 7.41/7.40 % set(auto2) -> assign(stats, some). 7.41/7.40 % set(auto2) -> clear(echo_input). 7.41/7.40 % set(auto2) -> set(quiet). 7.41/7.40 % set(auto2) -> clear(print_initial_clauses). 7.41/7.40 % set(auto2) -> clear(print_given). 7.41/7.40 assign(lrs_ticks,-1). 7.41/7.40 assign(sos_limit,10000). 7.41/7.40 assign(order,kbo). 7.41/7.40 set(lex_order_vars). 7.41/7.40 clear(print_given). 7.41/7.40 7.41/7.40 % formulas(sos). % not echoed (5752 formulas) 7.41/7.40 7.41/7.40 ============================== end of input ========================== 7.41/7.40 7.41/7.40 % From the command line: assign(max_seconds, 960). 7.41/7.40 7.41/7.40 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 7.41/7.40 7.41/7.40 % Formulas that are not ordinary clauses: 7.41/7.40 1 (all Z_1 all 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)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W))) # label(fact_2062_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 2 (all I all J all 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)) <-> 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))))) # label(fact_837_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 3 (all X all Q_3 all N all R_3 (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_3) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_3),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X)))))) # label(fact_875_divides__div__not) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 4 (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_2780_complex__i__mult__minus) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 5 (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_4977_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 6 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,uminus_uminus(X_a),B_2))))))) # label(fact_1902_le__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 7 (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_739_add__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 8 (all X_a (metric_space(X_a) -> (all X hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),X) = zero_zero(real)))) # label(fact_3541_dist__self) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 9 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> zero_zero(nat) = N)) # label(fact_156_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 10 (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)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),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_1645_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 11 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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))) & 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))))))))) # label(fact_2251_arcsin) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 12 (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_4439_Rat__induct) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 13 (all X_a (banach(X_a) -> (all F all C all N_3 ((all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_1)) -> 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_1)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_1))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)))))) # label(fact_4082_ratio__test__lemma2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 14 (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_2607_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 15 (all X_a (topological_space(X_a) -> (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),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),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,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_3))))))) # label(fact_4618_LIM__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 16 (all B all Q_3 all R_3 all B_5 all Q_5 all 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),Q_3)),R_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_4)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_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_5),Q_3))))))))) # label(fact_653_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 17 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_3)) <-> 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_3),B_2)))))) # label(fact_1112_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 18 (all M all N all Q_3 all R_3 (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_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = R_3)) # label(fact_3127_mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 19 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B))))))) # label(fact_212_add__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 20 (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),hAPP(nat,nat,suc,zero_zero(nat))),K_1)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_2),K_1) = N & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N)))))) # label(fact_3116_not__prime__ex__mk) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 21 (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_2981_compl__le__swap2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 22 (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_104_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 23 (all N hAPP(nat,nat,fact,hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,fact,N))) # label(fact_3571_fact_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 24 (all X_c all X_a all X_b all Z all C 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,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),P_4))))) # label(fact_4085_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 25 (all K (hAPP(int,int,bit1,K) = min <-> ti(int,K) = min)) # label(fact_667_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 26 (all A_3 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_3)) <-> one_one(nat) != A_3)) # label(fact_1258_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 27 (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_1260_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 28 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (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_2)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1) != ti(int,X_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),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_1),D)),Ta)))))))) # label(fact_4656_aset_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 29 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all L all F all G all A_3 ((all X_1 (ti(X_a,A_3) != ti(X_a,X_1) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,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),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),L),hAPP(X_a,filter(X_a),at(X_a),A_3)))))))) # label(fact_4791_LIM__equal) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 30 (all Xa (hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Xa),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2505_even__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 31 (all X_a all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_1))))) -> 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_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_2))) # label(fact_4886_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 32 (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_310_power__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 33 (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_3564_fact__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 34 (all X_a (comm_semiring_1(X_a) -> (all C_1 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_1)) -> 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_1)))))))) # label(fact_730_dvd__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 35 (all B all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) = one_one(int) -> (exists X_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(int),X_1),N)) & (all Y_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),Y_1),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_1)),B),N)) -> ti(int,Y_1) = ti(int,X_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),X_1)),B),N))))))) # label(fact_3503_zcong__lineq__unique) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 36 (all X_a all One all Times all A_3 all Na hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),Times,A_3),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_3),Na)) = 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_3),hAPP(nat,nat,suc,Na))) # label(fact_2867_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 37 (all X_a (real_normed_algebra(X_a) -> (all Xa_2 all R_3 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),X))))) # label(fact_4720_mult__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 38 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),hAPP(int,int,uminus_uminus(int),J_2))) # label(fact_3469_zgcd__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 39 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),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))))) # label(fact_3041_complex__mult__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 40 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2558_tan__sec) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 41 (all Code_numeral_3 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_3) != zero_zero(code_code_numeral)) # label(fact_2972_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 42 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)))))) # label(fact_3322_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 43 (all Na (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_2405_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 44 (all A_1 all C_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),A_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),C_1)) # label(fact_3762_eq__rat_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 45 (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_2983_compl__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 46 (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_303_succ__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 47 (all X_a (ord(X_a) -> ord_atMost(X_a) = ti(fun(X_a,fun(X_a,bool)),ord_atMost(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatMost_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 48 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,number_number_of(int),min))) # label(fact_1428_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 49 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,K_4)) # label(fact_2926_pred__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 50 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na))))) # label(fact_147_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 51 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_2969_complex__cnj__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 52 (all Xa all A_3 (zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),hAPP(real,real,uminus_uminus(real),A_3)) <-> A_3 = Xa)) # label(fact_1990_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 53 (all U all Ma all Na all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U)),Ma) = Na <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U)),Na) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U)),Ma)))) # label(fact_867_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 54 (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]. 7.41/7.40 55 (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_2493_minus__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 56 (all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_3),B_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,B_2),A_3)))) # label(fact_2876_coprime__commute) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 57 (all X_a (semiring_1(X_a) -> (all Inc all Na 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),Na),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,Na)),I)))) # label(fact_4188_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 58 (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_4119_summable__sums) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 59 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_2 all Wa 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,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),hAPP(int,X_a,number_number_of(X_a),Wa))),A_3)) <-> (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),Wa))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa))))) & (-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),Wa))) -> (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),Wa)),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_3),hAPP(int,X_a,number_number_of(X_a),Wa))),B_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),Wa)),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_3)))))))) # label(fact_1801_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 60 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all F_1 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_1)) -> hAPP(X_a,X_b,F,X_1) = 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_4797_setprod__1_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 61 (all X_a (linord20386208strict(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_480_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 62 (all X_a all G all A_2 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_2) = 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_2))) # label(fact_4273_Re_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 63 (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_524_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 64 (all V all 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))) = 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)))) # label(fact_1471_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 65 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int)))) # label(fact_3730_Frct__code__post_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 66 (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_3200_div__mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 67 (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_2283_abs__sgn) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 68 (all Ma all K all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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),Na),K))))) # label(fact_628_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 69 (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_4388_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 70 (all R_3 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_3)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_3)) # label(fact_2822_complex__of__real__i) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 71 (all K all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all D_2 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_2)))),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_2)),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_4298_sumr__pos__lt__pair) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 72 (all X_a (semiring_1(X_a) -> ti(fun(X_a,bool),iszero(X_a)) = iszero(X_a))) # label(tsy_c_Int_Oiszero_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 73 (all Xa all Ma (Ma = zero_zero(nat) | Xa = hAPP(nat,nat,suc,zero_zero(nat)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Ma))) # label(fact_1405_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 74 (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_4162_suminf__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 75 (all A_1 all B all C_1 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_1)) = 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_1)) # label(fact_1158_div__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 76 (all X_a finite_card(X_a) = ti(fun(fun(X_a,bool),nat),finite_card(X_a))) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 77 (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_3140_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 78 (all X_a (linorder(X_a) -> (all Xa all Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) -> (ti(X_a,Xa) = ti(X_a,Ya) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya))))))) # label(fact_564_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 79 (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_791_Euler_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 80 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all M_1 all F all L_2 all A_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),L_2),hAPP(X_a,filter(X_a),at(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),G),M_1),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4762_LIM__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 81 (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_2000_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 82 (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_439_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 83 (all Ma all K all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K) <-> K = zero_zero(nat) | Na = Ma)) # label(fact_606_mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 84 (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_1181_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 85 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z_1),X))))) # label(fact_4978_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 86 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F ((exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X1))) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4117_summable__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 87 (all Xa (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),Xa)))) # label(fact_1629_even__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 88 (all X_b all X_a (real_vector(X_a) -> (all G all A_2 all Xa 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_2)),Xa) = 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)),Xa)),A_2)))) # label(fact_4755_scaleR__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 89 (all K all F all Na all Ma ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),Na)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_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),Na)) -> (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,Na))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),Na)) & hAPP(nat,int,F,I_2) = ti(int,K) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2))))))))) # label(fact_1068_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 90 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2356_arccos__ubound) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 91 (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_1753_power__divide) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 92 (all X_a (order(X_a) -> (all C_1 all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_1))))))) # label(fact_507_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 93 (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_544_semiring__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 94 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_557_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 95 (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_2095_negative__zless__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 96 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat))) # label(fact_4989_max__0R) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 97 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_350_le0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 98 (all Xa all Ya (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Xa),Ya) = ii <-> zero_zero(real) = Xa & Ya = one_one(real))) # label(fact_2783_Complex__eq__i) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 99 (all X_a (linorder(X_a) -> (all Xa all Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) | ti(X_a,Xa) = ti(X_a,Ya))))) # label(fact_534_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 100 (all Xa all F ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_1)))) -> ((all N_1 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))),Xa))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4333_pos__summable) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 101 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all 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),plus_plus(X_a),A_1),C_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C_1)))) # label(fact_296_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 102 (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_2628_one__le__inverse) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 103 (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_2602_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 104 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (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_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_1))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),A_2),B_1)))))) # label(fact_3682_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 105 (all X_a (archim1727834104eiling(X_a) -> (all X all 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))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1)))) # label(fact_3619_floor__add__of__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 106 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5))))) # label(fact_4702_scaleR_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 107 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_1))) -> 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_2))))) # label(fact_4800_setsum__0_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 108 (all X_a (boolean_algebra(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Xa)),hAPP(X_a,X_a,uminus_uminus(X_a),Ya))))))) # label(fact_2984_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 109 (all X_a (banach(X_a) -> (all F all G ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> 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_1))),hAPP(nat,real,G,N_1))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4019_summable__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 110 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_280_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 111 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_177_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 112 (all X_a (real_normed_vector(X_a) -> (all X all Y all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C_1),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_1),hAPP(X_a,real,norm_norm(X_a),Y)))) -> zero_zero(X_a) = ti(X_a,X)))))) # label(fact_2028_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 113 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4834_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 114 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 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_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_3)),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),A_3),A_2)))))) # label(fact_4478_tendsto__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 115 (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_1169_div__less__dividend) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 116 (all N hAPP(nat,nat,suc,N) != N) # label(fact_1278_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 117 (all X_1 hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_1))) = 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_1)) # label(fact_4146_exp__fdiffs) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 118 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat)))) # label(fact_1254_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 119 (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_919_zcong__zmult__prop3) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 120 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2383_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 121 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),T_5)))))) # label(fact_2853_minf_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 122 (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_2001_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 123 (all X X = hAPP(real,real,ln,hAPP(real,real,exp(real),X))) # label(fact_1759_ln__exp) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 124 (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_1160_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 125 (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_1885_gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 126 (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_1311_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 127 (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_2430_two__realpow__gt) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 128 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),Xa)),zero_zero(int))))))) # label(fact_2905_floor__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 129 (all M all N (zero_zero(int) != ti(int,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)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N))) # label(fact_3811_Fract__add__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 130 (all X all Y (zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)))) # label(fact_3301_gcd__non__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 131 (all X_a (comm_ring_1(X_a) -> (all X all N ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)))))) # label(fact_2480_neg__power__if) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 132 (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]. 7.41/7.40 133 (all Real1 all Real2 all Real1_2 all Real2_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_2),Real2_2) <-> Real2 = Real2_2 & Real1 = Real1_2)) # label(fact_2759_complex_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 134 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all G all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) -> 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_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_1))))))))) # label(fact_3992_setprod__dvd__setprod__subset2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 135 (all Va (hAPP(int,nat,number_number_of(nat),Va) = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls)))) # label(fact_273_eq__number__of__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.40 136 (all X_a (real_normed_algebra(X_a) -> (all C all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_3)) -> 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)),F)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3))))))) # label(fact_4107_sums__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 137 (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_379_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 138 (all X_a (dense_linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1))))))) # label(fact_4261_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 139 (all K_4 hAPP(int,int,bit0,K_4) != min) # label(fact_671_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 140 (all L all U 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)))) # label(fact_3699_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 141 (all X_a (ring_1(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2)),ring_1_Ints(X_a)))))))) # label(fact_3823_Ints__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 142 (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_4870_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 143 (all X_a (ring_1(X_a) -> (all Na all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3),Na)),ring_1_Ints(X_a))))))) # label(fact_3828_Ints__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 144 (all Y all X all U_1 (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_1),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_1),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_1))))) # label(fact_2185_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 145 (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_523_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 146 (all P_1 all Ma all Na (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),Na))) <-> (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),Na),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),Na),hAPP(nat,nat,suc,Q_4)))))) | Na = zero_zero(nat) & hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))) # label(fact_1496_split__div_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 147 (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_243_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 148 (all Na all Xa (Xa != zero_zero(real) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (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),Xa))) & 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),Xa))),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)),Na))),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),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) = hAPP(real,real,exp(real),Xa) & 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_4296_Maclaurin__exp__lt) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 149 (all K all Na 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),Na),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),Na)))) # label(fact_763_zdvd__reduce) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 150 (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_3085_prime__impl__zprime__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 151 (all X all Y ((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)) & (zero_zero(nat) = Y -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y)))) # label(fact_3138_bezw_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 152 (all X_a (linord1117847801e_zero(X_a) -> (all Xa (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),Xa)),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),Xa)))))) # label(fact_2629_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 153 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_324_add__0__left) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 154 (all X_a (real_normed_field(X_a) -> (all Xa 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)),Xa),one_one(X_a)))))) # label(fact_3871_DERIV__ident) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 155 (all X_a (field_char_0(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)),field_char_0_Rats(X_a)))))))) # label(fact_3712_Rats__diff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 156 (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_3218_transfer__int__nat__factorial) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 157 (all P_1 all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (all N_1 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_3),B_2),hAPP(nat,nat,suc,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_3),B_2),N_1))))))) # label(fact_3168_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 158 (all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit1,L_4))) # label(fact_780_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 159 (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_2288_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 160 (all X_b all X_c all X_a (topological_space(X_c) & topological_space(X_b) & topological_space(X_a) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (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_3))) -> 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_3))))))) # label(fact_4919_isCont__o2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 161 (all M all N all K_4 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),plus_plus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),K_4))),N)) # label(fact_3470_zgcd__zadd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 162 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_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),B)),C_1)))) # label(fact_361_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 163 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Va (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),hAPP(int,int,number_number_of(int),Va))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),hAPP(int,X_a,number_number_of(X_a),Va))))))) # label(fact_3329_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 164 (all X_a (real_algebra_1(X_a) -> ti(fun(real,X_a),of_real(X_a)) = of_real(X_a))) # label(tsy_c_RealVector_Oof__real_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 165 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int)) = hAPP(int,rat,number_number_of(rat),K_4)) # label(fact_3797_rat__number__expand_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 166 (all X_a (archim1727834104eiling(X_a) -> (all Va all Xa (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),Va)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),Va)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))))))) # label(fact_3328_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 167 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3298_gcd__diff2__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 168 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2738_finite) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 169 (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_3049_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 170 (all X_a all A_2 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_2)) = ti(fun(X_a,bool),A_2)) # label(fact_2239_double__complement) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 171 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),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),Na))),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),Na),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_4228_setsum__add__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 172 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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),A_2) = one_one(X_b))))) # label(fact_3978_setprod__infinite) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 173 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 174 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),N),M)) # label(fact_3566_plus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 175 (all Xa all Ya (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),Ya)),hAPP(int,int,number_number_of(int),Xa)) = zero_zero(int) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),Xa)),hAPP(int,int,number_number_of(int),Ya))))) # label(fact_1429_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 176 (all X_a (real_normed_vector(X_a) -> (all A_1 all R_3 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),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_3),B))))) # label(fact_4712_scaleR_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 177 (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_2135_arctan__monotone) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 178 (all Wa (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Wa))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,Wa)))))) # label(fact_1607_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 179 (all X_a (ring_char_0(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3)),A_3))))) # label(fact_3836_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 180 (all N ti(int,N) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N))) # label(fact_3366_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 181 (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),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)) = 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))))) # label(fact_1117_div__add__self2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 182 (all Na all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),Na)),one_one(real))),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)))) # label(fact_2406_nat__less__real__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 183 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,ln,X)))) # label(fact_2420_ln__realpow) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 184 (all X_a all G all A_3 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),A_3),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,A_3)),A_2)))) # label(fact_4534_Re_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 185 (all X_a (ordere142940540dd_abs(X_a) -> (all A_3 (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_3))) <-> ti(X_a,A_3) != zero_zero(X_a))))) # label(fact_990_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 186 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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)),pi)) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y))) # label(fact_2346_arcsin__pi) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 187 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_936_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 188 (all B_2 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> 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_2)),Xa),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_2)),Xa)))))) # label(fact_3933_DERIV__log) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 189 (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_1043_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 190 (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_809_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 191 (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_808_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 192 (all X_a all F1 all F2 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)) = ti(X_a,F1)) # label(fact_4139_nat__case__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 193 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) <-> ti(X_a,Ya) != ti(X_a,Xa))))) # label(fact_535_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 194 (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_413_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 195 (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_3260_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 196 (all Ma hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))) # label(fact_3638_phi__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 197 (all X_a (order(X_a) -> strict_mono(nat,X_a) = ti(fun(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool)),strict_mono(nat,X_a)))) # label(tsy_c_Orderings_Oorder_Ostrict__mono_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 198 (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_1 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_1),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))))))) # label(fact_4781_scaleR__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 199 (all A_1 all B all C_1 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_1))),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_1))),C_1)) = 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_1)) # label(fact_1547_div__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 200 (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_633_real__mult__order) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 201 (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_895_zcong__scalar) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 202 (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))) -> (ti(int,K_4) != zero_zero(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),N))))) # label(fact_759_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 203 (all X_a (field_char_0(X_a) -> field_char_0_Rats(X_a) = ti(fun(X_a,bool),field_char_0_Rats(X_a)))) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 204 (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_1421_neg__mod__sign) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 205 (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_1356_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 206 (all P_1 all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (all N_1 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_3),B_2),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_3),B_2),N_1))))))) # label(fact_3165_Bolzano__bisect__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 207 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int))))) # label(fact_58_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 208 (all X_a all One all Times all A_3 ti(X_a,One) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_3),zero_zero(nat))) # label(fact_2866_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 209 (all Xa (hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) <-> 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)))),Xa)))) # label(fact_1626_int__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 210 (all X_b all X_a (real_normed_vector(X_a) & topological_space(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),hAPP(X_a,X_b,F,A_3)),hAPP(X_a,filter(X_a),at(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),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_3))),hAPP(X_a,X_b,F,A_3)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4603_LIM__isCont__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 211 (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_3361_real__of__int__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 212 (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),plus_plus(nat),M),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))))) # label(fact_465_power__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 213 (all X_a all X_b all A_2 all B_1 (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_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_3209_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 214 (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]. 7.41/7.41 215 (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Xa)),hAPP(int,real,real_1(int),Ya))))) # label(fact_3356_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 216 (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_575_power2__sum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 217 (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_2 all E ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y) != 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_2),E)))))) # label(fact_3175_prod__cases5) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 218 (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_4408_gcd__neg2__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 219 (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_847_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 220 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C_1))))))) # label(fact_506_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 221 (all B_2 all A_3 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_3),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_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),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_2)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4)))))))) # label(fact_1198_wset__mem__inv__mem) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 222 (all Ma all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)))) # label(fact_1026_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 223 (all X_a all B_1 all C all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),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_2),B_1)))))) # label(fact_2233_DiffI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 224 (all Na all Xa all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 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),Diff,M_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_1)))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),Xa))) & 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) = hAPP(real,real,F,Xa)))))) # label(fact_4312_Maclaurin__all__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 225 (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_2414_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 226 (all X_a (linordered_field(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_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_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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C_1),B))))))))) # label(fact_1875_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 227 (all X_b (number(X_b) & semiring(X_b) -> (all V all B all C_1 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(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_1)) = 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_1))))) # label(fact_460_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 228 (all X_a (sgn_if(X_a) -> (all X ((ti(X_a,X) = zero_zero(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),X) = zero_zero(X_a)) & (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,sgn_sgn(X_a),X) = hAPP(X_a,X_a,uminus_uminus(X_a),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)) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),X))))))) # label(fact_2315_sgn__if) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 229 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (zero_zero(X_b) != hAPP(X_a,X_b,F,A_3) -> 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_3))))))) # label(fact_4909_isCont__sgn) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 230 (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_1123_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 231 (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_1962_norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 232 (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(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) & (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(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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(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_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)),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)))) & (ti(int,A_1) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B) = hAPP(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_3070_divmod__int__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 233 (all Na (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),Na)),zero_zero(real))) <-> zero_zero(nat) = Na)) # label(fact_2393_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 234 (all X_b all X_a (real_normed_algebra(X_b) & power(X_b) & topological_space(X_a) -> (all Na all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> 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)),Na)),A_3)))))) # label(fact_4917_isCont__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 235 (all X_a (real_normed_field(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_2)) -> 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_2)),Y_2)))))))) # label(fact_4039_summable__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 236 (all Na hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),Na)),field_char_0_Rats(real)))) # label(fact_3700_Rats__real__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 237 (all Xa hAPP(rat,int,archim2085082626_floor(rat),Xa) = 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))),Xa))),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),Xa)),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_4174_floor__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 238 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 all C all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1))))))) # label(fact_737_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 239 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_b) & topological_space(X_a) -> (all F all A_3 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_3))) -> 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_3)))))))) # label(fact_4901_isCont__LIM__compose) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 240 (all A_1 hAPP(real,real,cos,A_1) = hAPP(complex,real,re,hAPP(real,complex,cis,A_1))) # label(fact_3051_Re__cis) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 241 (all U hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U)) = U) # label(fact_4342_card__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 242 (all X 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)))) = 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)))))) # label(fact_10_quartic__square__square) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 243 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int))) # label(fact_82_zadd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 244 (all X_c all X_a all X_b all R_2 all A_3 all B_2 all C (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_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),A_3),B_2)),C)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_2,A_3),B_2),C)))) # label(fact_4070_splitD_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 245 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_2)) -> 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_2))))) # label(fact_3878_Im_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 246 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (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),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_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),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4607_LIM__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 247 (all N hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N)))) # label(fact_2904_floor__minus__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 248 (all A_1 all 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)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3799_quotient__of__Fract) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 249 (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),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))) & (-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_1128_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 250 (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_2015_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 251 (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_3862_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 252 (all Xa (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,suc,Xa))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)))) # label(fact_2472_even__Suc) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 253 (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]. 7.41/7.41 254 (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_445_mult__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 255 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_2)) -> 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_2)) = hAPP(real,X_a,of_real(X_a),hAPP(fun(nat,real),real,suminf(real),X_2)))))) # label(fact_4047_of__real_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 256 (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_2934_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 257 (all X_a (field_char_0(X_a) & number_ring(X_a) -> (all Wa 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),Wa)),field_char_0_Rats(X_a)))))) # label(fact_3710_Rats__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 258 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,Xa)),hAPP(int,nat,nat_1,Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),Ya)))))) # label(fact_1028_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 259 (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_494_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 260 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(rat,real,ratreal,Xa)),hAPP(rat,real,ratreal,Ya))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Xa),Ya)))) # label(fact_3781_real__less__code) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 261 (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_4825_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 262 (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_2159_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 263 (all X_a (real_normed_vector(X_a) -> (all Xa all A_3 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)),Xa)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa)),hAPP(real,filter(real),at(real),A_3)))))) # label(fact_4758_scaleR__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 264 (all Nat all Nat_5 (Nat = Nat_5 <-> hAPP(nat,nat,suc,Nat_5) = hAPP(nat,nat,suc,Nat))) # label(fact_1276_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 265 (all X_a (real_normed_vector(X_a) -> (all Y_2 all B_2 all X_2 all A_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),X_2),A_3),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_2),B_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,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_2)),Y_2)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),B_2)),sequentially))))))) # label(fact_4765_scaleR_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 266 (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_2274_cos__le__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 267 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all F all Sb (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sb)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sb)) -> 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),Sb) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sb)) -> hAPP(X_a,X_b,F,I) = zero_zero(X_b)))))))) # label(fact_4327_setsum__nonneg__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 268 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> hAPP(X_a,X_b,F,X_1) = zero_zero(X_b))) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,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),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_4372_setsum__mono__zero__cong__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 269 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3798_Fract__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 270 (all X_a (linorder(X_a) -> (all Xa all Ya (ti(X_a,Xa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Xa),Ya) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_4845_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 271 (all Na all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,N_1)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))))) -> hBOOL(hAPP(nat,bool,P_1,Na))))) # label(fact_2832_nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 272 (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_545_mult__2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 273 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(X_a,real,norm_norm(X_a),A_1) = hAPP(real,real,abs_abs(real),hAPP(X_a,real,norm_norm(X_a),A_1))))) # label(fact_1946_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 274 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)) = ord_atLeastLessThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 275 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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_3),B_2)),zero_zero(rat)))))) # label(fact_3805_Fract__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 276 (all X (zero_zero(real) != X -> one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),X))) # label(fact_2625_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 277 (all X_a all A_2 ti(fun(X_a,bool),A_2) = 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_2))) # label(fact_2847_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 278 (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_200_add__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 279 (all A_1 all B all C_1 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_1) = 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_1))),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_1))),C_1))) # label(fact_1432_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 280 (all X_a (real_normed_vector(X_a) -> (all Xa (ti(X_a,Xa) != 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),Xa))))))) # label(fact_1998_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 281 (all R_3 all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_3)),hAPP(real,complex,cis,A_1))) # label(fact_3198_rcis__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 282 (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),times_times(real),Y),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)) = hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y))))) # label(fact_3443_log__powr) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 283 (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_3306_ceiling__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 284 (all N N = hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_984_nat__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 285 (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_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 286 (all A_3 all C all D_1 all B_2 (ti(int,B_2) != zero_zero(int) -> (zero_zero(int) != ti(int,D_1) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_2)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),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_3),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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),B_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),D_1)))))))) # label(fact_3801_less__rat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 287 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (((exists X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2))) -> zero_zero(nat) = one_one(nat)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)))) # label(fact_2751_card_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 288 (all X_a (field(X_a) -> (all Na all Xa (one_one(X_a) != ti(X_a,Xa) -> 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),Xa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na)) = 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),Xa),Na)),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Xa),one_one(X_a))))))) # label(fact_4197_geometric__sum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 289 (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_832_diff__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 290 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Xa)),one_one(real))) -> hAPP(real,real,arctan,Xa) = 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)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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),Xa)),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_3993_arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 291 (all X_a (ring_char_0(X_a) -> (all Wa all Z (ti(int,Z) = ti(int,Wa) <-> hAPP(int,X_a,ring_1_of_int(X_a),Z) = hAPP(int,X_a,ring_1_of_int(X_a),Wa))))) # label(fact_3600_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 292 (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_4882_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 293 (all X_a (power(X_a) -> power_power(X_a) = ti(fun(X_a,fun(nat,X_a)),power_power(X_a)))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 294 (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_1216_phi__prime) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 295 (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_1454_nat__one__le__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 296 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_4380_Fract__coprime) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 297 (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_1832_abs__divide) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 298 (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_597_real__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 299 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all Sb 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)),Sb)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sb))))))) # label(fact_4121_sums__Suc__imp) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 300 (all A_2 all B_1 (A_2 = B_1 <-> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_2))) # label(fact_3672_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 301 (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_1195_MultInv__prop2a) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 302 (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_1163_aux______3) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 303 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))))))) # label(fact_2910_one__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 304 (all X hAPP(real,real,cos,hAPP(real,real,arctan,X)) != zero_zero(real)) # label(fact_2277_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.41 305 (all X_b all X_a (minus(X_a) -> (all A_2 all B_1 all Xa hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_2,Xa)),hAPP(X_b,X_a,B_1,Xa)) = 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_2),B_1),Xa)))) # label(fact_2988_minus__apply) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 306 (all X_a (real_normed_field(X_a) -> (all Y_2 all B_2 all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_2),B_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(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_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)))))))) # label(fact_4114_sums__diff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 307 (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_3395_floor__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 308 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat))) # label(fact_603_mult__0__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 309 (all X_a (linordered_idom(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3))))) # label(fact_2317_sgn__1__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 310 (all M all 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) = 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)) # label(fact_1493_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 311 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(real)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,real,number_number_of(real),V) = hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_2423_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 312 (all X_2 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_2)) <-> (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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),hAPP(nat,real,X_2,M_2)),hAPP(nat,real,X_2,N_1)))),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,J_1))))))))))) # label(fact_3339_Cauchy__iff2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 313 (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_1525_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 314 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_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_3),B_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_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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_3)))))) # label(fact_425_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 315 (all R_3 all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_3) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int))) # label(fact_4431_normalize__coprime) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 316 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) <-> (exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists N_2 all N_1 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_2,N_1)),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,X_2,N_2))))),K_1))))))))) # label(fact_3516_Bseq__iff3) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 317 (all X_a all A_2 all B_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_2),B_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)),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_2),B_1)),B_1)) # label(fact_2243_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 318 (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_2007_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 319 (all P_1 all Na ((all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))) -> hBOOL(hAPP(nat,bool,P_1,X_1)))) <-> (all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))))) # label(fact_4561_all__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 320 (all X_a (semiring_div(X_a) -> (all C all B_2 all A_3 (ti(X_a,A_3) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_2),A_3) = ti(X_a,C) <-> ti(X_a,B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3))))))) # label(fact_1119_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 321 (all X_a all Q_1 all P_1 all Xa (hBOOL(hAPP(X_a,bool,P_1,Xa)) -> (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,Xa))))) # label(fact_4364_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 322 (all B all Bq all Br all A_1 all C_1 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_1),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_1),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_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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C_1),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_1))),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_1)))))))) # label(fact_3122_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 323 (all X_a all X_b (t2_space(X_b) -> (all L_1 all F all L all A_2 (-hBOOL(hAPP(filter(X_a),bool,trivial_limit(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),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_1),A_2)) -> ti(X_b,L_1) = ti(X_b,L))))))) # label(fact_4792_tendsto__unique) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 324 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all Xa all G all L 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),L),hAPP(X_a,filter(X_a),at(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),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)),Xa)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L),Xa)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4763_scaleR__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 325 (all X_a (real_normed_algebra(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(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_2108_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 326 (all X_a (semiring_div(X_a) -> (all D_1 all B_2 all C all A_3 (zero_zero(X_a) != ti(X_a,A_3) -> (zero_zero(X_a) != ti(X_a,C) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),D_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_2),A_3) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_2),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),D_1))))))))) # label(fact_1120_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 327 (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_543_mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 328 (all X_a (real_normed_field(X_a) -> (all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> 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_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))))) # label(fact_4106_sums__minus) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 329 (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_3065_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 330 (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_3261_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 331 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_1390_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 332 (all Xa all Ya all P_1 ((-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Ya) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),Xa),Ya))) & (hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Xa) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),Xa),Ya))))) # label(fact_163_int__if__cong) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 333 (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_492_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 334 (all Xa all A_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(int,real,real_1(int),A_3))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),Xa)),A_3)))) # label(fact_3392_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 335 (all Xa (Xa = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,Xa)),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)),Xa)))) # label(fact_2167_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 336 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) # label(fact_1993_minus__real__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 337 (all A_1 all 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))))) = 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))) # label(fact_786_zspecial__product) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 338 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min))) # label(fact_2016_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 339 (all P_4 (hBOOL(hAPP(int,bool,zprime,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),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4))))) # label(fact_1228_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 340 (all X_a (division_ring(X_a) -> inverse_inverse(X_a) = ti(fun(X_a,X_a),inverse_inverse(X_a)))) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 341 (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_34_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 342 (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_410_le__add1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 343 (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_4378_coprime__dvd__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 344 (all Xa (zero_zero(real) = hAPP(real,real,sqrt,Xa) <-> zero_zero(real) = Xa)) # label(fact_2126_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 345 (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_2454_sin__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 346 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_2 all F all A_3 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),A_3),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),B_2),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),A_3),B_2)),A_2))))))) # label(fact_4753_scaleR_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 347 (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_1180_MultInv__prop1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 348 (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),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_1),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_1))),hAPP(real,real,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_3945_DERIV__sin__circle__all) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 349 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Q_3),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,uminus_uminus(int),P_5)),hAPP(int,int,uminus_uminus(int),Q_3))))) # label(fact_3745_normalize__negative) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 350 (all X_a (linord219039673up_add(X_a) -> (all A_3 (ti(X_a,A_3) = zero_zero(X_a) <-> ti(X_a,A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))) # label(fact_1935_equal__neg__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 351 (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_3726_Frct__code__post_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 352 (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_1482_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 353 (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_4839_min__diff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 354 (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_2 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_2),I_2))) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),D_2),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_2),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_2),I_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3583_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 355 (all E_1 all B all D_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E_1),B)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),E_1) = one_one(int))))) # label(fact_4397_coprime__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 356 (all X_a (linordered_semidom(X_a) -> (all Xa all Ya all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2)) -> (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_2),Xa)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_2),Ya))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Xa),Ya))))))) # label(fact_239_power__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 357 (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_1742_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 358 (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_3264_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 359 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1)))) # label(fact_1370_power__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 360 (all X_a (field_char_0(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2)),field_char_0_Rats(X_a)))))))) # label(fact_3709_Rats__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 361 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = 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)))) # label(fact_870_zdiff__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 362 (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_1886_less__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 363 (all F all K_3 all Na ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),Na)) -> 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)),Na))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),K_3))))) # label(fact_4315_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 364 (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_3263_gcd__greatest__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 365 (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]. 7.41/7.42 366 (all N all M all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),R_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),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_3433_lemma__floor) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 367 (all X_a (comm_monoid_add(X_a) & metric_space(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_4355_suminf__eq__lim) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 368 (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_3757_quotient__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 369 (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_172_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 370 (all R_3 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),R_3)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_3)) # label(fact_2821_i__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 371 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,one_one(nat)),A_1))) # label(fact_2882_coprime__1_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 372 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,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))))))) # label(fact_3016_complex__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 373 (all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))) # label(fact_806_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 374 (all A_1 all B all Q_3 all R_3 (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_3))) -> (zero_zero(int) != ti(int,B) -> ti(int,R_3) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1619_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 375 (all X_a (ordere1490568538miring(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_433_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 376 (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_724_dvdI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 377 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_2 all A_3 (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_3))) -> (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_2))) -> 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_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_2)) = 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_3))),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_2)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat))))))))) # label(fact_4646_Cauchy__product) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 378 (all X_a (linord581940658strict(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_456_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 379 (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_3723_Frct__code__post_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 380 (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_3849_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 381 (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_873_zcong__refl) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 382 (all X_a (linord219039673up_add(X_a) -> (all A_3 (zero_zero(X_a) = ti(X_a,A_3) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),A_3))))) # label(fact_65_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 383 (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_1457_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 384 (all X_a all A_2 hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2) = 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_2)) # label(fact_4282_card__eq__setsum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 385 (all X_a (linordered_idom(X_a) -> (all Xa all Na ((hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) & zero_zero(X_a) = ti(X_a,Xa) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Na))) & zero_zero(nat) != Na <-> 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),Xa),Na)),zero_zero(X_a))))))) # label(fact_2508_power__le__zero__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 386 (all Xa 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),Xa),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),Xa))),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1567_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 387 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))) # label(fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 388 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1641_odd__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 389 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Xa)),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))))),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))))))),Xa),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)))),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),Xa)),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_3994_DERIV__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 390 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_602_mult__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 391 (all Xa all Ya 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Xa),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ya),Z))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya))))) # label(fact_636_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 392 (all P_1 all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_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(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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_3),B_2)))),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_3),B_2)))),zero_zero(real)),sequentially)) -> (exists L_3 ((all N_1 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_3),B_2),N_1))),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_3),B_2))),L_3),sequentially)) & (all N_1 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_3),B_2),N_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,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_3),B_2))),L_3),sequentially))))))))) # label(fact_4539_Bolzano__nest__unique) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 393 (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_1012_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 394 (all X_a all C all A_2 all B_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)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_2246_psubsetD) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 395 (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_2567_abs__inverse) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 396 (all N all X hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,exp(real),X)),N)) # label(fact_2401_exp__real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 397 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B 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)),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),times_times(X_a),A_1),B)),N)))) # label(fact_394_power__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 398 (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_4713_scaleR__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 399 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C_1 all D_3 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3)) = 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_1),D_3))))) # label(fact_293_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 400 (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_1866_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 401 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all 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),times_times(X_a),A_1),B)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C_1)))))) # label(fact_723_dvd__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 402 (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_2692_real__root__minus) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 403 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1) -> ti(X_a,C_1) = ti(X_a,B))))) # label(fact_292_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 404 (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_3997_lemma__sin__ext) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 405 (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_1937_minus__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 406 (all Xa 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)),Xa),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,Xa))),hAPP(real,real,sin,Xa))))) # label(fact_3932_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 407 (all A_1 all B (B != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),B)))) # label(fact_3285_gcd__le2__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 408 (all Na all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Na)),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),Na),Ma)))) # label(fact_3417_int__le__real__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 409 (all Ma all Na (Na = zero_zero(nat) & zero_zero(nat) = Ma <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na))) # label(fact_157_add__is__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 410 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)))))) # label(fact_2749_psubset__card__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 411 (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)))) = zero_zero(nat))) # label(fact_2503_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 412 (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_1663_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 413 (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_1435_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 414 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3793_real__times__code) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 415 (all X_a all A_2 all X_2 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_2),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),X_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_1746_UnionI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 416 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,Xa)),one_one(real))))) # label(fact_2148_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 417 (all X_a (linorder(X_a) -> (all Z all Xa all Ya (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),Xa),Ya))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Ya)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Xa)))))) # label(fact_4824_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 418 (all Va all K all A_3 all B_2 (B_2 != A_3 -> ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),Va),X_1),K))) -> hAPP(real,real,Va,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_3),B_2)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,Va,A_3)),hAPP(real,real,Va,B_2))),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]. 7.41/7.42 419 (all X_b all X_a all B_2 all F all Xa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> (hAPP(X_a,X_b,F,Xa) = ti(X_b,B_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),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_2)))))) # label(fact_3661_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 420 (all X hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)) = hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X))) # label(fact_3029_Re_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 421 (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_1871_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 422 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)) # label(fact_2885_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 423 (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_1782_divide__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 424 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),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_3),B_2)),zEven))))) # label(fact_1712_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 425 (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),minus_minus(X_a),B),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),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))))))) # label(fact_2619_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 426 (all B all A_1 all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),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) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_1433_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 427 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_4701_scaleR__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 428 (all Xa ((exists Y_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_1)) = Xa) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)))) # label(fact_2497_odd__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 429 (all Ma all Na all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) <-> Na = Ma))) # label(fact_696_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 430 (all C_1 all A_1 all B (B = A_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C_1),A_1))))) # label(fact_947_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 431 (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]. 7.41/7.42 432 (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_1 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_1)),X)))))))) # label(fact_2667_ex__less__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 433 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_412_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 434 (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_1 all Y_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_1),Y_1))) -> ((Y_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),Y_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,X_1),Y_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,A0),A1))))) # label(fact_3753_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 435 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_155_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 436 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> M = N))) # label(fact_950_dvd__antisym) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 437 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))) <-> 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)))),Xa)))))) # label(fact_2873_one__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 438 (all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_2 ((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_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Xa)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Xa),H_1))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2))))))) # label(fact_2663_DERIV__neg__dec__left) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 439 (all F all Ya all Xa all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Xa),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_3),B_2))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Ya),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_3),B_2))) -> ((all X_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_3),B_2))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),zero_zero(real))))) -> hAPP(real,real,F,Xa) = hAPP(real,real,F,Ya)))))) # label(fact_3703_DERIV__isconst3) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 440 (all Ya all Xa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) <-> Xa = Ya))) # label(fact_955_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 441 (all F all L all 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),F),L),hAPP(real,filter(real),at(real),C))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) & (all X_1 (X_1 != C & 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),X_1))),R_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,F,X_1)))))))))) # label(fact_4653_LIM__fun__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 442 (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_1982_norm__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 443 (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_249_not__one__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 444 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,Xa)),zero_zero(real)))))) # label(fact_1721_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 445 (all B_2 all A_3 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))))) # label(fact_1207_wset__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 446 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real))) # label(fact_2302_real__sgn__pos) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 447 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),one_one(int))))))) # label(fact_3324_ceiling__less__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 448 (all X_b all X_a (comm_monoid_add(X_a) -> (all 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),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_2) = zero_zero(X_a)))) # label(fact_4239_setsum__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 449 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))))))) # label(fact_228_add__increasing) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 450 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B 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),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1850_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 451 (all X_a ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_case(X_a)) = complex_case(X_a)) # label(tsy_c_Complex_Ocomplex_Ocomplex__case_res) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 452 (all X_a (real_normed_algebra(X_a) -> (all X zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a))))) # label(fact_1242_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 453 (all Ma all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = Ma & Na = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1381_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.42 454 (all X_a all A_3 all F all Va all Na 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,Va)))),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_3),F),Na)),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,Va)))),Na)),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_3),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,Va)))),Na)))) = 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_3),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),Va)),Na))) # label(fact_4179_nat__rec__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 455 (all X_a (real_normed_algebra(X_a) -> (all Xa_2 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),Y))))) # label(fact_1249_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 456 (all N N = hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N))) # label(fact_2370_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 457 (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_3396_floor__subtract) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 458 (all V_2 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),V_2) = 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_2))) & (-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_2),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)) = 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_2))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),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_2)) = hAPP(int,nat,number_number_of(nat),V))))) # label(fact_36_add__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 459 (all X_a all F all Xa all A_2 ((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_2)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(X_a,nat,F,I_2)),Xa))) -> one_one(nat) = 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_2)),Xa))) # label(fact_4155_setprod__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 460 (all X_a (boolean_algebra(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Xa)),hAPP(X_a,X_a,uminus_uminus(X_a),Ya))))))) # label(fact_2987_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 461 (all X_a (real_normed_algebra(X_a) -> (all Ya all A_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(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)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),Ya)),hAPP(X_a,filter(X_a),at(X_a),A_3)))))) # label(fact_4588_mult__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 462 (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),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,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)))) # label(fact_2937_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 463 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_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_4370_setsum__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 464 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_975_abs__add__abs) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 465 (all X_a (linordered_idom(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_3)),A_3)),zero_zero(X_a)))))))) # label(fact_3822_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 466 (all X_a all F all A_2 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_2) = 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_2))) # label(fact_3967_int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 467 (all P_5 hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),zero_zero(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) # label(fact_3748_normalize__denom__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 468 (all Z_1 hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_4875_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 469 (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]. 7.41/7.43 470 (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),J_2),I_1)),K_4) = 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))) # label(fact_853_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 471 (all V_2 all K_4 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K_4))))) # label(fact_648_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 472 (all M all R_3 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_3),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_3) = 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_3107_xzgcd__linear) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 473 (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_4033_fst__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 474 (exists K_2 ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) # label(fact_2991_cnj_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 475 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all Xa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Xa)) <-> ti(X_a,Xa) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F) & hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4120_sums__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 476 (all Na hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),sin_coeff),Na) = hAPP(nat,real,cos_coeff,Na)) # label(fact_4143_sin__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 477 (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_3318_floor__minus) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 478 (all X_a (field_inverse_zero(X_a) -> (all Z_1 all X all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_1881_add__num__frac) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 479 (all Ma all Na (ti(int,Na) = zero_zero(int) & zero_zero(int) = ti(int,Ma) <-> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),Na) = zero_zero(int))) # label(fact_4410_gcd__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 480 (all Xa all Na all Diff all F (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),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),Xa))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) -> 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),Xa))) & 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) = hAPP(real,real,F,Xa)))))) # label(fact_4305_Maclaurin__bi__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 481 (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_1418_pos__mod__sign) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 482 (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]. 7.41/7.43 483 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> 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_3)))))) # label(fact_4918_isCont__norm) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 484 (all Na ((exists M_2 Na = 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))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)))) # label(fact_2524_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 485 (all X_a all A_2 all B_1 (-hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),B_1),A_2)) & hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_2),B_1)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less(filter(X_a)),A_2),B_1)))) # label(fact_4535_less__filter__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 486 (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_2494_minus__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 487 (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_4833_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 488 (all X_a (real_vector(X_a) -> (all X all Y all Xa_2 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_2)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_2)) = 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_2)))) # label(fact_4695_scaleR__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 489 (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_2065_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 490 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),one_one(X_a))))))) # label(fact_3327_ceiling__le__one) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 491 (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]. 7.41/7.43 492 (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_4433_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 493 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)),A_1)) # label(fact_3354_powr__powr__swap) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 494 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),d22set,A_3))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)))) # label(fact_1223_d22set__g__1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 495 (all X_a (real_field(X_a) -> (all X all Y (Y != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)))))) # label(fact_2814_nonzero__of__real__divide) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 496 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (zero_zero(X_a) != ti(X_a,Xa) | ti(X_a,Ya) != 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),Xa),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),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_100_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 497 (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,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_3766_minus__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 498 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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_1))))) -> 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_2))))))) # label(fact_4176_setprod__pos) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 499 (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_3454_zgcd__zdvd1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 500 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2570_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 501 (all Wa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z)))) # label(fact_289_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 502 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (M != N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_403_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 503 (all X all N_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),N),N_4)) -> (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_4),X)))))))) # label(fact_2716_real__root__increasing) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 504 (all X_a (real_normed_vector(X_a) -> (all X_2 all K_3 ((all N_1 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_2,N_1))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)))))) # label(fact_3525_BseqI_H) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 505 (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_3259_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 506 (all Xa hAPP(rat,product_prod(int,int),quotient_of,Xa) = 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),Xa)),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_4436_quotient__of__def) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 507 (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_3156_snd__conv) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 508 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1) != ti(int,X_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_1)) -> 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_1),D)))))))) # label(fact_4655_aset_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 509 (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),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)) = 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))))))) # label(fact_1884_diff__frac__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 510 (all L all U 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)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))))) # label(fact_3694_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 511 -(all M1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),v),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),w),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),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),M1)) # label(fact_1155__096_B_Bthesis_O_A_I_B_Bm1_O_Av_A_094_A2_A_L_Aw_A_094_A2_A_061_A_I1_A_) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 512 (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_744_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 513 (all Xa all Ya (hAPP(int,real,real_1(int),Ya) = hAPP(int,real,real_1(int),Xa) <-> ti(int,Xa) = ti(int,Ya))) # label(fact_3353_real__of__int__inject) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 514 (all Xa (Xa = hAPP(real,real,hAPP(real,fun(real,real),powr,Xa),one_one(real)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)))) # label(fact_3404_powr__one__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 515 (all X_a (ordered_ring(X_a) -> (all A_3 all E_2 all C all B_2 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_3),B_2)),E_2)),C)),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_3),E_2)),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),B_2),E_2)),D_1))))))) # label(fact_775_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 516 (all K (pls = hAPP(int,int,bit0,K) <-> pls = ti(int,K))) # label(fact_70_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 517 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),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_1),D)),Ta))))))) # label(fact_4663_bset_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 518 (all Xa (one_one(real) = hAPP(real,real,sqrt,Xa) <-> one_one(real) = Xa)) # label(fact_2129_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 519 (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_3346_real__number__of) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 520 (all X_a (ordered_ring(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_434_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 521 (all X_b all X_a (real_normed_vector(X_b) & ord(X_a) -> (all X_2 all M_1 ((all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_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,X_2,M_1)),hAPP(X_a,X_b,X_2,N_1)))),one_one(real))))) -> (all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_1)) -> 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_2,N_1))),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_2,M_1))))))))))) # label(fact_2115_lemmaCauchy) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 522 (all R_3 exists X_1 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)) = R_3 & one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)) & (all Y_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) & 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_1))) & R_3 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) -> Y_1 = X_1)) & 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_1))))) # label(fact_4437_quotient__of__unique) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 523 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_788_zdiff__power3) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 524 (all N all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,Z_1)),N) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)))) # label(fact_1047_nat__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 525 (all Diff all F all Na all H ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) & 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(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)),Na)) & 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),T_4),zero_zero(real))) & 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)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4)))))) # label(fact_4310_Maclaurin__minus__objl) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 526 (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_495_mult__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 527 (all A_1 all B all C_1 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_1) = 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_1)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C_1))),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_1)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C_1))),C_1))) # label(fact_1372_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 528 (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_2680_odd__real__root__power__cancel) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 529 (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_608_power__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 530 (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) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),M)))) # label(fact_3241_coprime__exp2__nat) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 531 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Xa hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),exp(X_a)),Xa))))) # label(fact_4929_isCont__exp) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 532 (all N all M ((zero_zero(nat) = M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = N) & (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))))) # label(fact_1466_add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 533 (all X_a all X_b (linordered_semidom(X_b) -> (all G all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_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_1)),hAPP(X_a,X_b,G,X_1))) & 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_1))))) -> 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_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2))))))) # label(fact_4177_setprod__mono) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 534 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y))))) # label(fact_4700_scaleR__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 535 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),Z_4))))) # label(fact_1042_nat__add__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 536 (all X_a (ordered_ab_group_add(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_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_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))))) # label(fact_1932_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 537 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)))))) # label(fact_1986_dvd__div__neg) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 538 (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_2579_inverse__divide) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 539 (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]. 7.41/7.43 540 (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),times_times(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),times_times(real),X),Y))))) # label(fact_2795_of__real__mult) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 541 (all C (zero_zero(rat) = C <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(rat,fun(nat,rat),combk(rat,nat),C))))) # label(fact_4877_vanishes__const) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 542 (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_1386_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 543 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1))) # label(fact_1257_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 544 (all X_a all A_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_2),A_2))) # label(fact_2210_subset__refl) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 545 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),min)) # label(fact_2932_add__Min__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 546 (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_3627_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 547 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Xa)) -> 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),Xa))),zero_zero(real)),sequentially)))) # label(fact_4457_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 548 (all X_a all G all A_2 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_2) = 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_2))) # label(fact_4275_cnj_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 549 (all X_4 all Y_3 hAPP(real,real,sin,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_4),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_4),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_3),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),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_4),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_4),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_3),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_2363_sin__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 550 (all Q_5 all R_4 all A_1 all B all Q_3 all R_3 (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_3))) -> (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_4))) -> (ti(int,B) != zero_zero(int) -> ti(int,Q_5) = ti(int,Q_3))))) # label(fact_1613_unique__quotient) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 551 (all X_a (order(X_a) -> (all A_3 all B_2 all C all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3)) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C),D_1))))))) # label(fact_4550_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 552 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2739_finite__code) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 553 (all Xa (zero_zero(real) = Xa <-> -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),Xa),Xa))))) # label(fact_631_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 554 (all Xa hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arctan),Xa),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),Xa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2656_DERIV__arctan) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 555 (all Na all Ma hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,Na)),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),Na))),Ma)) # label(fact_4858_min__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 556 (all N all M all A_1 all 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),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_4375_coprime__exp2__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 557 (all D_3 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),A_1))) # label(fact_4415_coprime__lmult__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 558 (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_1909_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 559 (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_2)) -> 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_2)),Y_2)))))) # label(fact_4879_vanishes__add) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 560 (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,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)) = 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))) # label(fact_1452_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 561 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 all X_1 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_1),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))))) # label(fact_4783_scaleR__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 562 (all W ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),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))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))))) # label(fact_3919_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 563 (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_4381_gcd__0__int) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 564 (all A_9 all B_8 all Q_6 all Y (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) = ti(int,A_9) -> ((-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))) & (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))) -> (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_1478_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 565 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)))) # label(fact_1702_even__odd__disj) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 566 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_166_one__neq__zero) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 567 (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,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_2297_sin__cos__squared__add2) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 568 (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_21_int__power) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 569 (all X_a all X_b all A_2 all B_2 all F all Xa (hAPP(X_b,X_a,F,Xa) = ti(X_a,B_2) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),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_2)))))) # label(fact_3654_image__eqI) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 570 (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_816_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 571 (all Xa all Ya (Xa = Ya <-> hAPP(nat,int,semiring_1_of_nat(int),Xa) = hAPP(nat,int,semiring_1_of_nat(int),Ya))) # label(fact_162_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 572 (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_2085_negative__zle__0) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 573 (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_1916_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 574 (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_2179_real__sqrt__ge__abs1) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 575 (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_267_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 576 (all X_a (ring_n68954251visors(X_a) -> (all A_3 all B_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_2) = zero_zero(X_a) <-> ti(X_a,A_3) = zero_zero(X_a) | zero_zero(X_a) = ti(X_a,B_2))))) # label(fact_375_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 577 (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(int,X_a,ring_1_of_int(X_a),K) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),K))))) & (zero_zero(int) = ti(int,K) -> zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),K)))))) # label(fact_4005_of__int__num) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 578 (all X_b all X_a (field(X_a) -> (all F all A_2 all Ra 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_2)),Ra) = 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)),Ra)),A_2)))) # label(fact_4244_setsum__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.41/7.43 579 (all X_a (ring_div(X_a) -> (all A_1 all B all C_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),minus_minus(X_a),A_1),B)),C_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),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1))),C_1)))) # label(fact_1299_mod__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 580 (all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)))) # label(fact_1627_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 581 (all X_a (semiring_char_0(X_a) -> (all Ma all Na (hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma) = hAPP(nat,X_a,semiring_1_of_nat(X_a),Na) <-> Na = Ma)))) # label(fact_161_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 582 (all M all N all R_4 all S_4 all S_3 all T_6 all T_5 all Rn all Sn_1 all Tn_1 all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_3)) -> (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_4),R_3),S_4),S_3),T_6),T_5) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) = ti(int,R_4) -> (ti(int,R_3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn_1),N)) = ti(int,Rn)))))) # label(fact_3110_xzgcda__linear) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 583 (all X_a (archim1727834104eiling(X_a) -> (all Va all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),Va)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))) <-> 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),Va)),Xa)))))) # label(fact_2912_number__of__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 584 (all Xa (hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),Xa))))) # label(fact_2484_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 585 (all M all N all R_4 all S_4 all S_3 all T_6 all T_5 all R_3 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),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),R_3),S_4),S_3),T_6),T_5) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_3),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_4),R_3)),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_4),R_3)),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_4),R_3)),T_5)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),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),R_3),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_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_4),T_6))))) # label(fact_3108_xzgcda_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 586 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2252_sin__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 587 (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_902_zcong__zpower) # label(axiom) # label(non_clause). [assumption]. 7.46/7.43 588 (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_1 (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_1),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_1)))) -> ((all T1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T1),S)) -> (all T2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T2),S)) -> (ti(fun(X_a,bool),T2) != ti(fun(X_a,bool),T1) -> (all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),T1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),T2)) -> hAPP(X_a,X_b,F,X_1) = zero_zero(X_b))))))))) -> hAPP(fun(fun(X_a,bool),bool),X_b,hAPP(fun(fun(X_a,bool),X_b),fun(fun(fun(X_a,bool),bool),X_b),big_co1399186613setsum(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F)),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),S)))))))) # label(fact_4337_setsum__UNION__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 589 (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_419_add__leE) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 590 (all X_a (number_ring(X_a) -> (all Ya (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),Ya))))) <-> hAPP(int,X_a,number_number_of(X_a),Ya) = one_one(X_a))))) # label(fact_2119_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 591 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,cos,X) -> (exists N_1 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_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(nat,bool,even_odd_even(nat),N_1))))))) # label(fact_2531_cos__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 592 (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_4492_LIMSEQ__const) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 593 (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_652_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 594 (all B_1 all K all Diff all H all Na ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (Na = hAPP(nat,nat,suc,K) -> (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),Na)) -> 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),Na),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_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),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),Na),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),Na),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),Na),hAPP(nat,nat,suc,M_2))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_1),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),Na),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),Na),hAPP(nat,nat,suc,M_2))))))))))))))) # label(fact_4295_Maclaurin__lemma2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 595 (all X_a all Ra ((all X_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),X_1)),Ra))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,refl(X_a),Ra)))) # label(fact_3579_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 596 (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_1256_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 597 (all P_5 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> -(hBOOL(hAPP(nat,bool,prime,P_5)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B))))) # label(fact_3086_coprime__prime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 598 (all X_a all X_c all X_b all F all Xa all G (hAPP(X_c,X_b,G,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),Xa)) = hAPP(X_c,X_b,F,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),Xa)) <-> 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),Xa) = 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),Xa))) # label(fact_4091_apsnd__eq__conv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 599 (all U all Ma all Na 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)),Ma)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U)),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)),Na)))))) # label(fact_869_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 600 (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_2310_sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 601 (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]. 7.46/7.44 602 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3143_mod__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 603 (all X_a (real_normed_algebra(X_a) -> (all Y zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y)))) # label(fact_1240_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 604 (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_600_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 605 (all Xa 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),Xa),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),Xa)),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1564_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 606 (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_4512_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 607 (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_1445_diff__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 608 (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_1282_mod__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 609 (all X_a all G all A_2 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_2)) = 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_2)) # label(fact_4274_Im_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 610 (all X_a all C all A_2 all B_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)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_2189_subsetD) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 611 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,A_1))) # label(fact_1996_Log_Olog__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 612 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1419_pos__mod__conj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 613 (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),div_div(int),K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4)))) # label(fact_2188_z3div__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 614 (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_783_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 615 (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_346_int__ge__induct) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 616 (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_2298_sin__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 617 (all X_a (group_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_1921_minus__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 618 (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_2691_real__root__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 619 (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_640_zmult__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 620 (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]. 7.46/7.44 621 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),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)))) = hAPP(nat,nat,fact_fact(nat),N))) # label(fact_2556_fact__reduce__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 622 (all Xa all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),sr,P_4))))) # label(fact_1542_SRStar__SR__prop) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 623 (all X_a all M_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,finite_finite_1(list(X_a)),M_1)) -> (exists N_1 all X_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_1),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_1)),N_1)))))) # label(fact_3582_finite__maxlen) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 624 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),Xa)),hAPP(real,real,exp(real),Ya))))) # label(fact_1756_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 625 (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_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))))))) # label(fact_2825_of__real_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 626 (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_4699_scaleR_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 627 (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]. 7.46/7.44 628 (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_4873_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 629 (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_3473_zgcd__geq__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 630 (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_2226_arctan__lbound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 631 (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_1862_frac__less2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 632 (all Xa hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sqrt),Xa))) # label(fact_4930_isCont__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 633 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_2 all A_3 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_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),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_3))),B_2)),one_one(X_b))),S) = hAPP(X_a,X_b,B_2,A_3)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_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),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_3))),B_2)),one_one(X_b))),S) = one_one(X_b)))))) # label(fact_3983_setprod__delta_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 634 (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_1165_div__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 635 (all X_a (real_normed_vector(X_a) -> (all X_2 all A_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_2),A_3),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_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3)),sequentially)))))) # label(fact_4469_LIMSEQ__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 636 (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_2477_odd__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 637 (all Xa all Na (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Xa),Na))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) & Na != zero_zero(nat))) # label(fact_1609_even__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 638 (all Xa 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))))),Xa),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,Xa))),hAPP(real,real,cos,Xa))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,Xa))),hAPP(real,real,cos,Xa)))))) # label(fact_3942_DERIV__cos__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 639 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_3)) -> 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3)))))))) # label(fact_327_add__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 640 (all X_a (real_normed_vector(X_a) -> (all Ra_1 all R_3 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),X))))) # label(fact_4711_scaleR__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 641 (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_518_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 642 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists R_1 exists A_4 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,sin,A_4)) = Y & X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,cos,A_4)))))) # label(fact_2560_polar__ex1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 643 (all X_a all X_b all X_c all Xa 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,Xa)))) # label(fact_3178_prod__induct3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 644 (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_2180_real__sqrt__ge__abs2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 645 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all B_2 all C all Wa (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_2),C)),hAPP(int,X_a,number_number_of(X_a),Wa))) <-> (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),B_2),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),Wa)),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(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),hAPP(int,X_a,number_number_of(X_a),Wa)),C)),B_2))) & (-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(int,X_a,number_number_of(X_a),Wa))))))))) # label(fact_1794_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 646 (all X_a all F1 all F2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),zero_zero(nat)) = ti(X_a,F1)) # label(fact_4181_nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 647 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_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),times_times(X_a),A_3),B_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),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_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)))))) # label(fact_424_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 648 (all X_a (linordered_semidom(X_a) -> (all N all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),R_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),R_3),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_3),hAPP(nat,nat,suc,N))),R_3))))))) # label(fact_1456_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 649 (all R_3 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_3))),one_one(real))),R_3))) # label(fact_3428_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 650 (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,zprime,P_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_1)))))) # label(fact_928_zprime__factor__exists) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 651 (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_2254_sin__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 652 (all X_a (real_n2089651433ebra_1(X_a) -> hAPP(X_a,real,norm_norm(X_a),one_one(X_a)) = one_one(real))) # label(fact_1980_norm__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 653 (all Na all Xa exists T_4 (hAPP(real,real,sin,Xa) = 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))),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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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),Na))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) & 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),Xa))))) # label(fact_4268_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 654 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hAPP(X_a,X_a,exp(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,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_4775_lemma__exp__ext) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 655 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),K)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),K))))))) # label(fact_4961_atMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 656 (all X_a (ring_div(X_a) -> (all A_1 all B all C_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),minus_minus(X_a),A_1),B)),C_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),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_1))),C_1)))) # label(fact_1301_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 657 (all N_3 ((exists M_2 all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_3683_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 658 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),K_4) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)))) # label(fact_3594_number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 659 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,Na))))) # label(fact_1332_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 660 (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_3825_Ints__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 661 (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 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_4),Q_4) = ti(int,M_5)))) # label(fact_1521_zmod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 662 (all A_3 all B_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)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_3) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_3),B_2)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),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_2),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_3),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_2))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_3),B_2)))) # label(fact_1660_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 663 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3608_complex__Im__of__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 664 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),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(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)))) # label(fact_3035_complex__Im__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 665 (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)),posDivAlg,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))))) & (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))))) # label(fact_1648_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 666 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (Na = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na)),Ma))))) # label(fact_879_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 667 (all X_a all Na all F all C all H ((all N_1 hAPP(nat,X_a,F,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),C),H),N_1)) -> hAPP(nat,X_a,F,hAPP(nat,nat,suc,Na)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),H,Na),hAPP(nat,X_a,F,Na)))) # label(fact_4357_def__nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 668 (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_1929_norm__minus__commute) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 669 (all X_a (linordered_idom(X_a) -> (all A_3 (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_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)))))) # label(fact_2280_sgn__greater) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 670 (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_1350_StandardRes__prop1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 671 (all R_3 hAPP(real,real,norm_norm(real),R_3) = hAPP(real,real,abs_abs(real),R_3)) # label(fact_1947_real__norm__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 672 (all A_2 hAPP(fun(nat,bool),nat,finite_card(nat),A_2) = 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_2))) # label(fact_3671_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 673 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))))))) # label(fact_449_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 674 (all X_a (linordered_field(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)))))))) # label(fact_1823_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 675 (all X_a (ab_group_add(X_a) -> (all A_3 all B_2 all C all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1) -> (ti(X_a,A_3) = ti(X_a,B_2) <-> ti(X_a,C) = ti(X_a,D_1)))))) # label(fact_715_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 676 (all K all N_1 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_1))),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_1),K)))) # label(fact_4200_sumr__offset4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 677 (all Xa all Wa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),Wa) <-> 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),Xa),hAPP(int,nat,number_number_of(nat),Wa)))))) # label(fact_152_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 678 (all X_a (real_normed_algebra(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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_2)),Ya) = 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_2)),Ya)))))) # label(fact_4013_mult__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 679 (all X_a all X_b (order(X_b) & order(X_a) -> (all C all A_3 all F all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_b,X_a,F,B_2))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_2),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_b,X_a,F,C))))))))) # label(fact_2855_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 680 (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_3817_Rat__induct__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 681 (all F all L all 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),F),L),hAPP(real,filter(real),at(real),C))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) & (all X_1 (X_1 != C & 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),X_1))),R_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),zero_zero(real)))))))))) # label(fact_4652_LIM__fun__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 682 (all Na 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))),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)))),Na)))) # label(fact_4264_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 683 (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_4964_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 684 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all Ra all G 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),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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),Ra)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4761_scaleR__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 685 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),A_1)) # label(fact_1306_zmod__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 686 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),Xa)),Ya)) <-> 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),Xa),Ya))))) # label(fact_2022_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 687 (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_2700_real__root__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 688 (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_852_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 689 (all X_a (topological_space(X_a) -> at(X_a) = ti(fun(X_a,filter(X_a)),at(X_a)))) # label(tsy_c_Limits_Oat_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 690 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_571_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 691 -(all S_1 all W_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,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),W_1))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) & ti(int,W_1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),y),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))))) # label(fact_926__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An_) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 692 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_1393_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 693 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),C_1)))))) # label(fact_1092_div__mult__swap) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 694 (all Ma all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na) = zero_zero(nat) <-> zero_zero(nat) = Na | Ma = zero_zero(nat))) # label(fact_604_mult__is__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 695 (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),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_935_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 696 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 697 (all X hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) = hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X))) # label(fact_3368_real__of__int__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 698 (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_4426_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 699 (all X_c all X_a all X_b all C all P_4 all Q_2 (ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C),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),Q_2))) # label(fact_4020_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 700 (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),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)) = 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)))))) # label(fact_4691_scaleR_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 701 (all X_a (idom(X_a) -> (all Xa all Ya (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Ya),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),Xa),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) <-> ti(X_a,Xa) = hAPP(X_a,X_a,uminus_uminus(X_a),Ya) | ti(X_a,Xa) = ti(X_a,Ya))))) # label(fact_2009_realpow__two__disj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 702 (all A_1 all B all C_1 all Q_3 all R_3 (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_1),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_3))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C_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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C_1),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_3)),C_1))),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_3)),C_1))))))) # label(fact_3121_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 703 (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_2010_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 704 (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_632_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 705 (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_136_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 706 (all Ma (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),Ma) = one_one(int) <-> hAPP(int,int,abs_abs(int),Ma) = one_one(int))) # label(fact_3489_zgcd__0__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 707 (all Na (hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) <-> zero_zero(nat) = Na)) # label(fact_27_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 708 (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_370_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.44 709 (all X_b all X_a all P_1 all Ya all Xa (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Ya),Xa)) -> 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),Xa),Ya))),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),Xa),Ya)))))) # label(fact_3163_exI__realizer) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 710 (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_2918_floor__eq4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 711 (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_2640_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 712 (all Z all Ma ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma)))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> Ma = zero_zero(nat)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,Z)),Ma)))) # label(fact_1056_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 713 (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_3272_gcd__add2__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 714 (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_4383_gcd__add__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 715 (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]. 7.46/7.45 716 (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]. 7.46/7.45 717 (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,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))))) # label(fact_4768_nonzero__inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 718 (all X_a (order(X_a) -> (all Xa all Ya 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),Ya),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Xa)),hAPP(nat,X_a,F,Ya)))))))) # label(fact_4815_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 719 (all X_b all X_a all B_1 all A_2 ((-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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_2),B_1)) = zero_zero(nat)) & (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)) = 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_2),B_1))))) # label(fact_3205_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 720 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),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_3),B_2)),zOdd))))) # label(fact_1711_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 721 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa)))),hAPP(X_a,X_a,F,Xa)))),combi(X_a))),D),hAPP(X_a,filter(X_a),at(X_a),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),F),Xa),D)))))) # label(fact_4645_DERIV__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 722 (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_904_zcong__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 723 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> zero_zero(X_b) = hAPP(X_a,X_b,G,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),G),A_2) = zero_zero(X_b)))))) # label(fact_4334_setsum_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 724 (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) = zero_zero(real)) & (zero_zero(real) != X -> hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_3445_powr__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 725 (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_923_zpower__zdvd__prop2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 726 (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_2809_of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 727 (all X_a (real_normed_field(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> 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_2)),Ya))))))) # label(fact_4129_divide_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 728 (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_1464_Suc__diff__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 729 (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)) & (N = zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N) = one_one(X_a)))))) # label(fact_924_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 730 (all X_a all A_2 all B_1 (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_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_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)),A_2),B_1)))) # label(fact_2844_Pow__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 731 (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_3606_of__int__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 732 (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,nat_1,Xa)))))) # label(fact_2517_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 733 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 ((all X_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_2053_divide_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 734 (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_1898_log__base__10__eq1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 735 (all X_a (ring_1(X_a) & real_normed_vector(X_a) -> (all C all Xa (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))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa)))) -> 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))),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),Xa)),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))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa))))))))) # label(fact_4134_diffs__equiv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 736 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),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,B) = ti(X_a,C_1))))) # label(fact_290_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 737 (all Z_1 hAPP(complex,real,norm_norm(complex),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))))) # label(fact_3038_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 738 (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_750_le__imp__power__dvd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 739 (all Xa 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),Xa))),hAPP(real,real,cos,Xa)))) # label(fact_4124_cos__converges) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 740 (all X all Y all M (one_one(nat) = 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))) # label(fact_3317_invertible__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 741 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))))) # label(fact_1953_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 742 (all X_a (real_normed_field(X_a) -> (all G all E_2 all F all Xa 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),Xa),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),Xa),E_2)) -> (hAPP(X_a,X_a,G,Xa) != 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)),Xa),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,Xa))),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,Xa)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,G,Xa)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))))) # label(fact_3928_DERIV__quotient) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 743 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B))))) # label(fact_2599_divide__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 744 (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_3247_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 745 (all X_a (real_algebra_1(X_a) -> (all Xa (Xa = zero_zero(real) <-> hAPP(real,X_a,of_real(X_a),Xa) = zero_zero(X_a))))) # label(fact_2794_of__real__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 746 (all X_a all X_c all X_b (topological_space(X_b) & real_normed_vector(X_c) -> (all F all Xa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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_1)),Xa)))) -> 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_2)),Xa))))))) # label(fact_4947_isCont__setsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 747 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> (exists Y_1 (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),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),Y_1)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,A_3)),hAPP(real,real,F,B_2)))))) # label(fact_3551_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 748 (all B_2 all A_3 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)))))) # label(fact_1206_wset__g__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 749 (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]. 7.46/7.45 750 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_325_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 751 (all X_b all X_a (uminus(X_a) -> (all A_2 all Xa hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_2,Xa)) = hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_2),Xa)))) # label(fact_2990_uminus__apply) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 752 (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_3402_ge__one__powr__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 753 (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_1176_inv__g__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 754 (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_2589_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 755 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,suc,N)),N)) # label(fact_3287_coprime__Suc__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 756 (all Xa hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),cos),Xa))) # label(fact_4928_isCont__cos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 757 (all A_3 all C all D_1 all B_2 (ti(int,B_2) != zero_zero(int) -> (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_3),B_2)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),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_3),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),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),B_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),D_1)))))))) # label(fact_3806_le__rat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 758 (all Code_numeral_4 hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_4) != zero_zero(code_code_numeral)) # label(fact_2971_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 759 (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_898_zcong__zmult__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 760 (all X_a (real_normed_vector(X_a) -> (all K all Sb all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (ti(X_a,Sb) = 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),Sb),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_4196_suminf__minus__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 761 (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_2685_real__root__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 762 (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_189_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 763 (all X_a (real_normed_algebra(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> 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),Xa)),X_2))))))) # label(fact_4127_mult__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 764 (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_1103_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 765 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (zero_zero(X_a) = ti(X_a,Xa) & zero_zero(X_a) = ti(X_a,Ya) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_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),Xa),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),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))))))) # label(fact_333_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 766 (all X_a all X_b (real_normed_field(X_b) -> (all F all Xa all F_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all N_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_1),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_1)),Xa),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F_2,Xa),N_1))))) -> 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)),Xa),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,Xa)),S)))))))) # label(fact_4331_DERIV__setsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 767 (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_748_power__le__dvd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 768 (all L all U hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U)) # label(fact_4249_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 769 (all X_a (real_algebra_1(X_a) -> (all F all X_1 hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),F),X_1)) = 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_1)))) # label(fact_4137_diffs__of__real) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 770 (all L all U 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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U),hAPP(nat,nat,suc,L))) # label(fact_3701_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 771 (all X_a all X_b all Xa all Ya 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,Xa),Ya)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,Xa),Ya))))) # label(fact_4367_predicate2D) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 772 (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_1013_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 773 (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 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_5),B_3) & ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_3),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) & 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)))))) # label(fact_4802_gcd__coprime__exists__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 774 (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_2409_sin__npi2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 775 (all Diff all F all Na 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)),Na)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) -> 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)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))) = 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_4308_Maclaurin__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 776 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_1275_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 777 (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_3549_norm__conv__dist) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 778 (all B all A_1 (A_1 != zero_zero(nat) | B != zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3316_div__gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 779 (all X_a (order(X_a) -> (all Na all N_6 all F ((all N_1 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,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_6)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_6)))))))) # label(fact_1573_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 780 (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_3466_zgcd__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 781 (all Sb all Ta all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Sb),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_3),Sb)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_2),Ta))),pair_less))))) # label(fact_3510_pair__lessI2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 782 (all X_a (archim1804426504_field(X_a) -> (all X exists N_1 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_1)))))) # label(fact_2836_ex__le__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 783 (all X_b all X_a all X_c (comm_monoid_add(X_c) -> (all F all R_2 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_2)))),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_2))))),T_3)))))) # label(fact_4210_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 784 (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_2633_inv__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 785 (all X_a (real_normed_field(X_a) -> (all C 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))))))) # label(fact_4035_summable__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 786 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,exp(real),X))))) # label(fact_2810_exp__of__real) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 787 (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_1747_exp__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 788 (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)) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = M))) # label(fact_1536_mod__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 789 (all A_1 all B all C_1 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_1) = 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_1))) # label(fact_3244_gcd__assoc__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 790 (all Z_1 exists R_1 exists A_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_1)),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_2831_complex__split__polar) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 791 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),K_4) = ti(int,K_4))) # label(fact_3479_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 792 (all X_a (topological_space(X_a) -> (all L all X_2 all Xa (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_2),Xa),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_2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),L))),Xa),sequentially))))))) # label(fact_4467_LIMSEQ__linear) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 793 (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_3729_Frct__code__post_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 794 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1)),one_one(nat))))) # label(fact_2532_odd__square) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 795 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),K)))) # label(fact_4960_finite__atMost) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 796 (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_3371_powr__ge__pzero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 797 (all A_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),A_3),zero_zero(real)),sequentially)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_3,N_1)))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,hAPP(nat,nat,suc,N_1))),hAPP(nat,real,A_3,N_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,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)))),A_3))),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)))),A_3))),sequentially)))))) # label(fact_4540_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 798 (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_2172_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 799 (all X_a (ring_1(X_a) -> (all F all Na all Ra 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)),Ra)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na)) = 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)),Na))),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),Na)),Ra))))) # label(fact_4219_sumr__diff__mult__const2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 800 (all N hAPP(int,nat,number_number_of(nat),N) = hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N))) # label(fact_1670_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 801 (all X_a (ordered_ab_group_add(X_a) -> (all Xa all Ya 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),Ya)),hAPP(X_a,X_a,uminus_uminus(X_a),Xa)) = 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),Xa),Ya))))) # label(fact_4551_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 802 (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_1250_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 803 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4568_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 804 (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_3114_divmod__nat__step) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 805 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) # label(fact_367_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 806 (all Xa (zero_zero(real) != hAPP(real,real,cos,Xa) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),tan),Xa),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,Xa)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2655_DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 807 (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,B) = ti(int,A_1))))))) # label(fact_916_zcong__zless__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 808 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,exp(real),Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)))) # label(fact_1785_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 809 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zOdd))))) # label(fact_1713_even__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 810 (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_3215_fact__ge__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 811 (all N zero_zero(real) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi))) # label(fact_2408_sin__npi) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 812 (all X_a (number_ring(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),min)) = hAPP(int,X_a,number_number_of(X_a),min))) # label(fact_3616_of__int__m1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 813 (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_3079_prime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 814 (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_402_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 815 (all X_a (comple44059174attice(X_a) -> (all Z all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)),Z)))))) # label(fact_2726_complete__lattice__class_OSup__least) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 816 (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)),P_5)))) # label(fact_1070_Wilson__Russ) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 817 (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_4034_snd__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 818 (all X_a all X_b all X_c all F all Xa hAPP(product_prod(X_a,X_c),X_a,product_fst(X_a,X_c),Xa) = 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),Xa))) # label(fact_4093_fst__apsnd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 819 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),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)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),D),E_3)))))))) # label(fact_3866_DERIV__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 820 (all X_a (division_ring(X_a) -> (all A_3 all B_2 all C (zero_zero(X_a) != ti(X_a,C) -> (ti(X_a,B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C) = ti(X_a,A_3)))))) # label(fact_1848_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 821 (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_2012_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 822 (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_1 all K_1 (hBOOL(hAPP(int,bool,P_1,X_1)) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),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_1)))) <-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))) # label(fact_4668_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 823 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,re,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_3044_complex__Re__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 824 (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_651_even__power__le__0__imp__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 825 (all L all U hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U),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))) # label(fact_4286_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 826 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_2)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),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_1),D)),Ta)))))))) # label(fact_4664_aset_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 827 (all Xa all Ya (Xa = Ya <-> hAPP(real,real,sqrt,Ya) = hAPP(real,real,sqrt,Xa))) # label(fact_2123_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 828 (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_1669_natceiling__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 829 (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_1185_MultInv__prop5) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 830 (all D all Xa (Xa != zero_zero(real) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> D = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,Xa))),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),Xa),zero_zero(real))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,Xa)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),Xa),D)))))) # label(fact_2657_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 831 (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_2687_real__root__mult__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 832 (all X_a (real_normed_vector(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a))))) # label(fact_4731_scaleR_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 833 (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_1093_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 834 (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_3434_real__of__int__div2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 835 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> zero_zero(X_a) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))))) # label(fact_3995_suminf__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 836 (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_912_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 837 (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_1142_MultInvPair__distinct) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 838 (all X_a (order(X_a) -> (all Ya all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) <-> ti(X_a,Ya) = ti(X_a,Xa)))))) # label(fact_509_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 839 (all U all Ma all Na 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U)),Ma)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U)),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)),Na)))))) # label(fact_877_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 840 (all Na all Ma all F ((all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_1))),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,hAPP(nat,nat,suc,N_1)))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Na)),hAPP(nat,nat,F,Ma))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Ma)),hAPP(nat,nat,F,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))))) # label(fact_1569_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 841 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))) <-> 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)),Xa)))))) # label(fact_3335_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 842 (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_264_zero__zle__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.45 843 (all Z all Ya all Xa all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Xa),X_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Ya),Xa)) -> ((all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Ya),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_2))))))) # label(fact_3732_SupInf_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 844 (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]. 7.46/7.46 845 (all Xa all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))))) # label(fact_2684_real__root__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 846 (all R_3 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_3))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_3),one_one(real))))) # label(fact_3427_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 847 (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_2166_real__sqrt__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 848 (all X_a (archim1727834104eiling(X_a) -> (all Z all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))) <-> 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))),Xa)))))) # label(fact_3637_le__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 849 (all P_1 all Na all K ((zero_zero(int) = ti(int,K) -> hBOOL(hAPP(int,bool,P_1,Na))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & ti(int,Na) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),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),K),I_2)),J_1) = ti(int,Na) -> hBOOL(hAPP(int,bool,P_1,J_1))))) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Na),K))))) # label(fact_1473_split__zmod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 850 (all Xa 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))))),Xa),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,Xa))),hAPP(real,real,sin,Xa)))))) # label(fact_3941_DERIV__cos__realpow2b) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 851 (all X_a (division_ring(X_a) -> (all A_1 all B all C_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_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)),C_1)))) # label(fact_1831_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 852 (all X_a (real_n1866405975lgebra(X_a) -> (all X_2 all A_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_2),A_3),sequentially)) -> (ti(X_a,A_3) != 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_2)))))))) # label(fact_4458_Bseq__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 853 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2358_arccos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 854 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya_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),Y)),Ya_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),times_times(X_a),X),Ya_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya_1))))) # label(fact_1247_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 855 (all I all J (ti(int,I) = zero_zero(int) & zero_zero(int) = ti(int,J) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I),J) = zero_zero(int))) # label(fact_3460_zgcd0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 856 (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_1099_div__prop1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 857 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1))),C_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),A_1),B)),C_1)))) # label(fact_1293_mod__add__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 858 (all Z_1 hAPP(complex,complex,cnj,hAPP(complex,complex,cnj,Z_1)) = Z_1) # label(fact_2959_complex__cnj__cnj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 859 (all X hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(real,real,exp(real),one_one(real))),X)) # label(fact_2034_log__ln) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 860 (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_501_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 861 (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]. 7.46/7.46 862 (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_190_power__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 863 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),hAPP(real,real,sqrt,Ya))))) # label(fact_2125_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 864 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_1908_minus__mult__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 865 (all B all A_1 all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),B))))) # label(fact_886_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 866 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),zero_zero(int)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_3)))) # label(fact_910_zcong__zero__equiv__div) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 867 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3145_mod__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 868 (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]. 7.46/7.46 869 (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_332_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 870 (all U_1 all V all X all Y (X = Y -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U_1)),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_1)),Y))),V))))) # label(fact_1197_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 871 (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_144_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 872 (all X_a all P_1 ti(fun(X_a,bool),P_1) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) # label(fact_75_Collect__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 873 (all A_1 all B ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> (zero_zero(int) = ti(int,A_1) | 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) | 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),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_3952_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 874 (all X_a (real_normed_algebra(X_a) -> (all C 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)) = 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))))) # label(fact_4015_suminf__mult2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 875 (all A_3 all A_2 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_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> 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_2),Ma),A_3)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3648_RRset2norRR__correct2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 876 (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_1088_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 877 (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_749_dvd__power__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 878 (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_1168_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 879 (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]. 7.46/7.46 880 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),Na))) <-> Ma != zero_zero(nat) | Na != zero_zero(nat))) # label(fact_3284_gcd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 881 (all Xa all Ya all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ya),Z))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Z)))) # label(fact_3257_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 882 (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_3124_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 883 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))))) # label(fact_220_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 884 (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) = hAPP(real,real,sgn_sgn(real),X))) # label(fact_2311_real__sgn__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 885 (all N all M 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)) # label(fact_811_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 886 (all M all N (zero_zero(nat) = 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) -> M = N))) # label(fact_804_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 887 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_743_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 888 (all X_a (real_vector(X_a) -> (all A_3 all Xa all Ya (ti(X_a,Ya) = ti(X_a,Xa) | zero_zero(real) = A_3 <-> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Ya) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa))))) # label(fact_4728_scaleR__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 889 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_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_1)),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_2)),zero_zero(X_b))))))) # label(fact_4335_setsum__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 890 (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_1218_int__nat__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 891 (all A_3 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_3),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_3)) -> 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_3),P_4)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_3),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_3954_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 892 (all W hAPP(int,int,number_number_of(int),hAPP(int,int,uminus_uminus(int),W)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))) # label(fact_2063_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 893 (all A_3 all B_2 ((exists X_1 exists Y_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_2),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_3),Y_1)) | 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_3),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_2),Y_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_3),B_2)))) # label(fact_2921_coprime__bezout) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 894 (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_3062_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 895 (all K all F all Na ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),Na)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_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,Na))) -> (exists I_2 (hAPP(nat,int,F,I_2) = ti(int,K) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),Na)))))))) # label(fact_1065_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 896 (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_2828_expi__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 897 (all X_a (archim1727834104eiling(X_a) -> (all Va all Xa (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),Va)),one_one(X_a))),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),Va)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))))))) # label(fact_3236_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 898 (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_1630_two__times__even__div__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 899 (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_1809_real__less__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 900 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,sgn_sgn(X_a),Y))))) # label(fact_2265_sgn__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 901 (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_1245_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 902 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1))))))) # label(fact_522_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 903 (all Xa 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,Xa)))) # label(fact_1202_d22set__induct__old) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 904 (all X_a one_frac(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)))) # label(fact_3819_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 905 (all X_a (linordered_semidom(X_a) -> (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na))))))) # label(fact_208_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 906 (all X_a (semiring_1(X_a) -> semiring_1_of_nat(X_a) = ti(fun(nat,X_a),semiring_1_of_nat(X_a)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 907 (all X_a (real_field(X_a) -> (all Na all Xa all Ya 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),Xa)))),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),Na)))))),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),Ya)),hAPP(nat,fun(nat,nat),minus_minus(nat),Na))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na)) = 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),Na)))),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),Xa),Ya)),Na))))) # label(fact_4689_exp__series__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 908 (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_1642_even__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 909 (all X_b all X_a (topological_space(X_a) & real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all L all A_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),L),hAPP(X_a,filter(X_a),at(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),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_3))))))) # label(fact_4620_LIM__of__real) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 910 (all X_a (topological_space(X_a) -> (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,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_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),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4617_LIM__rabs__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 911 (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_2485_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 912 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> ti(int,Xa) = 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),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1737_even__div__2__prop2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 913 (all Ma all Na hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),Ma),hAPP(nat,nat,suc,Na)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,Na)),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)),Na))),Ma)) # label(fact_4987_max__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 914 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) & Xa != Ya <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)))) # label(fact_959_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 915 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = ti(int,K_4)) # label(fact_78_add__Pls__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 916 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all A_3 ((all R_1 (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_1 (ti(X_a,A_3) != ti(X_a,X_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_1),A_3)),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_1)),L_2)),R_1)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4789_metric__LIM__I) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 917 (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_3790_real__minus__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 918 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G 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)),hAPP(X_a,filter(X_a),at(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),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4604_LIM__add__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 919 (all G all Xa (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),Xa)) -> 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))))))),Xa)))) # label(fact_4131_sums__if_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 920 (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_1611_not__neg__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 921 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),B_1),A_2))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_1))))) -> 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_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),B_1))))))))) # label(fact_4319_setsum__mono3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 922 (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_4060_rat__inverse__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 923 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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(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_1))),F)),zero_zero(X_b))),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),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_2))),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_1)))))))) # label(fact_4215_setsum__restrict__set_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 924 (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_1899_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 925 (all X_a code_c600343653l_case(X_a) = ti(fun(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a))),code_c600343653l_case(X_a))) # label(tsy_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 926 (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_2178_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 927 (all X_a (semiring_0(X_a) & power(X_a) -> (all W ((hAPP(int,nat,number_number_of(nat),W) = 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)),hAPP(int,nat,number_number_of(nat),W))) & (hAPP(int,nat,number_number_of(nat),W) != zero_zero(nat) -> zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W))))))) # label(fact_11_power__0__left__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 928 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_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),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_2))))))) # label(fact_330_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 929 (all X1_2 all X2_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X1_2),X2_2),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X1_2) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X2_2)))) # label(fact_1470_StandardRes__prop2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 930 (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_106_of__nat__less__two__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 931 (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_2588_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 932 (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_3374_powr__less__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 933 (all X_a (linordered_semidom(X_a) -> (all Ma all Na all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_3)) -> (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),Na) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),Ma) <-> Ma = Na))))) # label(fact_184_power__inject__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 934 (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) = one_one(int) | zero_zero(int) = ti(int,X)))) # label(fact_336_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 935 (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_2985_compl__less__swap2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 936 (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_3286_gcd__le1__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 937 (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_282_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 938 (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_2930_pred__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 939 (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_3082_prime__divexp__n) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 940 (all A_1 hAPP(real,real,sin,A_1) = hAPP(complex,real,im,hAPP(real,complex,cis,A_1))) # label(fact_3052_Im__cis) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 941 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2784_Complex__mult__i) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 942 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_392_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 943 (all Xa all Ya (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),Xa),Ya)),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)))) # label(fact_1220_odd__mult__odd__prop) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 944 (all X_a all X_b (real_normed_field(X_b) -> (all G all B_2 all F all A_3 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),A_3),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),B_2),A_2)) -> (ti(X_b,B_2) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_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_3),B_2)),A_2)))))))) # label(fact_4465_tendsto__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 945 (all X_a (linordered_semidom(X_a) -> (all Ma all Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))))) # label(fact_170_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 946 (all N zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),zero_zero(real))) # label(fact_2674_real__root__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 947 (all X_a (linordered_idom(X_a) -> (all Xa all Na (zero_zero(nat) = Na | ti(X_a,Xa) != zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)) <-> 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),Xa),Na))))))) # label(fact_2509_zero__less__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 948 (all R_3 all A_1 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_3),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_3),hAPP(real,real,sin,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),R_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2295_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 949 (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_2719_real__root__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 950 (all I all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,P_1,N_1)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_1693_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 951 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Xa 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),Xa))),hAPP(X_a,X_a,exp(X_a),Xa)))))) # label(fact_4777_exp__converges) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 952 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> N = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1231_divides__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 953 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L_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),L_2),hAPP(X_a,filter(X_a),at(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),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_3))))))) # label(fact_4593_LIM__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 954 (all Ma all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Ma),Xa)) <-> (exists Y_1 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_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Xa),Ma))))) # label(fact_795_QuadRes__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 955 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_3)) -> 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_3))))))) # label(fact_4912_isCont__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 956 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C_1 all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C_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),times_times(X_a),A_6),B_5)),C_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),times_times(X_a),A_1),B)),C_1)))))) # label(fact_1289_mod__mult__cong) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 957 (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_3651_ex__le__of__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 958 (all Na (hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) <-> 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)))),Na)))) # label(fact_2521_even__dvd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 959 (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_1239_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 960 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all C all B_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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),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(X_a),A_3),B_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))) & zero_zero(X_a) != ti(X_a,C))))) # label(fact_1843_divide__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 961 (all X_a all D all B_1 all A_2 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_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)),D),B_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,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_2),B_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)),C_2),D)))))) # label(fact_2212_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 962 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1) <-> hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) # label(fact_2237_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 963 (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_2501_even__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 964 (all X hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2998_complex__Im__cnj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 965 (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_2525_lemma__even__div2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 966 (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_527_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 967 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zEven))))) # label(fact_1700_even__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 968 (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_1303_dvd__mod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 969 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_2858_dense__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 970 (all Ma all Na (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),Na) = one_one(int) <-> ti(int,Ma) = one_one(int) & ti(int,Na) = one_one(int) | hAPP(int,int,number_number_of(int),min) = ti(int,Na) & ti(int,Ma) = hAPP(int,int,number_number_of(int),min))) # label(fact_691_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 971 (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_1049_Little__Fermat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 972 (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_2996_code__numeral_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 973 (all Z_1 Z_1 = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1))) # label(fact_3025_complex__surj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 974 (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),M),hAPP(nat,nat,suc,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),M),K_4)),hAPP(nat,nat,suc,J_2)))) # label(fact_1453_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 975 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_3)) -> 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3)))))))) # label(fact_233_add__le__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 976 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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_2)))))) # label(fact_3845_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 7.46/7.46 977 (all P_1 ((all X_1 exists D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all A_4 all 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_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_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_4),B_4))))))) & (all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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(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_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 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_3230_lemma__BOLZANO2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 978 (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_3227_fact__reduce__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 979 (all X_a (ring_1(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3)),ring_1_Ints(X_a))))))) # label(fact_3832_Ints__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 980 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Xa)),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)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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),Xa)),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_4006_summable__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 981 (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]. 7.46/7.47 982 (all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_2 ((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_2)) -> 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),Xa),H_1))),hAPP(real,real,F,Xa)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2))))))) # label(fact_2665_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 983 (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_2309_sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 984 (all A_3 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_3),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_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),P_4)))) # label(fact_717_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 985 (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_287_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 986 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W))))) # label(fact_6_add__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 987 (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_1 (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_1 (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_579_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 988 (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_4403_gcd__greatest__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 989 (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_2136_arctan__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 990 (all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_3)) -> (exists N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),R_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))))))) # label(fact_3447_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 991 (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),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_359_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 992 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all Xa 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),Xa)))))))) # label(fact_4774_summable__norm__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 993 (all X_a all B_1 all Xa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_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_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),B_1))))) # label(fact_2205_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 994 (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_1979_abs__le__D2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 995 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_474_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 996 (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_4252_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 997 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_3310_ceiling__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 998 (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)),hAPP(int,int,uminus_uminus(int),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))))) # label(fact_2104_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 999 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_2898_floor__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1000 (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_3744_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1001 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_130_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1002 (all Xa (hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) <-> (exists Y_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_1) = Xa))) # label(fact_2496_even__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1003 (all P_1 all Ya all Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Xa),Ya))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ya),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Xa),hAPP(int,int,uminus_uminus(int),Ya)))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),Xa)),Ya))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ya),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),Xa)),hAPP(int,int,uminus_uminus(int),Ya)))))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Xa),Ya)))))))) # label(fact_4427_gcd__cases__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1004 (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_2377_tan__periodic__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1005 (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_2077_diff__int__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1006 (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_3057_cis__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1007 (all X_a all A_2 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)) = 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_2)) # label(fact_4256_real__of__card) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1008 (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_4817_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1009 (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),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),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))))) # label(fact_1262_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1010 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1))),C_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),A_1),B)),C_1)))) # label(fact_1292_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1011 (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_2389_real__of__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1012 (all P_5 all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)) # label(fact_1515_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1013 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1) = Z_1) # label(fact_623_real__mult__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1014 (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_4829_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1015 (all Xa 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),Xa))))) # label(fact_4056_summable__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1016 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))))) # label(fact_371_number__of__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1017 (all Xa all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Xa),X_2)) -> ((exists Z_2 all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_2)))))) # label(fact_3721_Sup__upper__EX) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1018 (all X_b all X_c all X_a all X_d all X_e all F all G all P_4 hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_4) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_4))) # label(fact_4030_split__twice) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1019 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_1481_realpow__two__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1020 (all X_a (linorder(X_a) -> (all Ma all Na (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),Na))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ma),Na)))))) # label(fact_4347_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1021 (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_3384_powr__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1022 (all Xa (hAPP(int,real,real_1(int),Xa) = zero_zero(real) <-> zero_zero(int) = ti(int,Xa))) # label(fact_3347_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1023 (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_1101_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1024 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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,Xa)),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)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_3),D)))))))) # label(fact_3886_DERIV__chain_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1025 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa),D)) <-> 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,Xa)))),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)),Xa))),D),hAPP(X_a,filter(X_a),at(X_a),Xa))))))) # label(fact_4626_DERIV__iff2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1026 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 (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_3)),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_3)))))) # label(fact_1954_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1027 (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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),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),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))))) # label(fact_369_mult__number__of__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1028 (exists K_2 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) # label(fact_3047_Re_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1029 (all X_a (real_normed_vector(X_a) -> (all K all F all Sb (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sb)) -> 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),Sb),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_4194_sums__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1030 (all X_a (linord1278240602ring_1(X_a) -> (all V all U_1 all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_537_convex__bound__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1031 (all X_a all X_b (field_inverse_zero(X_b) -> (all F all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_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),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_2))))) # label(fact_3984_setprod__dividef) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1032 (all M all N all Q_3 all R_3 (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_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = Q_3)) # label(fact_3126_div__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1033 (all Ma all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,Wa)),Ma))))) # label(fact_1055_nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1034 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> 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_2)) = hAPP(complex,real,re,hAPP(fun(nat,complex),complex,suminf(complex),X_2)))) # label(fact_4075_Re_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1035 (all A_3 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_3),Ma)))) # label(fact_3233_Bnor__fin) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1036 (all Xa all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Xa),zero_zero(int)),P_4)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),Xa)))) # label(fact_909_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1037 (all X_a (power(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]. 7.46/7.47 1038 (all Na all A_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),A_3),zero_zero(real)),sequentially)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_3,N_1)))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,hAPP(nat,nat,suc,N_1))),hAPP(nat,real,A_3,N_1)))) -> 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)))),A_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),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Na)))),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)))),A_3)))))))) # label(fact_4541_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1039 (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_3005_Im_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1040 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all A_3 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),of_real(X_a)),A_3))))) # label(fact_4916_of__real_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1041 (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_2515_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1042 (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_846_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1043 (all X_c all X_b all X_a (topological_space(X_c) & topological_space(X_b) & real_normed_vector(X_a) -> (all G all L all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),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),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_3)))) -> ((exists D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all X_1 (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_1),A_3))),D_2)) & ti(X_a,X_1) != ti(X_a,A_3) -> hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,F,A_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_3))))))))) # label(fact_4900_isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1044 (all P_1 ((exists X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(hAPP(int,bool,P_1,X_1)))) <-> (exists X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1)))))) # label(fact_266_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1045 (all A_3 all X_2 all Xa (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_2),Xa),sequentially)) -> ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_2,N_1)),A_3)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),A_3))))) # label(fact_4518_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1046 (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_182_zero__less__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1047 (all X_a (linordered_idom(X_a) -> (all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_982_abs__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1048 (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_1157_div__le__dividend) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1049 (all X_b all X_c all X_a all F1 all A_3 all B_2 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_3),B_2)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_3),B_2)) # label(fact_3180_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1050 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_973_abs__mult__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1051 (all X_a (comm_monoid_add(X_a) -> (all F all Na all Ma ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),Na))) = 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,Na)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),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,Na))) = zero_zero(X_a)))))) # label(fact_4631_setsum__cl__ivl__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1052 (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_318_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1053 (all X_a all X_b all F all G ((all X_1 hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,X_1)) -> ti(fun(X_a,X_b),G) = ti(fun(X_a,X_b),F))) # label(fact_73_ext) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1054 (all Na ((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) = Na) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)))) # label(fact_2522_even__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1055 (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_1172_nat__div__distrib) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1056 (all Xa all Ya (Ya = Xa <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,Ya) = hAPP(quickcheck_code_int,int,quickcheck_int_of,Xa))) # label(fact_3188_code__int_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1057 (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_3288_gcd__add__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1058 (all Ra 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),Ra)),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))))),Ra),sequentially))) # label(fact_4456_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1059 (all 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)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B)) # label(fact_1652_posDivAlg__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1060 (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_819_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1061 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Xa)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa))))))) # label(fact_4053_complete__algebra__summable__geometric) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1062 (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_1488_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1063 (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_3390_floor__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1064 (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_1577_mod__induct) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1065 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_142_gr0I) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1066 (all X_a all F all A_2 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = 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_2))) # label(fact_4277_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1067 (all A_1 all B all C_1 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_1))),C_1) = 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_1)) # label(fact_1308_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1068 (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_2551_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1069 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)))) # label(fact_1678_natceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1070 (all Na all Va 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,Va)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),Na),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,Na)),hAPP(int,nat,number_number_of(nat),Va))) # label(fact_4821_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1071 (all Xa 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)),Xa),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,Xa))),hAPP(real,real,sin,Xa)))))) # label(fact_3935_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1072 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,H,X_1))) -> 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_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2)))))) # label(fact_4794_setprod_Ocong) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1073 (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_1455_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1074 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_3332_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1075 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_2887_coprime__Suc0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1076 (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_971_abs__ge__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1077 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5))))) # label(fact_1243_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1078 (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_1102_zdiv__mono1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1079 (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_552_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1080 (all Ya 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)),Ya)))) = hAPP(real,real,arctan,Ya)) # label(fact_4159_arctan__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1081 (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_420_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1082 (all X hAPP(int,int,succ,hAPP(int,int,pred,X)) = ti(int,X)) # label(fact_2924_succ__pred) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1083 (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_2586_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1084 (all N exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_6),hAPP(nat,nat,suc,hAPP(nat,nat,fact,N)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)))) # label(fact_3576_euclid__bound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1085 (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_4866_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1086 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 ((all X_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_2052_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1087 (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_1136_Euler__part3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1088 (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),J_2),I_1)),K_4) = 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))) # label(fact_854_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1089 (all X_a (power(X_a) -> hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),one_one(X_a)),times_times(X_a)) = power_power(X_a))) # label(fact_2863_power__power__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1090 (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_1861_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1091 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,Y) = ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_533_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1092 (all M ((zero_zero(nat) != M -> hAPP(nat,nat,fact_fact(nat),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))))) & (M = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),M) = one_one(nat)))) # label(fact_2555_fact__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1093 (all F all J all Na 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)),Na))),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),Na)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na))))) = hAPP(real,real,F,H)))) # label(fact_4299_Maclaurin__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1094 (all X_a (power(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) -> (all A_3 all Na (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),Na) = zero_zero(X_a) <-> zero_zero(nat) != Na & zero_zero(X_a) = ti(X_a,A_3))))) # label(fact_188_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1095 (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_4037_summable__rabs__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1096 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a)))))) # label(fact_4007_summable__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1097 (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_1694_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1098 (all Ma all X_1 all Xa_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),Xa_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma),X_1),Xa_1)))) # label(fact_4897_zcongm__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1099 (all X_a (number_ring(X_a) -> (all Wa 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),Wa)),ring_1_Ints(X_a)))))) # label(fact_3829_Ints__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1100 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1101 (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_3585_norRRset__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1102 (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_2481_power__even__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1103 (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_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),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_4841_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1104 (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_2977_times_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1105 (all X_b all X_a (real_vector(X_a) -> (all A_3 all G all A_2 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),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_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_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_3)),G)),A_2)))) # label(fact_4756_scaleR__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1106 (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_488_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1107 (all Xa all A_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),Xa),A_2)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),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_2))))) # label(fact_3673_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1108 (all P_4 all Na (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),Na))) <-> hBOOL(hAPP(nat,bool,prime,P_4)) & one_one(nat) = Na)) # label(fact_3084_prime__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1109 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),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,Na)),Xa),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),Na))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_2671_DERIV__even__real__root) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1110 (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_2318_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1111 (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_2285_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1112 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Xa)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,Xa))))) # label(fact_1674_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1113 (all X hAPP(rat,int,archim2085082626_floor(rat),X) = hAPP(real,int,archim2085082626_floor(real),hAPP(rat,real,ratreal,X))) # label(fact_3768_real__floor__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1114 (all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C)),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))),zero_zero(real)),sequentially)))) # label(fact_4462_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1115 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)))) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),zero_zero(real))))) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,A_3))))))) # label(fact_4951_DERIV__isconst1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1116 (all X_b all X_a all R_2 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_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),T_3)) -> 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_2),X_1)))) = K)) -> 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_2)))),S))))) # label(fact_4325_setsum__multicount) # label(axiom) # label(non_clause). [assumption]. 7.46/7.47 1117 (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_3330_ceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1118 (all A_3 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(real,int,archim2085082626_floor(real),Xa))) <-> 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_3)),one_one(real))),Xa)))) # label(fact_3438_less__floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1119 (all X_a all C_2 all A_2 all B_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)),A_2),B_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)),B_1),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_2),C_2))))) # label(fact_2201_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1120 (all X_a all X_b all A_2 all B_1 (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_2),B_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)))) # label(fact_3210_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1121 (all Na 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),Na),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)),Na))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4301_series__pos__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1122 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),zero_zero(int)),X)) # label(fact_4382_gcd__0__left__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1123 (all Xa (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1498_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1124 (all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C)),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)),zero_zero(real)),sequentially)))) # label(fact_4463_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1125 (all Na all N_6 all F ((all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_1))),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,hAPP(nat,nat,suc,N_1)))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_6)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Na)),hAPP(nat,nat,F,N_6))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_6)),hAPP(nat,nat,F,Na)))))) # label(fact_1570_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1126 (all Ma all Va (hAPP(int,int,number_number_of(int),Va) = hAPP(nat,int,semiring_1_of_nat(int),Ma) <-> Ma = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),Va)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),Va))))) # label(fact_1045_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1127 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_563_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1128 (all Va all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(int,nat,number_number_of(nat),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1))))) # label(fact_154_less__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1129 (all Q_3 ((all A_4 all B_4 (Q_3 = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (zero_zero(int) != ti(int,A_4) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) != one_one(int))))) -> Q_3 = zero_zero(rat))) # label(fact_4438_Rat__cases__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1130 (all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> hAPP(int,nat,nat_1,Z_1) = zero_zero(nat))) # label(fact_1608_neg__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1131 (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_194_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1132 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) -> 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),Na)) = 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)),Na))))))) # label(fact_4232_setsum__head__upt__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1133 (all Na 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),Na)) <-> ti(int,Ma) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Na),Ma)))) # label(fact_3482_zdvd__iff__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1134 (all X_a (division_ring(X_a) -> (all A_1 all B all C_1 (zero_zero(X_a) != ti(X_a,C_1) -> (ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1) = ti(X_a,A_1)))))) # label(fact_1854_eq__divide__imp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1135 (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_2156_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1136 (all X_a (semiring_1(X_a) -> 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),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_4_zero__power2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1137 (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_2184_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1138 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(real,fun(nat,real),power_power(real),Xa)))))) # label(fact_3847_Bseq__realpow) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1139 (all P_1 ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (exists X_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_1))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))))) # label(fact_1003_ex__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1140 (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_1296_mod__add__self1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1141 (all Xa all Ya (zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),Xa) & hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Ya)),hAPP(product_prod(int,int),int,product_snd(int,int),Xa)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Xa)),hAPP(product_prod(int,int),int,product_snd(int,int),Ya)) & zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),Ya) <-> 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)),Xa),Ya)),ratrel)))) # label(fact_3754_ratrel__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1142 (all X_b all X_a (semiring_1(X_a) -> (all F all A_2 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_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_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_2)))) # label(fact_4218_of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1143 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),one_one(real))))) # label(fact_2150_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1144 (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_1323_zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1145 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),nat_tr1645093318rphism(X_a,X_b)) = nat_tr1645093318rphism(X_a,X_b)) # label(tsy_c_Nat__Transfer_Otransfer__morphism_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1146 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)) # label(fact_805_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1147 (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_3090_prime__nd__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1148 (all X_a (real_normed_vector(X_a) -> (all Ra all A_3 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),Ra)),A_3))))) # label(fact_4937_scaleR__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1149 (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),hAPP(int,X_a,ring_1_of_int(X_a),Z_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),Z_2),one_one(int))))))))) # label(fact_3642_floor__exists) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1150 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_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),minus_minus(X_a),A_3),B_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)))))) # label(fact_752_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1151 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya_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),X),Y)),Ya_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),Ya_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya_1))))) # label(fact_1246_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1152 (all Na all Ma (hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),Na),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,Na)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))))) # label(fact_3186_less__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1153 (all C_1 all D_3 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_1),D_3),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_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D_3)),M))))) # label(fact_901_zcong__zdiff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1154 (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_2144_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1155 (all N all I_1 ((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)) & (zero_zero(code_code_numeral) != I_1 -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N) = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),I_1),one_one(code_code_numeral))),hAPP(nat,nat,suc,N))))) # label(fact_1743_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1156 (all X_a all C_2 all A_2 all B_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)),A_2),B_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)),B_1),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_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)),C_2),A_2)) = ti(fun(X_a,bool),A_2)))) # label(fact_2211_double__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1157 (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_2155_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1158 (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_1 all K_1 (hBOOL(hAPP(int,bool,P1,X_1)) <-> hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))))) -> ((exists Z_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Z_2)) -> (hBOOL(hAPP(int,bool,P_1,X_1)) <-> hBOOL(hAPP(int,bool,P1,X_1))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2869_minusinfinity) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1159 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_944_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1160 (all X_a (real_normed_vector(X_a) -> (all R_3 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_1 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_3),X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))))) # label(fact_4785_scaleR__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1161 (all Xa hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),Xa)),ring_1_Ints(real)))) # label(fact_3827_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1162 (all X_a (ordered_semiring(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_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_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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_432_mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1163 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_120_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1164 (all Z all Xa all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Xa),X_2)) -> ((all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_2)))))) # label(fact_3722_SupInf_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1165 (all X_a all F all A_2 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_2)) = 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_2)) # label(fact_3969_real__of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1166 (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_803_dvd__diffD1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1167 (all X_a (real_vector(X_a) -> (all X all Xa_2 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),X)),Xa_2) = 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_2))))) # label(fact_4739_scaleR__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1168 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1169 (all X_a (linord219039673up_add(X_a) -> (all A_3 (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_3)),A_3)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)))))) # label(fact_1955_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1170 (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_713_dvd__refl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1171 (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_4973_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1172 (all Y all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),N) -> Y = hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2678_odd__real__root__unique) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1173 (all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_1307_zmod__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1174 (all X_a all A_2 (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_2))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_2)))) # label(fact_2744_finite__UnionD) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1175 (all X_a (linorder(X_a) -> (all Xa all Ya 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),Xa),Ya)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Z)))))) # label(fact_4855_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1176 (all R_3 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_3),hAPP(complex,real,re,X)) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X))) # label(fact_4706_Re_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1177 (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_3096_prime__coprime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1178 (all Na hAPP(nat,fun(nat,bool),ord_atMost(nat),Na) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na)) # label(fact_4967_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1179 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2320_sin__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1180 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,K_4))) # label(fact_2925_pred__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1181 (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(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),P_5),Q_3))))) # label(fact_4435_normalize__stable) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1182 (all X_a (real_normed_field(X_a) -> (all Y_2 all B_2 all X_2 all A_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_2),A_3),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_2),B_2),sequentially)) -> (zero_zero(X_a) != ti(X_a,B_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(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_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),B_2)),sequentially)))))))) # label(fact_4466_LIMSEQ__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1183 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (exists N_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,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_1),X))))),X))))) # label(fact_1064_best__division__abs) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1184 (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_314_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1185 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = zero_zero(nat)) # label(fact_1531_mod__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1186 (all Ma all Xa hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),Xa) = 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)),Xa)),hAPP(int,fun(int,bool),norRRset,Ma))) # label(fact_3908_noXRRset__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1187 (all V_2 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_2))) -> 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_2)),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_2))) -> 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_2))),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_2)),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_2)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K_4)))) # label(fact_1621_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1188 (all M all N all S_4 all S_3 all T_6 all T_5 all R_4 all R_3 all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_4),R_3) = ti(int,K_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_3)) -> (exists Sn exists Tn hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_4),R_3),S_4),S_3),T_6),T_5))))) # label(fact_3505_xzgcd__correct__aux1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1189 (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_2682_real__root__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1190 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> 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_2))))) # label(fact_4072_cnj_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1191 (all X_a all A_2 all B_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)),A_2),B_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,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_1)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))))) # label(fact_2195_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1192 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_562_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1193 (all Z_1 all X all D_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_3)) -> 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_3)))))) # label(fact_1059_incr__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1194 (all Na hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) = Na) # label(fact_3894_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1195 (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_996_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1196 (all X_a (field(X_a) -> (all X all Y all Z_1 (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)))))) # label(fact_1880_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1197 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),Xa)),one_one(real))))) # label(fact_1787_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1198 (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_1425_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1199 (all X_a (preorder(X_a) -> (all P_1 all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) -> hBOOL(P_1)))))) # label(fact_525_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1200 (all X_a (real_normed_field(X_a) -> (all Y_2 all F all Xa all X_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),Xa),X_2)) -> (ti(X_a,X_2) = ti(X_a,Y_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),Xa),Y_2))))))) # label(fact_2647_DERIV__cong) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1201 (all A_3 all B_2 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_3)) <-> 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_3),B_2)))))) # label(fact_3077_prime__divprod__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1202 (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),zero_zero(nat)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),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),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))))) # label(fact_1631_power__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1203 (all X_a (field_char_0(X_a) -> (all Na 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),Na)),field_char_0_Rats(X_a)))))) # label(fact_3716_Rats__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1204 (all Diff all F all Na all H (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),Na)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) & 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)) & 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)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))))))) # label(fact_4306_Maclaurin__objl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1205 (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_647_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1206 (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_3275_gcd__red__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1207 (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_769_zprime__zdvd__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1208 (all A_1 all 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)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N)) # label(fact_3058_DeMoivre) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1209 (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_4985_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1210 (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_1389_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1211 (all U_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U_1),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),U_1)))) # label(fact_2171_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1212 (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_4105_sums__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1213 (all N hAPP(nat,real,real_1(nat),N) = hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_3363_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1214 (all Xa (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)))) # label(fact_1703_odd__iff__not__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1215 (all X all 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))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_3397_ceiling__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1216 (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_178_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1217 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2231_arcsin__ubound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1218 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_2425_natfloor__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1219 (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_1616_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1220 (all A_1 all 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)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_2764_complex__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1221 (all X_a all X_b all A_2 all B_1 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_2),B_1)),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_2)))) # label(fact_4948_fin__bijRl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1222 (all R_3 all A_1 hAPP(real,real,abs_abs(real),R_3) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1))) # label(fact_3191_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1223 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),pls)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),Xa)),zero_zero(X_a))))))) # label(fact_235_le__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1224 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Ya all G 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),G),L),hAPP(X_a,filter(X_a),at(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),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)),Ya)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),L),Ya)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4579_divide_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1225 (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_4891_EulerFermat_Oaux) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1226 (all A_3 all B_2 ((all D_2 (one_one(int) = ti(int,D_2) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_2),A_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_2),B_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_2)))) <-> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),B_2) = one_one(int))) # label(fact_4432_coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1227 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,Na)),Xa)))) # label(fact_4904_isCont__real__root) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1228 (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_1187_MultInv__prop3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1229 (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_2486_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1230 (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_2789_complex_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1231 (all X_a (no_zero_divisors(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]. 7.46/7.48 1232 (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_1 exists Y_1 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_1)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_1))))) # label(fact_3115_bezout__prime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1233 (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_1942_minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1234 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),Xa)))))) # label(fact_2907_zero__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1235 (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_941_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1236 (all M_5 all D_4 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_5),D_4) -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_4),Q_4) = M_5))) # label(fact_1576_mod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1237 (all X_a (ab_group_add(X_a) -> (all F all K all Na 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),Na),K)))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))))) # label(fact_4203_sumr__offset) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1238 (all P_1 all Ma all Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> ((Na = Ma -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))))) # label(fact_141_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1239 (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_829_divides__exp) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1240 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all K all F all L_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),L_2),hAPP(X_a,filter(X_a),at(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),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_3),K)))))))) # label(fact_4610_LIM__offset) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1241 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N))) # label(fact_2903_floor__eq3) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1242 (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_943_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1243 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all Na 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),Na)) = 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,Na)))))) # label(fact_4209_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1244 (all V_2 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_2)) = 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_2)))) # label(fact_1510_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1245 (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,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 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_1532_mod__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1246 (all X hAPP(complex,complex,inverse_inverse(complex),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)))))))) # label(fact_3015_complex__inverse__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1247 (all P_1 all Na ((exists X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) & hBOOL(hAPP(nat,bool,P_1,X_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),Na)))))) # label(fact_4225_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1248 (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_3546_dist__triangle__half__r) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1249 (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_1183_MultInv__zcong__prop1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1250 (all P_1 all Na all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Na),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)) -> (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) = Na -> hBOOL(hAPP(nat,bool,P_1,I_2)))))) & (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1170_split__div) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1251 (all X hAPP(real,real,cos,X) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi)))) # label(fact_2332_cos__periodic) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1252 (all X_b all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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_2))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))))) # label(fact_3666_card__image__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1253 (all Xa all Ya (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),Xa),Ya)),zEven)) <-> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven))))) # label(fact_1699_even__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1254 (all X hAPP(real,real,exp(real),X) = hAPP(real,real,abs_abs(real),hAPP(real,real,exp(real),X))) # label(fact_1758_abs__exp__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1255 (all X_a (linordered_semidom(X_a) -> (all K all F all K_3 all Na ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),Na)) -> 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),Na),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),Na)),K_3)))))))) # label(fact_4300_real__setsum__nat__ivl__bounded2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1256 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) <-> 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_3)),zero_zero(X_a))))))) # label(fact_1949_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1257 (exists K_2 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) # label(fact_3014_Im_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1258 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (ti(int,P_5) != hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) -> (hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) != ti(int,P_5) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)))))) # label(fact_704_prime__g__5) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1259 (all Z (Z = zero_zero(complex) <-> zero_zero(complex) = hAPP(complex,complex,cnj,Z))) # label(fact_2967_complex__cnj__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1260 (all Xa all Na all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),hAPP(nat,nat,suc,Na))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ya),hAPP(nat,nat,suc,Na)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Xa),Ya)))) # label(fact_1408_exp__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1261 (all A_1 all C_1 all D_3 all B (ti(int,B) != zero_zero(int) -> (ti(int,D_3) != zero_zero(int) -> 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_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D_3)) = 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_1),D_3))))) # label(fact_3807_add__rat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1262 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),one_one(real)))))) # label(fact_2705_real__root__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1263 (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_1486_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1264 (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_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3137_div__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1265 (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,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_1967_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1266 (all A_1 all B all C_1 all D_3 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_1),D_3)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C_1))) # label(fact_3767_divide__rat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1267 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),M_2)))))) # label(fact_3692_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1268 (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_3003_Im_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1269 (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_2403_natfloor__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1270 (all 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)) = hAPP(rat,int,archim2085082626_floor(rat),P_4)) # label(fact_4054_rat__floor__code) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1271 (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_2733_SRStar__finite) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1272 (all X_a (linorder(X_a) -> (all Ma all I all Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),Na)) -> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),Na),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),Na)))))) # label(fact_4220_ivl__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1273 (all R_3 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_3) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3749_normalize__denom__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1274 (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_2121_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1275 (all X_a (field(X_a) -> (all A_1 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),one_one(X_a)),A_1)))) # label(fact_2603_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.48 1276 (all X_a (ring_1(X_a) -> (all C all X_1 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),X_1)) = 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)),X_1)))) # label(fact_4140_diffs__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1277 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all F all L_2 all A_3 ((all R_1 (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_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_1),A_3)),S_1)) & ti(X_a,A_3) != ti(X_a,X_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_1)),L_2)),R_1)))))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4676_LIM__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1278 (all D_3 all I_1 (ti(int,I_1) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),I_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),D_3)),hAPP(int,int,abs_abs(int),I_1)))))) # label(fact_1027_dvd__imp__le__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1279 (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_421_real__add__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1280 (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_1943_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1281 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),B)),C_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),A_1),B)),C_1)))) # label(fact_1294_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1282 (all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (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,Na),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Ya))))) # label(fact_2695_real__root__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1283 (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_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_1),N) = A_1))))) # label(fact_341_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1284 (all A_3 all B_2 all Q_2 all Ra (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_3),B_2),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),Ra))) -> 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_3)),B_2),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),Ra),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),Ra),zero_zero(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B_2),Ra))))))) # label(fact_2102_zminus1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1285 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_2 all A_3 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_3),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),fequal(X_a),A_3))),B_2)),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_3),S)) -> hAPP(X_a,X_b,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),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_3))),B_2)),zero_zero(X_b))),S)))))) # label(fact_4237_setsum__delta_H) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1286 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2)))))))) # label(fact_443_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1287 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> -(all K_1 ti(int,Xa) != 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))))) # label(fact_1233_zOddE) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1288 (all X_a all X_b (real_normed_algebra(X_b) -> (all G all B_2 all F all A_3 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),A_3),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),B_2),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),A_3),B_2)),A_2))))))) # label(fact_4481_mult_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1289 (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_4420_invertible__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1290 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))))))) # label(fact_244_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1291 (all L_4 hAPP(int,int,bit0,L_4) != min) # label(fact_670_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1292 (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_3471_zgcd__pos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1293 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> ti(fun(fun(nat,X_a),X_a),suminf(X_a)) = suminf(X_a))) # label(tsy_c_Series_Osuminf_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1294 (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_451_mult__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1295 (all X_a all A_2 all B_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)),A_2),B_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)),A_2),B_1)))) # label(fact_2199_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1296 (all X_a all Q_1 all P_1 all A_3 (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4894_someI2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1297 (all X_a (ordere142940540dd_abs(X_a) -> (all A_3 (ti(X_a,A_3) = 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_3)),zero_zero(X_a))))))) # label(fact_987_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1298 (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_362_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1299 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1558_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1300 (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_1968_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1301 (all X hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,sqrt,hAPP(real,real,inverse_inverse(real),X))) # label(fact_2562_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1302 (all Na 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)),Na)) = hAPP(nat,nat,fact_fact(nat),Na)) # label(fact_4565_fact__altdef__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1303 (all Y exists X_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)))))),X_1)) & Y = hAPP(real,real,tan,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)))))))) # label(fact_2458_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1304 (all X_a all C_2 all A_2 ((all X_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)),X_3),A_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)),X_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)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2)),C_2)))) # label(fact_2722_Union__least) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1305 (all K all Ma all Na (K = zero_zero(nat) | Ma = Na <-> 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),Na))) # label(fact_605_mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1306 (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_2914_floor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1307 (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_4851_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1308 (all X_a all P_3 all X_1 (hBOOL(hAPP(X_a,bool,P_3,X_1)) -> hBOOL(hAPP(X_a,bool,P_3,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_3))))) # label(fact_4809_tfl__some) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1309 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_2 all A_3 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_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),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_3))),B_2)),one_one(X_b))),S) = one_one(X_b)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),S)) -> hAPP(X_a,X_b,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_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_3))),B_2)),one_one(X_b))),S)))))) # label(fact_3982_setprod__delta) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1310 (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_1615_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1311 (all A_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),A_3),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_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,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)))),A_3))),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)))),A_3))),sequentially))))) # label(fact_4527_summable__Leibniz_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1312 (all B all D_3 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),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_3),B))))) # label(fact_825_divides__add__revr) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1313 (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_3098_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1314 (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_121_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1315 (all X_a (archim1727834104eiling(X_a) -> (all Z all Xa (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)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))))))) # label(fact_3620_less__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1316 (all Z_1 -(all M_2 all N_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_1)) != ti(int,Z_1))) # label(fact_1685_int__diff__cases) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1317 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),E_3)) -> (zero_zero(X_a) != hAPP(X_a,X_a,G,Xa) -> 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)),Xa),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),hAPP(X_a,X_a,G,Xa))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,Xa)),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,Xa)),hAPP(X_a,X_a,G,Xa))))))))))) # label(fact_3846_DERIV__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1318 (all N (zero_zero(nat) != N -> 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) = one_one(nat))) # label(fact_3312_coprime__minus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1319 (all L all U hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U) = 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),one_one(int)))) # label(fact_4597_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1320 (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_2635_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1321 (all X_a (comm_monoid_add(X_a) -> (all F all Na all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),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,Na))) = zero_zero(X_a)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),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,Na))) = 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),Na))),hAPP(nat,X_a,F,Na))))))) # label(fact_4231_setsum__op__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1322 (all X_a (order(X_a) -> (all Na all Ma all F ((all N_1 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,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))))))) # label(fact_1578_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1323 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Xa),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),Ya),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),Xa),Ya)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1738_even__sum__div__2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1324 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (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_3),B_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_3))))) # label(fact_3812_zero__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1325 (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_3146_mod__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1326 (all Xa (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)))) # label(fact_1701_not__odd__impl__even) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1327 (all Xa all Ya (hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ya)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Ya))))) # label(fact_2506_even__power__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1328 (all X_a all A_2 all X_1 (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_2)),X_1)) <-> 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_1),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2))))) # label(fact_4896_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1329 (all X_a (dvd(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]. 7.46/7.49 1330 (all X_a all X_b (ordere779506340up_add(X_b) & semiring_1(X_b) -> (all F all K_3 all A_2 ((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_2)) -> 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_2)),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_2))),K_3))))))) # label(fact_4323_setsum__bounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1331 (all B all D_3 all A_1 all C_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D_3)) -> 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_1),D_3)))))) # label(fact_3266_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1332 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_2)) -> 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_2))))) # label(fact_3877_Re_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1333 (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_4077_finite__psubset__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1334 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,Xa)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,Ya)))))) # label(fact_1739_neg__one__power__parity) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1335 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 all X_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))) # label(fact_2109_divide_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1336 (all Xa all Ya (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),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))))) = zero_zero(real) <-> zero_zero(real) = Ya & Xa = zero_zero(real))) # label(fact_109_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1337 (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_4425_gcd__ge__0__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1338 (all K_4 all L_4 hAPP(int,int,bit1,K_4) != hAPP(int,int,bit0,L_4)) # label(fact_68_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1339 (all Xa all Na (zero_zero(nat) = Na | zero_zero(int) != ti(int,Xa) <-> 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),Xa)),Na))))) # label(fact_1035_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1340 (all Xa 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),Xa))))) # label(fact_4049_summable__cos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1341 (all X_a all X_b (topological_space(X_b) -> tendsto(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool))),tendsto(X_a,X_b)))) # label(tsy_c_Limits_Otendsto_res) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1342 (all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),one_one(nat))) <-> one_one(nat) = A_3)) # label(fact_1259_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1343 (all A_3 all B_2 all C all Xa (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(int,nat,nat_1,Xa)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_3),B_2) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,Xa))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_3),B_2) -> (exists K_1 ti(int,A_3) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,Xa)))))))) # label(fact_3499_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1344 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_33_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1345 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),ln),Xa)))) # label(fact_4905_isCont__ln) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1346 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4972_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1347 (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_1412_mod__div__equality) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1348 (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_529_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1349 (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),minus_minus(real),X),one_one(real)) = hAPP(real,real,ln,X) -> one_one(real) = X))) # label(fact_1716_ln__eq__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1350 (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_1343_le__SucI) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1351 (all X hAPP(complex,complex,uminus_uminus(complex),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)))) # label(fact_3040_complex__minus__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1352 (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]. 7.46/7.49 1353 (all X_a (number(X_a) -> (all Wa all Xa (hAPP(int,X_a,number_number_of(X_a),Wa) = ti(X_a,Xa) <-> hAPP(int,X_a,number_number_of(X_a),Wa) = ti(X_a,Xa))))) # label(fact_41_number__of__reorient) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1354 (all X_a (linordered_idom(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3),A_3)),zero_zero(X_a))))))) # label(fact_44_even__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1355 (all X (one_one(real) = hAPP(real,real,cos,X) -> hAPP(real,real,sin,X) = zero_zero(real))) # label(fact_2258_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1356 (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_1156_div__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1357 (all X_a (semiring_div(X_a) -> (all Ma all K all Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Na)) -> (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),Na)))))))) # label(fact_1305_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1358 (all X_a all X_b all C 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),P_4)) -> -(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) = ti(product_prod(X_a,X_b),P_4) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C,X_1),Y_1)))))) # label(fact_4088_splitE) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1359 (all X_a all F all Xa all A_2 ((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_2)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(X_a,int,F,I_2)),Xa))) -> 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_2)),Xa))) # label(fact_4441_setprod__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1360 (all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B_1))))) # label(fact_2737_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1361 (all A_3 all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_3),hAPP(int,nat,nat_1,Xa))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_3)),hAPP(int,nat,nat_1,Xa))))) # label(fact_2101_neg__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1362 (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),one_one(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))))) # label(fact_3135_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1363 (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 -> zero_zero(real) = Y)) # label(fact_2175_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1364 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_1395_mult__Suc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1365 (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_3655_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1366 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))) # label(fact_3667_Bnor__in__RsetR) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1367 (all Z_1 exists A_4 exists R_1 Z_1 = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_1)),hAPP(complex,complex,expi,A_4))) # label(fact_2939_complex__expi__Ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 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_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_1976_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1369 (all X_a (real_algebra_1(X_a) -> (all Xa all Ya (Ya = Xa <-> hAPP(real,X_a,of_real(X_a),Ya) = hAPP(real,X_a,of_real(X_a),Xa))))) # label(fact_2791_of__real__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1370 (all X_a (real_normed_algebra(X_a) -> (all R_3 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),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,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),A_1)),B)))) # label(fact_4722_mult_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1371 (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_1367_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1372 (all C_1 all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C_1))))) # label(fact_952_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1373 (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_3225_fact__less__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1374 (all X_a (linordered_field(X_a) -> (all B_2 all A_3 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)),A_3)) <-> 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_3),C)),B_2))))))) # label(fact_1890_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1375 (all A_3 all B_2 all A_2 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_2),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),A_2)) -> ti(int,B_2) = ti(int,A_3))))))) # label(fact_3646_RRset__zcong__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1376 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa) <-> zero_zero(real) = Xa))) # label(fact_2683_real__root__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1377 (all X_a all C 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),C),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_2),B_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1)))) # label(fact_2241_DiffD2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1378 (all B all A_1 (ti(int,B) != zero_zero(int) | zero_zero(int) != ti(int,A_1) -> (exists C_4 exists D_2 (ti(int,A_1) = 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) & hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_4),D_2) = 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_2) = ti(int,B))))) # label(fact_3509_make__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1379 (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_2616_left__inverse) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1380 (all A_3 all B_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) = zero_zero(complex) <-> A_3 = zero_zero(real) & zero_zero(real) = B_2)) # label(fact_2757_Complex__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1381 (all X_b (number(X_b) & ring(X_b) -> (all V all B all C_1 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_1)) = 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_1))))) # label(fact_756_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1382 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all Ma all F all L all Xa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa)))))))) # label(fact_4576_LIM__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1383 (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_1527_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1384 (all A_3 all B_2 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),A_3),K)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),K)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)))))) # label(fact_3496_zcong__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1385 (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_1415_StandardRes__ubound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1386 (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_1928_number__of__minus) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1387 (all Xa hAPP(real,real,ln,Xa) = 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))),Xa))) # label(fact_4161_ln__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1388 (all N hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N)) = hAPP(int,nat,number_number_of(nat),N)) # label(fact_1665_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1389 (all X_a (ring_1(X_a) -> (all N hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_3611_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1390 (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_4514_summable__LIMSEQ__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1391 (all P_5 all R_3 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),R_3),S_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_3),Q_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),P_5),S_3))))) # label(fact_3750_normalize__crossproduct) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1392 (all Xa 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),Xa))))) # label(fact_4048_summable__sin) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1393 (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)) -> zero_zero(int) = ti(int,A_1))))) # label(fact_915_zcong__zless__0) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1394 (all A_3 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),P_4)) -> hAPP(int,nat,nat_1,A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),P_4))))) # label(fact_3229_Bnor__prime) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1395 (all X_a all X_b (real_n2089651433ebra_1(X_a) & metric_space(X_b) -> (all M_1 all F all L_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),L_2),hAPP(X_a,filter(X_a),at(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),M_1),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> ti(X_b,L_2) = ti(X_b,M_1)))))) # label(fact_4595_LIM__unique) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1396 (all Na 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),Na)) -> (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),Na),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))))) # label(fact_841_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1397 (all X_a (real_normed_field(X_a) -> (all Na all F all Xa all D (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),Xa),D)) -> 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)),Na)),Xa),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),Na)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_3918_DERIV__power) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1398 (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,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_2436_add__tan__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1399 (all Ma all Na (hAPP(nat,nat,suc,Na) = Ma | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,suc,Na))))) # label(fact_1341_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1400 (all X_a (semiring_div(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> 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_1087_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1401 (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_4883_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1402 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_1)) -> one_one(nat) = hAPP(X_a,nat,F,X_1))) <-> one_one(nat) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),F_1)))) # label(fact_3965_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1403 (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),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1))))) # label(fact_957_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1404 (all X_c all X_b all X_a (metric_space(X_a) & topological_space(X_c) & topological_space(X_b) -> (all G all C all F all B_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),B_2),hAPP(X_a,filter(X_a),at(X_a),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),G),C),hAPP(X_b,filter(X_b),at(X_b),B_2))) -> ((exists D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all X_1 (ti(X_a,X_1) != ti(X_a,A_3) & 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_1),A_3)),D_2)) -> ti(X_b,B_2) != hAPP(X_a,X_b,F,X_1))))) -> 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),hAPP(X_a,filter(X_a),at(X_a),A_3))))))))) # label(fact_4627_metric__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1405 (all N all M ((M = zero_zero(nat) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) & (zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N))))) # label(fact_876_mult__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1406 (all X_2 all A_3 (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_2),A_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,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_2)),hAPP(complex,real,re,A_3)),sequentially)))) # label(fact_4536_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1407 (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_3484_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1408 (all K all Ma all Na (zero_zero(nat) = K | Ma = Na <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma))) # label(fact_693_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1409 (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_4495_LIMSEQ__Suc__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1410 (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_613_le__square) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1411 (all X_a (real_normed_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> 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_2006_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1412 (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_1755_exp__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1413 (all X_a all A_2 all B_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,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_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)),B_1),A_2)))) # label(fact_2196_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1414 (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),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(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))))) # label(fact_338_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1415 (all L all U 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)))) # label(fact_4270_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1416 (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)))) # label(fact_1127_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1417 (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_3289_coprime__common__divisor__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1418 (all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (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,Na),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Ya))))) # label(fact_2701_real__root__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1419 (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))) -> (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_855_divides__rev) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1420 (all K_4 all 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)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),hAPP(int,int,succ,L_4)))) # label(fact_309_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1421 (all X_a (idom(X_a) -> (all A_3 all C all B_2 (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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_2),C))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)) | zero_zero(X_a) = ti(X_a,C))))) # label(fact_746_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1422 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> X = hAPP(real,real,arctan,hAPP(real,real,tan,X))))) # label(fact_2453_arctan__tan) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1423 (all U hAPP(int,nat,nat_1,U) = 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))) # label(fact_4285_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1424 (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_1114_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1425 (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_224_zadd__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1426 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2299_cos__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1427 (all X_a all X_b all X_c all X_1 all Xa_1 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_1),Xa_1) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),X_1,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Xa_1)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Xa_1))) # label(fact_4041_split__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.49 1428 (all Ya 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),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)),Ya)))),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,Ya)))),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,Ya)))))),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)),Ya)))),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,Ya)))),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,Ya)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_1),zero_zero(real)))) # label(fact_3944_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1429 (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_731_one__dvd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1430 (all X all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D_3)) -> 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_3))),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_3))),hAPP(nat,real,real_1(nat),D_3))) = 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_3)))) # label(fact_2432_real__of__nat__div__aux) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1431 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all A_3 all B_2 all Wa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),hAPP(int,X_a,number_number_of(X_a),Wa)))) <-> (-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),Wa))) -> (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),Wa)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa))))) & (-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),Wa)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),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),Wa))) -> 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_3),hAPP(int,X_a,number_number_of(X_a),Wa))),B_2))))))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1432 (all X_a (ring_11004092258visors(X_a) -> (all A_3 (ti(X_a,A_3) = zero_zero(X_a) <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a))))) # label(fact_5_zero__eq__power2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1433 (all U_1 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_1),U_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)))) # label(fact_1988_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1434 (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_1557_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1435 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M) = hAPP(int,int,abs_abs(int),M)) # label(fact_3477_zgcd__0__left) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1436 (all X_a (order(X_a) -> (all X_2 ((all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,M_2)),hAPP(nat,X_a,X_2,N_1))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_4158_monoI1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1437 (all X_b all X_a (real_normed_algebra(X_a) -> (all Xa all G all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),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_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_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),Xa)),G)),A_2)))) # label(fact_4213_mult__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1438 (all Na all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & 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),Na)) -> 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_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)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))) = hAPP(real,real,F,H))))) # label(fact_4307_Maclaurin2__objl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1439 (all C all Xa all Ta all A_3 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),D_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D_1))),Ta)))))) # label(fact_764_zdvd__period) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1440 (all X_b all X_a (semiring_0(X_a) -> (all F all A_2 all Ra 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_2)),Ra) = 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)),Ra)),A_2)))) # label(fact_4241_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1441 (all B_2 all A_3 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_3),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_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_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),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_2)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4)))))))))) # label(fact_1199_wset__inv__mem__mem) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1442 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3569_fact__lt) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1443 (all D_1 all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_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),Xa),Y_1))),D_1)) -> hAPP(real,real,F,Y_1) = hAPP(real,real,F,Xa))) -> L = zero_zero(real))))) # label(fact_2661_DERIV__local__const) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1444 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3))) # label(fact_664_real__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1445 (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)) -> (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_2714_real__root__pos__unique) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1446 (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_2804_of__real__diff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1447 (all X_a (real_normed_field(X_a) -> (all Ya all A_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(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)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),Ya)),hAPP(X_a,filter(X_a),at(X_a),A_3)))))) # label(fact_4578_divide_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1448 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4))) # label(fact_611_add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1449 (all N zero_zero(real) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi))) # label(fact_2376_tan__npi) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1450 (all C_1 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (B = C_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C_1))))) # label(fact_951_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1451 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_92_number__of__add) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1452 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all B_1 all F all Sb (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sb)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sb)) -> 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_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),Sb) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sb)) -> 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_1))))))))) # label(fact_4326_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1453 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D)) -> (all X_1 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_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D))),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_1),Ta))))))))) # label(fact_719_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1454 (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_2986_compl__less__swap1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1455 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)))) # label(fact_3307_ceiling__one) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1456 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) & A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N) & (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) & hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_1),N) = A_1 -> X_1 = Y_1))))))) # label(fact_340_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1457 (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_1767_exp__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1458 (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_427_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1459 (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_1819_exp__bound) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1460 (all F all Na all Ra 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)),Na))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),Ra)) = 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)),Ra)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) # label(fact_4205_sumr__diff__mult__const) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1461 (all X_a (real_field(X_a) & field_inverse_zero(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))) # label(fact_2805_of__real__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1462 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> (exists 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),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),Y_1)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,A_3)),hAPP(real,real,F,B_2)))))) # label(fact_2865_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1463 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 all C all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2))))))) # label(fact_738_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1464 (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_4510_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1465 (all X_2 all A_3 (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_2),A_3),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_2)),hAPP(complex,complex,cnj,A_3)),sequentially)))) # label(fact_4532_cnj_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1466 (all X_b all X_a all F all A_2 all B_1 (ti(fun(X_a,bool),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_2) -> hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_2)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))) # label(fact_3658_image__Pow__surj) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1467 (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_2771_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1468 (all X_a (group_add(X_a) -> (all A_3 (ti(X_a,A_3) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))) # label(fact_1936_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1469 (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_4813_someI__ex) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1470 (all X_a (comple44059174attice(X_a) -> (all Va all U all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Va),U)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Va),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)))))))) # label(fact_1817_complete__lattice__class_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1471 (all Z_1 hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,im,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1))) # label(fact_3010_Im__sgn) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1472 (all X_b all X_c all X_a all F all A_3 all B_2 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,A_3),B_2) = 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_3),B_2))) # label(fact_4021_split__conv) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1473 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int)) = ti(int,Z_1)) # label(fact_406_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1474 (all R_3 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_3)),hAPP(int,real,number_number_of(real),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_3))),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),S_3)))) # label(fact_3802_Ratreal__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1475 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Xa 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),Xa))) = hAPP(X_a,X_a,exp(X_a),Xa)))) # label(fact_4776_exp__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1476 (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)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = Qr_1)) # label(fact_3125_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1477 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_453_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1478 (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_556_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1479 (all C_1 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_1),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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C_1)))))) # label(fact_840_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1480 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all Xa (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),Xa)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4941_isCont__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1481 (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_570_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1482 (all X_a all F1 all F2 all Code_numeral hAPP(code_code_numeral,X_a,F2,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))) # label(fact_3556_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1483 (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_374_mult__zero__right) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1484 (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_1790_exp__ln) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1485 (all Ya all Xa (hBOOL(hAPP(int,bool,nat_is_nat,Xa)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Xa),Ya))))) # label(fact_4880_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1486 (all X_a (real_normed_vector(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_2)) -> 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_2)),Xa))))))) # label(fact_4742_scaleR__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1487 (all X_a (order(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) <-> 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),Xa)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Ya))))))) # label(fact_4962_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1488 (all X_4 all Y_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_4),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_4),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_3),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_4),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_4),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_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2361_cos__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1489 (all Xa (hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),Xa)) = Xa <-> (exists N_1 Xa = hAPP(int,real,real_1(int),N_1)))) # label(fact_3365_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1490 (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]. 7.46/7.50 1491 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,X)))) # label(fact_2047_log__base__10__eq2) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1492 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all Na ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_2)) -> hAPP(nat,X_a,F,M_2) = zero_zero(X_a))) -> 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)),Na)))))))) # label(fact_4318_series__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1493 (all X all Y X = hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_3019_Re) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1494 (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_2544_fact__gt__zero__nat) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1495 (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_2026_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1496 (all X_b all X_a (order(X_a) & order(X_b) -> (all C all F all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,B_2))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_3))))))))) # label(fact_2861_xt7) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1497 (all X_a (divisi14063676e_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2573_inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1498 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,Xa)),hAPP(real,real,ln,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))))) # label(fact_1717_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1499 (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_3197_rcis__divide) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1500 (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_2547_fact__dvd) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1501 (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),E),D2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E))))))) # label(fact_2754_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1502 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))))) # label(fact_3875_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1503 (all A_1 all B ((zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),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))) & (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))))) # label(fact_2090_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1504 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K all A_3 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_3))))) # label(fact_4921_isCont__const) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1505 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) # label(fact_3132_div__int__def) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1506 (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]. 7.46/7.50 1507 (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_2572_field__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1508 (all X_a (linorder(X_a) -> (all A_3 all B_2 all C 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),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_3),B_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> ti(X_a,A_3) = ti(X_a,C))))))) # label(fact_4223_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1509 (all X_a all A_2 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_2)),pow(X_a))))) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) # label(fact_4453_Pow__Compl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1510 (all Xa all Ya (Xa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Xa),Ya) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)))) # label(fact_3255_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1511 (all X_b all X_a (topological_space(X_a) & real_n2089651433ebra_1(X_b) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_3)) -> 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_3)))))) # label(fact_4915_isCont__of__real) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1512 (all X_a (boolean_algebra(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = ti(X_a,X)))) # label(fact_2979_double__compl) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1513 (all C_1 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_1),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C_1),B))))) # label(fact_826_divides__mul__l) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1514 (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_553_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1515 (all X_a (ring_1(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_2)),ring_1_Ints(X_a)))))))) # label(fact_3830_Ints__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1516 (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_942_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1517 (all X all Y all K_4 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y) -> (exists I_2 exists J_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),J_1) = Y & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2) = X))))) # label(fact_3451_prime__power__mult) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1518 (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_760_zdvd__mono) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1519 (all X_b all X_a all X all Y all A_1 (ti(X_a,A_1) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X),Y)) -> ti(X_a,A_1) = ti(X_a,Y))) # label(fact_3157_snd__eqD) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1520 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),A_1),B)),C_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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1))),C_1)))) # label(fact_1295_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1521 (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_3613_ceiling__of__int) # label(axiom) # label(non_clause). [assumption]. 7.46/7.50 1522 (all X all Y hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),X),Y)) # label(fact_3545_dist__complex__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1523 (all X_a all Ra all A_3 ((exists X_1 (ti(X_a,A_3) = ti(X_a,X_1) & (all Xa_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),Ra,Xa_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),Ra),Xa_1)))))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),Ra),A_3)))) # label(fact_2944_accp_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1524 (all X_a (order(X_a) -> (all Xa all Ya (ti(X_a,Ya) != ti(X_a,Xa) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)))))) # label(fact_569_order__less__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1525 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 (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_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)))))) # label(fact_2594_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1526 (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_3254_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1527 (all R_3 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),R_3) = hAPP(real,real,abs_abs(real),R_3)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),zero_zero(real))) -> hAPP(real,real,abs_abs(real),R_3) = R_3))) # label(fact_2025_real__abs__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1528 (all B_2 all A_3 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)))) # label(fact_3234_Bnor__mem__zg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1529 (all X_a (linord20386208strict(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_478_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1530 (all Xa all Na (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Na))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(int,real,number_number_of(real),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,Xa)),hAPP(int,nat,number_number_of(nat),Na))))))) # label(fact_1659_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1531 (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_3577_weak__decr__stable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1532 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))) # label(fact_812_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1533 (all Xa all Ya (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)))) # label(fact_958_dvd_Oless__le__not__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1534 (all X_a (field_char_0(X_a) -> (all Na all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3),Na)),field_char_0_Rats(X_a))))))) # label(fact_3713_Rats__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1535 (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_1878_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1536 (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_615_mult__le__mono1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1537 (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_3631_ceiling__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1538 (all X_a (real_normed_algebra(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))) # label(fact_1238_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1539 (all Xa (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)))),Xa)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)))) # label(fact_2520_nat__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1540 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_1270_lessI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1541 (all Y Y = hAPP(real,real,tan,hAPP(real,real,arctan,Y))) # label(fact_2375_tan__arctan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1542 (all X_a (real_normed_vector(X_a) -> (all Xa (zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),Xa) <-> zero_zero(X_a) = ti(X_a,Xa))))) # label(fact_1963_norm__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1543 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya_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),Y)),Ya_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),Ya_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya_1))))) # label(fact_1752_divide_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1544 (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_255_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1545 (all X_a (group_add(X_a) -> (all A_1 all B (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = ti(X_a,B))))) # label(fact_1961_minus__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1546 (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(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_eq(int),B),zero_zero(int))) | 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_1647_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1547 (all X_a (metric_space(X_a) -> ti(fun(fun(nat,X_a),bool),cauchy(X_a)) = cauchy(X_a))) # label(tsy_c_SEQ_OCauchy_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1548 (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_3213_fact__neg__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1549 (all K all Ma all Na (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),Na))) <-> zero_zero(nat) = K | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)))) # label(fact_842_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1550 (all Xa all Ya (hAPP(complex,complex,cnj,Ya) = hAPP(complex,complex,cnj,Xa) <-> Ya = Xa)) # label(fact_2960_complex__cnj__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1551 (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_3791_real__uminus__code) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1552 (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_1994_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1553 (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_1740_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1554 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_1411_mod__div__equality2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1555 (all A_1 all B all C_1 all D_3 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_1),D_3)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),C_1)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D_3))) # label(fact_2765_complex__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1556 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,N)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,N)))))) # label(fact_339_number__of1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1557 (all X_2 all A_3 (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_2),A_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,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_2)),hAPP(complex,real,im,A_3)),sequentially)))) # label(fact_4537_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1558 (all X_a (no_zero_divisors(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,B) | zero_zero(X_a) = ti(X_a,A_1))))) # label(fact_377_divisors__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1559 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_2)),one_one(rat)))))) # label(fact_3810_Fract__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1560 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),X) = hAPP(int,int,abs_abs(int),X)) # label(fact_4390_gcd__idem__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1561 (all X_a (linord219039673up_add(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))))))) # label(fact_1950_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1562 (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_2341_sin__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1563 (all X_a all F all A_2 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_2)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_2)) # label(fact_3970_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1564 (all X_a all A_1 all B hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B)) = hAPP(int,X_a,hAPP(int,fun(int,X_a),frac(X_a),A_1),B)) # label(fact_4445_Nitpick_Ofrac__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1565 (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),gcd_gcd(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_4417_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1566 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(int,int,fact_fact(int),N) != zero_zero(int))) # label(fact_3216_fact__nonzero__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1567 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),A_3)) <-> 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_3),B_2)))))) # label(fact_3809_one__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1568 (all X_a (ring_1(X_a) -> (all Na 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),Na)),ring_1_Ints(X_a)))))) # label(fact_3834_Ints__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1569 (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_1720_ln__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1570 (all P_1 all Na all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Na),K))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & 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) = ti(int,Na) & 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))))) & (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_eq(int),J_1),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),K),I_2)),J_1) = ti(int,Na) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),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_1126_split__zdiv) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1571 (all X all Y hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2755_complex__norm) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1572 (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_1388_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1573 (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_1893_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.50 1574 (all X_a (real_normed_field(X_a) -> (all Ya all X_2 all A_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_2),A_3),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_2)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),Ya)),sequentially)))))) # label(fact_4497_divide_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1575 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all Wa all B_2 all C ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),Wa)),C)),B_2))) & (-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),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),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),Wa)),C)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),Wa)),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),Wa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C))))))) # label(fact_1803_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1576 (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_1396_mult__Suc__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1577 (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_3838_Ints__induct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1578 (all X_a all A_2 all B_1 (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_2),B_1)),finite_psubset(X_a))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)))) # label(fact_3204_in__finite__psubset) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1579 (all X_a (plus(X_a) & dvd(X_a) & linorder(X_a) -> (all D_1 all Sb exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Sb))) <-> 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_1),Sb)))))))) # label(fact_1214_minf_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1580 (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_995_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1581 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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_1),A_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_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),B_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(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_2),B_1))))))) # label(fact_4260_setsum__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1582 (all R_3 all A_1 hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(real,real,cos,A_1))) # label(fact_3194_Re__rcis) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1583 (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_1927_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1584 (all X_a all A_2 all B_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)),A_2),B_1)) <-> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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)),A_2),B_1)))) # label(fact_2198_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1585 (all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)) <-> (exists K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),K_1)) = ti(int,B_2)))) # label(fact_908_zcong__iff__lin) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1586 (all Ma all Na hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),Ma),hAPP(nat,nat,suc,Na)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),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)),Na))),Ma)) # label(fact_4857_min__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1587 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_4)) -> (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_4)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_237_power__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1588 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),hAPP(real,real,cos,X)))) # label(fact_2289_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1589 (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 | zero_zero(nat) = X)) # label(fact_1373_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1590 (all X_a (archim1804426504_field(X_a) -> (all X exists X_1 ((all Y_1 (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_1),one_one(int))))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Y_1)),X)) -> ti(int,Y_1) = ti(int,X_1))) & 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_1),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),X_1)),X)))))) # label(fact_3641_floor__exists1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1591 (all X all Z_1 all D_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_3)) -> 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_3))),Z_1)))) # label(fact_1058_decr__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1592 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Xa all C 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)),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))),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)))),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),Xa)),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))),power_power(X_a)))),Xa),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))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa)))))))))))) # label(fact_4151_termdiffs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1593 (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_3228_length__around__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1594 (all X_a all F all A_2 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_2)) = 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_2)) # label(fact_3968_real__of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1595 (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)) -> (ti(int,X) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)) -> 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_913_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1596 (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_4975_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1597 (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_1842_divide__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1598 (all X_a (real_normed_algebra(X_a) -> (all C all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_3)) -> 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C))))))) # label(fact_4108_sums__mult2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1599 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_167_zero__neq__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1600 (all X_a (real_normed_field(X_a) -> (all Xa (ti(X_a,Xa) != 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)),Xa),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),Xa)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_3917_DERIV__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1601 (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_1762_ln__x__over__x__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1602 (all X_a (power(X_a) & semiring_0(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) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N) = one_one(X_a)))))) # label(fact_112_power__0__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1603 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),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)))),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),Xa),one_one(real)))),suc))) = hAPP(real,real,ln,Xa)))) # label(fact_4004_ln__series) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1604 (all X_a all A_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_2),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_2))))) # label(fact_2850_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1605 (all X_a all A_2 (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_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_2746_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1606 (all X_a (topological_space(X_a) -> (all G all L 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),L),hAPP(X_a,filter(X_a),at(X_a),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,L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4574_cnj_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1607 (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_1810_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1608 (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_1360_pos__mod__bound) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1609 (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_1661_SRStar__card) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1610 (all X_b all X_a (comm_monoid_add(X_a) -> (all H all G all S all R_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,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_2,Y1),Y2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,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_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,H,X_1)),hAPP(X_b,X_a,G,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_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),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_4820_setsum_Orelated) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1611 (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_1196_MultInv__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1612 (all X_a (field_char_0(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),field_char_0_Rats(X_a))) -> (zero_zero(X_a) != ti(X_a,A_3) -> 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_3)),field_char_0_Rats(X_a)))))))) # label(fact_3704_nonzero__Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1613 (all Na (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Na)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Na),zero_zero(int))))) # label(fact_3408_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1614 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N) = N) # label(fact_622_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1615 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (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_2))) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_2))))) # label(fact_3689_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1616 (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_4698_scaleR__left__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1617 (all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),A_1) = one_one(real)))) # label(fact_2030_log__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1618 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_937_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1619 (all X all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),X)),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)) # label(fact_2069_zminus__zmod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1620 (all F all G all Na 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)))),Na))) = 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)),Na))),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)),Na)))) # label(fact_4262_sum__split__even__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1621 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> ti(int,M) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),M))) # label(fact_3472_zgcd__self) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1622 (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_1320_mod__mod__is__mod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1623 (all Xa 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))))),Xa),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,Xa)),hAPP(real,real,sin,Xa))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Xa)),hAPP(real,real,sin,Xa)))))) # label(fact_3939_DERIV__sin__realpow2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1624 (all X_b all X_a (ring_1(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 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_2)) = 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_2)))) # label(fact_3956_of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1625 (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_985_zdvd__antisym__abs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1626 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1)) # label(fact_405_zmult__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1627 (all X_a (plus(X_a) & linorder(X_a) & dvd(X_a) -> (all D_1 all Sb exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_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_1),Sb))) <-> 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_1),Sb)))))))) # label(fact_1213_pinf_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1628 (all P_1 all Na all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> ((all I_2 all J_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) = ti(int,Na) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Na),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Na),K)))))) # label(fact_1499_split__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1629 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),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))) # label(fact_3150_div__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1630 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 ((all X_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_2826_of__real_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1631 (all X_a all X_b (order(X_a) & order(X_b) -> (all F all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_2)),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_3)),C)))))))) # label(fact_2856_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1632 (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_565_not__leE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1633 (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_1190_aux______2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1634 (all X all 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)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))) # label(fact_3364_real__of__int__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1635 (all A_1 all C_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,A_1)),C_1) = 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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),C_1))),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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),C_1))),C_1))) # label(fact_1555_div__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1636 (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),A_1),one_one(X_a))))) # label(fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1637 (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_2357_arccos__cos2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1638 (all Xa (Xa = zero_zero(real) <-> one_one(real) = hAPP(real,real,exp(real),Xa))) # label(fact_1771_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1639 (all A_3 all B_2 (hAPP(rat,product_prod(int,int),quotient_of,A_3) = hAPP(rat,product_prod(int,int),quotient_of,B_2) <-> B_2 = A_3)) # label(fact_3738_quotient__of__inject__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1640 (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_2799_of__real__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1641 (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_2713_real__root__pow__pos2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1642 (all B_2 all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)) <-> 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_3),B_2)))))) # label(fact_1110_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1643 (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_1167_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1644 (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_3109_xzgcd__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1645 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),Xa),hAPP(real,real,inverse_inverse(real),Xa))))) # label(fact_2652_DERIV__ln) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1646 (all W hAPP(int,complex,number_number_of(complex),W) != ii) # label(fact_2779_complex__i__not__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1647 (all Xa all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),sr,P_4))) -> ti(int,Xa) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),Xa))) # label(fact_1273_StandardRes__SR__prop) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1648 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_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)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1))))) # label(fact_1304_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1649 (all K_4 all L_4 hAPP(int,int,bit1,L_4) != hAPP(int,int,bit0,K_4)) # label(fact_69_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1650 (all X_a all A_2 all B_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)),A_2),B_1)) & ti(fun(X_a,bool),B_1) != ti(fun(X_a,bool),A_2) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_2),B_1)))) # label(fact_2197_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1651 (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_3814_rat__floor__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1652 (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_315_zero__le__power2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1653 (all X hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi))) # label(fact_2392_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1654 (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,abs_abs(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,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_1858_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1655 (all M hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,one_one(int)),M) = one_one(int)) # label(fact_3459_zgcd__1__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1656 (all X_a (number_semiring(X_a) -> (all N hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_97_number__of__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1657 (all A_3 (zero_zero(nat) != A_3 <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),zero_zero(nat))))) # label(fact_1253_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1658 (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_1131_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1659 (all X_a (real_normed_algebra(X_a) -> (all Ya all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> 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_2)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),Ya))))))) # label(fact_4110_mult__left_Osums) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1660 (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_1469_div__geq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1661 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))) # label(fact_2120_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1662 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_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_3)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3),B_2)),zero_zero(X_a))))))) # label(fact_1844_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1663 (all X_a (semiring_1(X_a) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)))) # label(fact_191_of__nat__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1664 (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_3446_ln__powr__bound2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1665 (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_1364_power__0__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1666 (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_1872_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1667 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3))) # label(fact_368_zmult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1668 (all X_a (linordered_idom(X_a) -> (all Xa all Na (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),Xa),Na)),zero_zero(X_a))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),zero_zero(X_a))))))) # label(fact_2491_power__less__zero__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1669 (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]. 7.53/7.51 1670 (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_171_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1671 (all X_a all A_2 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_2))) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2)) # label(fact_2240_Compl__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1672 (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_3103_prime__ge__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1673 (all V hAPP(complex,real,im,hAPP(int,complex,number_number_of(complex),V)) = zero_zero(real)) # label(fact_3004_complex__Im__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1674 (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_2793_of__real_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1675 (all A_3 all B_2 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_3))),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_2)))))),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_2))),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_2))))),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_2)))),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_2))),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_3),B_2)) # label(fact_4058_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1676 (all X_a (division_ring(X_a) -> (all B all A_1 all C_1 (ti(X_a,C_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),C_1) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1)))))) # label(fact_1853_divide__eq__imp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1677 (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_3217_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1678 (all A_2 (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_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_2)))) # label(fact_3670_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1679 (all X_a all X_b (comm_semiring_1(X_b) & no_zero_divisors(X_b) -> (all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_2) <-> (exists X_1 (zero_zero(X_b) = hAPP(X_a,X_b,F,X_1) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2))))))))) # label(fact_3977_setprod__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1680 (all N (zero_zero(nat) != N -> (exists M_2 N = hAPP(nat,nat,suc,M_2)))) # label(fact_2790_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1681 (all X_b all X_a all R_2 all Xa all Ya (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),Xa),Ya)),R_2)) <-> 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_2),Xa),Ya)))) # label(fact_3068_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1682 (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_2133_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1683 (all X_a (real_normed_field(X_a) -> (all Na all F all Xa all D (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),Xa),D)) -> 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,Na))),Xa),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),Na))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,Xa)),Na))))))))) # label(fact_3916_DERIV__power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1684 (all X_a (linorder(X_a) -> (all B all D_3 all A_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_3)) -> 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_1),D_3)))))))) # label(fact_4853_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1685 (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_2143_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1686 (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_467_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1687 (all A_3 all Ra (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ra)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),A_3)) -> (exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> 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_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),N_1))))),Ra))))))) # label(fact_4083_suminf__exist__split) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1688 (all L all U hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U) = 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),L)))) # label(fact_4292_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1689 (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 -> (B = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_6),B_5))))) # label(fact_3311_gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1690 (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]. 7.53/7.51 1691 (all P_1 all A_3 all B_2 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_3),B_2),zero_zero(nat)) = hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_3),B_2)) # label(fact_3166_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1692 (all X_a (field(X_a) & number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))))) # label(fact_2621_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1693 (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_2138_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1694 (all X_b all X_a all Q_1 all P_1 all Xa all Ya (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Xa),Ya)) -> (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,Xa),Ya))))) # label(fact_4368_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1695 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),Xa),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,Xa))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2654_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1696 (all X hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi)))) # label(fact_2440_tan__periodic) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1697 (all X_a ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_rec(X_a)) = complex_rec(X_a)) # label(tsy_c_Complex_Ocomplex_Ocomplex__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1698 (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_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))))) # label(fact_2106_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1699 (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_2262_sgn__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1700 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_149_not__less0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1701 (all A_3 all B_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),A_3),B_2)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),zOdd))))) # label(fact_1709_even__plus__odd__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1702 (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_2339_cos__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1703 (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_1438_one__less__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1704 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),W),Z_1))))) # label(fact_3586_of__int__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1705 (all Y exists X_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)))))),X_1)) & hAPP(real,real,tan,X_1) = Y & (all 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)))))) & Y = hAPP(real,real,tan,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)) -> Y_1 = 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)))))))) # label(fact_2459_tan__total) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1706 (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_4986_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1707 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(real,fun(nat,real),power_power(real),Xa)))))) # label(fact_3951_monoseq__realpow) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1708 (all Z all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,Wa)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z))))) # label(fact_1032_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1709 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all Ra all G 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),G),L),hAPP(X_a,filter(X_a),at(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),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),Ra)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),Ra),L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4757_scaleR__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1710 (all X_b all X_a all R_2 all K all Ta all Sb (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sb)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ta)) -> ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),Ta)) -> hAPP(X_b,nat,K,X_1) = 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)),Sb))),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_2),X_1)))))) -> 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_2)))),Sb))))) # label(fact_4330_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1711 (all X_2 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)) -> 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_2))))) # label(fact_4876_vanishes__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1712 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),Y) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))) # label(fact_1887_abs__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1713 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) != one_one(int))))) # label(fact_1178_inv__not__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.51 1714 (all A_3 all C all D_1 all B_2 (zero_zero(int) != ti(int,B_2) -> (zero_zero(int) != ti(int,D_1) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_3),D_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B_2) <-> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_2) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D_1))))) # label(fact_3760_eq__rat_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1715 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) <-> zero_zero(nat) = Na)) # label(fact_283_int__le__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1716 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,Xa)) = hAPP(int,int,number_number_of(int),min)))) # label(fact_1229_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1717 (all X_a (linordered_ring(X_a) & monoid_mult(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_2489_zero__le__even__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1718 (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_2 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_2))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y))) # label(fact_3176_prod__cases4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1719 (all A_1 ((-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> A_1 = hAPP(real,real,abs_abs(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) = hAPP(real,real,uminus_uminus(real),A_1)))) # label(fact_2024_abs__real__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1720 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X)))) # label(fact_2041_aux5) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1721 (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_641_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1722 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,G,X_1))) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,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),G),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_4442_setsum__mono__zero__cong__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1723 (all X_a (topological_space(X_a) -> (all A_3 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),combi(X_a)),A_3))))) # label(fact_4920_isCont__ident) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1724 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,real,norm_norm(X_a),X)))) # label(fact_1925_norm__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1725 (all A_1 all B hAPP(rat,rat,sgn_sgn(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),times_times(int),hAPP(int,int,sgn_sgn(int),A_1)),hAPP(int,int,sgn_sgn(int),B)))) # label(fact_3803_sgn__rat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1726 (all A_3 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_3)),hAPP(complex,filter(complex),at(complex),A_3)))) # label(fact_4573_cnj_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1727 (all X_a all G all A_3 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),A_3),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,A_3)),A_2)))) # label(fact_4531_cnj_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1728 (all Va (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),Va) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) # label(fact_2936_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1729 (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_3185_int__of__number) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1730 (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_1095_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1731 (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)),P_5))))))) # label(fact_1071_Euler__part1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1732 (all X_a (comm_monoid_add(X_a) -> (all F all Na all Ma ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),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),Na))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,Na))) = 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,Na)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),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,Na)))))))) # label(fact_4628_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1733 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),Xa)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2872_floor__le__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1734 (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_2294_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1735 (all A_3 all B_2 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_3),B_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (all N_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_3),B_2),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_3),B_2),N_1)))))))))) # label(fact_3170_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1736 (all X_a (ring_char_0(X_a) & number_ring(X_a) -> (all Wa (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,Wa)))) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),Wa))))))) # label(fact_2157_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1737 (all U all F ((all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,F,N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_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)))))) # label(fact_4190_finite__less__ub) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1738 (all L all U 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)))) # label(fact_4558_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1739 (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_1529_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1740 -(all X_1 all Y_1 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))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_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),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_591__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1741 (all X_2 all A_3 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_2),A_3)) -> 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_2)),hAPP(complex,real,im,A_3))))) # label(fact_4142_Im_Osums) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1742 (all Ra 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),Ra)),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)))),Ra),sequentially))) # label(fact_4508_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1743 (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_1560_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1744 (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_2478_power__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1745 (all K_4 zero_zero(rat) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),K_4)) # label(fact_3764_rat__number__collapse_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1746 (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_473_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1747 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_1535_mod__geq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1748 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_2 all C all Wa (hAPP(int,X_a,number_number_of(X_a),Wa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C) <-> (ti(X_a,C) != zero_zero(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),Wa)),C) = ti(X_a,B_2)) & (ti(X_a,C) = zero_zero(X_a) -> hAPP(int,X_a,number_number_of(X_a),Wa) = zero_zero(X_a)))))) # label(fact_1778_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1749 (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_3752_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1750 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,real,real_1(int),X) = hAPP(nat,real,real_1(nat),hAPP(int,nat,nat_1,X)))) # label(fact_3419_real__nat__eq__real) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1751 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_5),Q_3))))) # label(fact_466_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1752 (all X_a (linordered_idom(X_a) -> (all Xa all A_3 all Ra (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),Xa),A_3))),Ra)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),Ra))) & 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_3),Ra)),Xa)))))) # label(fact_1138_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1753 (all X_a all X_b all X_c all X_d all X_e all X_f all Xa all P_1 ((all A_4 all B_4 all C_4 all D_2 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_2),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,Xa)))) # label(fact_3172_prod__induct6) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1754 (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_2413_natfloor__subtract) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1755 (all X_a (field_char_0(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_2),field_char_0_Rats(X_a))) -> (ti(X_a,B_2) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),B_2)),field_char_0_Rats(X_a))))))))) # label(fact_3705_nonzero__Rats__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1756 (all Xa all Ya (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Xa),Ya))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Ya)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Ya)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)))) # label(fact_2482_even__difference__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1757 (all X_a (ordered_ring(X_a) -> (all A_3 all E_2 all C all B_2 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_3),E_2)),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),B_2),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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),minus_minus(X_a),B_2),A_3)),E_2)),D_1))))))) # label(fact_772_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1758 (all X_a (real_normed_algebra(X_a) -> (all Y_2 all B_2 all X_2 all A_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_2),A_3),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_2),B_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),times_times(X_a)),X_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_2)),sequentially))))))) # label(fact_4484_LIMSEQ__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1759 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_4)) -> (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_4)))))))) # label(fact_216_power__increasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1760 (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_262_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1761 (all X_c all X_a all X_b all C 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),P_4),Z)) -> -(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) = 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,X_1),Y_1),Z)))))) # label(fact_4084_splitE_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1762 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (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),hAPP(X_a,filter(X_a),at(X_a),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),L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4616_LIM__norm) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1763 (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_3456_zgcd__zmult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1764 (all A_3 all B_2 all Ma (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_2),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma))))))) # label(fact_3498_Bnor__mem__if) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1765 (all X_a (real_normed_algebra(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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_2)),Ya))))))) # label(fact_4029_mult__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1766 (all Z all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Z),X_2)) -> ((all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Z)))) -> Z = hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_2)))) # label(fact_3731_Sup__eq__maximum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1767 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2270_cos__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1768 (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_2677_real__root__commute) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1769 (all Na all Xa 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),Xa))) & hAPP(real,real,exp(real),Xa) = 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),Xa))),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)),Na))),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),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))))) # label(fact_4297_Maclaurin__exp__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1770 (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_2176_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1771 (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_976_abs__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1772 (all X_a (dense_linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1))))))) # label(fact_4555_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1773 (all X exists N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_1)))) # label(fact_2724_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1774 (all Ma all K all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na)) | zero_zero(nat) = K <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))))) # label(fact_843_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1775 (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_2492_minus__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1776 (all X_a (real_normed_vector(X_a) -> (all Xa all A_3 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)),Xa)),A_3))))) # label(fact_4936_scaleR__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1777 (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_1533_mod__less__divisor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1778 (all X_a all Xa ti(X_a,Xa) = 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)),Xa))) # label(fact_4811_some__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1779 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_1313_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1780 (all K_3 all K all F ((all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_1)),K_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),K),hAPP(nat,real,F,N_1))))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),F)))) # label(fact_4339_BseqI2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1781 (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_3478_zgcd__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1782 (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_3100_divmod__int__correct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1783 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A_1))) # label(fact_1130_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1784 (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_905_zcong__not) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1785 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_1748_exp__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1786 (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_3626_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1787 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> (all D_1 all Sb exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),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_1),Sb))) <-> -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_1),Sb)))))))) # label(fact_1203_minf_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1788 (all X_a all X_b (real_normed_field(X_b) -> (all Ya all G all A_3 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),A_3),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)),Ya)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_3),Ya)),A_2)))))) # label(fact_4498_divide_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1789 (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_3343_ceiling__eq2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1790 (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),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),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M)) # label(fact_1310_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1791 (all X_a (field_inverse_zero(X_a) -> (all X all Z_1 all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))) # label(fact_1879_add__frac__num) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1792 (all X_a (real_normed_field(X_a) -> (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Xa)),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),Xa)),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)),Xa)))))))) # label(fact_4125_geometric__sums) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1793 (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_3274_gcd__exp__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1794 (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_1173_add__self__div__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1795 (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_111_one__less__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1796 (all R_3 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_3),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(int),R_3),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_3)))))) # label(fact_577_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1797 (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_1719_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1798 (all Xa 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)))),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),Xa)),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,Xa)))) # label(fact_4103_sin__paired) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1799 (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_1813_half) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1800 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),Xa),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),Xa))))) # label(fact_2653_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1801 (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_2792_of__real__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1802 (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,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_1906_minus__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1803 (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]. 7.53/7.52 1804 (all Na all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,Na)) -> (exists K_1 (hBOOL(hAPP(nat,bool,P_1,K_1)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),Na))))))) # label(fact_659_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1805 (all R_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_3),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_3))))) # label(fact_3426_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1806 (all L all U hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U))) # label(fact_4564_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1807 (all X_a (ord(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X))))) # label(fact_4861_min__leastL) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1808 (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_988_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1809 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1) -> ti(X_a,C_1) = ti(X_a,B))))) # label(fact_291_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1810 (all X_a all Xs all Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys) -> Xs != Ys)) # label(fact_3581_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1811 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K_3 all F all L_2 all Xa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))) -> (ti(X_b,L_2) = ti(X_b,K_3) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),K_3),hAPP(X_a,filter(X_a),at(X_a),Xa)))))))) # label(fact_4596_LIM__cong__limit) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1812 (all X_a all G all B_2 all F all A_3 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_3),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_2),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_3),B_2)),Net))))) # label(fact_4530_tendsto__Complex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1813 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all Xa all G 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),zero_zero(real)),hAPP(X_a,filter(X_a),at(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),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)),Xa)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4771_scaleR__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1814 (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]. 7.53/7.52 1815 (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_4187_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1816 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> (Ma = Na <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,Ma)))))) # label(fact_1387_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1817 (all X hAPP(real,real,sqrt,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,X))) # label(fact_2132_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1818 (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_4511_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1819 (all T_1 ord(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1820 (all G all Xa all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),Xa),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)),Xa),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,Xa)))),Ma))))) # label(fact_3900_DERIV__fun__cos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1821 (all K all Ma all Na (Ma = Na <-> 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),Na))) # label(fact_128_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1822 (all R_3 all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),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_3)),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3199_rcis__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1823 (all X_a (semiring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1824 (all Xa all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Xa),Ma) -> 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),Xa)),Ma))))) # label(fact_3643_noX__is__RRset) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1825 (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_2994_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1826 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> (hAPP(int,nat,nat_1,Xa) = hAPP(int,nat,nat_1,Ya) <-> ti(int,Xa) = ti(int,Ya))))) # label(fact_1001_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1827 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),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)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D),E_3)))))))) # label(fact_3865_DERIV__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1828 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_1528_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1829 (all 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)) = power_1(X_a)) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1830 (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_1329_less__SucI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1831 (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]. 7.53/7.52 1832 (all X_a all C all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))))) # label(fact_2234_ComplI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1833 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all C 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),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(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),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)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4772_scaleR_OLIM__left__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1834 (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_2479_Parity_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1835 (all Z_1 ((all N_1 ti(int,Z_1) != hAPP(nat,int,semiring_1_of_nat(int),N_1)) -> -(all N_1 ti(int,Z_1) != hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))))) # label(fact_3553_int__cases) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1836 (all Xa all Ya (-hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Ya)) | hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) & hBOOL(hAPP(int,bool,even_odd_even(int),Ya)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),Ya))))) # label(fact_1601_even__difference) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1837 (all A_3 all B_2 all C (zero_zero(real) != C -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A_3) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B_2) <-> A_3 = B_2))) # label(fact_609_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1838 (all Y all X ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)))) # label(fact_1506_tsub__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1839 (all N all K_4 all M (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M) = one_one(int) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),M) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),M)))) # label(fact_3457_zgcd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1840 (all X_a (real_normed_field(X_a) -> (all Y_2 all B_2 all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_2),B_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(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_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2)))))))) # label(fact_4115_sums__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1841 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,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_2598_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1842 (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]. 7.53/7.52 1843 (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_409_le__add2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1844 (all X_a (real_normed_vector(X_a) -> (all X_2 all K_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_3)) -> ((all N_1 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_2,N_1))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2))))))) # label(fact_3523_BseqI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1845 (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_196_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1846 (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),powr,X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,ln,X))))) # label(fact_3430_ln__powr) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1847 (all X_a all X_b all X_c all Z all C 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),P_4))) -> -(all X_1 all Y_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),X_1),Y_1) = 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,X_1),Y_1))))))) # label(fact_4087_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1848 (all Z all Wa (ti(int,Wa) != ti(int,Z) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),Wa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),Wa)))) # label(fact_223_zless__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1849 (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_3061_Diff__infinite__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1850 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all X_2 all L_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),X_2),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> (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_3),sequentially)) & (all N_1 hAPP(nat,X_a,S_2,N_1) != ti(X_a,A_3)) -> 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_2),S_2)),L_2),sequentially)))))))) # label(fact_4680_LIMSEQ__SEQ__conv1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1851 (all X_a (real_normed_vector(X_a) -> (all X_2 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_2),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_2)))))) # label(fact_3863_Bseq__offset) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1852 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)))))) # label(fact_3518_Cauchy__Bseq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1853 (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]. 7.53/7.52 1854 (all X_a all X_b (zero(X_a) & metric_space(X_a) & real_n2089651433ebra_1(X_b) -> (all A_3 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_3))))))) # label(fact_4592_LIM__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.52 1855 (all D_3 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),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_3),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B))))) # label(fact_2895_coprime__divprod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1856 (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_1 (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_1))),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_1)),Y)),X))))))) # label(fact_2462_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1857 (all Xa 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)),Xa),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,Xa)),hAPP(real,real,sin,Xa))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Xa)),hAPP(real,real,sin,Xa)))))) # label(fact_3861_DERIV__sin__sin__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1858 (all A_3 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),re),A_3))) # label(fact_4934_Re_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1859 (all X_b all X_c all X_a (semiring_0(X_a) -> (all F all A_2 all G all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_2)),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_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(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_1)),A_2)))) # label(fact_4240_setsum__product) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1860 (all L (hAPP(int,int,bit1,L) = min <-> min = ti(int,L))) # label(fact_666_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1861 (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]. 7.53/7.53 1862 (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) = 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))))) # label(fact_1970_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1863 (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_3953_arg__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1864 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3575_div__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1865 (all X_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),X_1) = hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,X_1))) # label(fact_4148_cos__fdiffs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1866 (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_515_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1867 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)))) # label(fact_2896_floor__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1868 (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_1550_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1869 (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_2935_number__of__pred) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1870 (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_714_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1871 (all Xa hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sin),Xa))) # label(fact_4927_isCont__sin) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1872 (all X_a all X_c all X_b all F all Xa all Ya 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),Xa),Ya)) = 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),Xa),hAPP(X_c,X_b,F,Ya))) # label(fact_4094_apsnd__conv) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1873 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),zero_zero(X_a))))))) # label(fact_3323_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1874 (all R_3 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_3) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3))) # label(fact_4430_quotient__of__coprime) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1875 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1316_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1876 (all U all Ma all Na 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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U)),Na) = 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)),Na) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U)),Ma)))) # label(fact_864_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1877 (all X_a (real_normed_vector(X_a) -> (all X_2 all A_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),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_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3)),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_2),A_3),sequentially)))))) # label(fact_4470_LIMSEQ__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1878 (all X all Y (X = Y -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_956_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1879 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all A_3 all B_2 all Wa ((zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),Wa) -> ti(X_a,A_3) = zero_zero(X_a)) & (hAPP(int,X_a,number_number_of(X_a),Wa) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa)) = ti(X_a,B_2)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),hAPP(int,X_a,number_number_of(X_a),Wa)) = ti(X_a,A_3))))) # label(fact_1776_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1880 (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_259_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1881 (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),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_1973_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1882 (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_970_abs__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1883 (all X_a (real_algebra_1(X_a) -> (all Z_1 hAPP(real,X_a,of_real(X_a),hAPP(int,real,ring_1_of_int(real),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))) # label(fact_3598_of__real__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1884 (all X_a (number_ring(X_a) -> (all V all 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)) = 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)))))) # label(fact_2082_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1885 (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> ((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)),hAPP(int,int,F,X_1))))) -> 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_2)))))) # label(fact_3964_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1886 (all A_2 all B_1 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_2),B_1)),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_2)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),B_1)),Ma)))) # label(fact_4899_bijzcong__zcong__prod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1887 (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_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),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> ((all X_1 (ti(X_a,A_3) != ti(X_a,X_1) -> 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_1)),Ma)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_1)),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_3)))))))) # label(fact_4681_metric__LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 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),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1731_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1889 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_2 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),F),A_2) = 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_2))))) # label(fact_3971_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1890 (all X_a (real_algebra_1(X_a) & real_normed_vector(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_2807_of__real_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1891 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A_2),B_1)) <-> 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_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_1))))))) # label(fact_3691_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1892 (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_312_power2__ge__self) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1893 (all X_a all X_b all A_3 all B_2 all A_8 all B_7 all Ra all Sb (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_2),B_7)),Sb)) & ti(X_a,A_8) = ti(X_a,A_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),A_3),A_8)),Ra)) <-> 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_3),B_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),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),Ra),Sb))))) # label(fact_3512_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1894 (all A_1 all B all M hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),M)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),M))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) # label(fact_1459_zcong__zmod__aux) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1895 (all A_3 all B_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)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_2))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),zero_zero(int))) -> (-(zero_zero(int) = ti(int,B_2) | zero_zero(int) = ti(int,A_3)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_3),B_2) = 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_3),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_3),B_2))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B_2),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_3),B_2)))) & (ti(int,B_2) = zero_zero(int) | ti(int,A_3) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_3),B_2) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),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_3)),hAPP(int,int,uminus_uminus(int),B_2)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_3),B_2)))) # label(fact_3946_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1896 (all X_a (division_ring(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),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_2631_inverse__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1897 (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_1194_Int2_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1898 (all Z_3 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_3)) -> (ti(int,Z) = ti(int,Z_3) <-> hAPP(int,nat,nat_1,Z) = hAPP(int,nat,nat_1,Z_3))))) # label(fact_1000_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1899 (all Va (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),Va) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls)))) # label(fact_274_eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1900 (all X_a (comm_semiring_1(X_a) -> (all C_1 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_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C_1))))))) # label(fact_712_dvd__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1901 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),Xa)),zero_zero(X_a))))))) # label(fact_49_less__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1902 (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),zero_zero(int)),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(int),K),I)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) | zero_zero(int) = ti(int,K))) # label(fact_1113_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1903 (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_1839_divide__neg__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1904 (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)),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))))) # label(fact_4806_split__paired__Eps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1905 (all X_b all X_a (comm_monoid_mult(X_a) & semiring_1(X_a) -> (all F all A_2 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_2) = 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_2))))) # label(fact_3955_of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1906 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all N one_one(X_a) = 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)),N))))) # label(fact_1029_abs__power__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1907 (all C_1 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> (C_1 = B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C_1),A_1))))) # label(fact_938_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1908 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int)) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_2915_floor__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1909 (all Z_1 ti(int,Z_1) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z_1))) # label(fact_2057_zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1910 (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_1523_inc__induct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1911 (all A_3 all A_2 all Ma ((hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> 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_3)),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_2),Ma),A_3)) & (-(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),Ma)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma))) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),Ma),A_3) = zero_zero(int)))) # label(fact_4180_RRset2norRR__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1912 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya_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),Y)),Ya_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),Ya_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya_1))))) # label(fact_1751_divide_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1913 (all C_1 all A_1 all B all Q_3 all R_3 (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_3))) -> (zero_zero(int) != ti(int,B) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C_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),Q_3),C_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_mod(int),Q_3),C_1))),R_3)))))))) # label(fact_1581_zmult2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1914 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_91_add__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1915 (all X_a (number_ring(X_a) -> (all V all C_1 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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),hAPP(int,X_a,number_number_of(X_a),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_1)))) # label(fact_2093_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1916 (all B all Q_5 all R_4 all Q_3 all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_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),B),Q_3)),R_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(int),R_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))) # label(fact_583_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1917 (all X_a (comm_semiring_1(X_a) -> (all C_1 all D_3 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_1),D_3)) -> 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))) # label(fact_725_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1918 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),A_3)) -> 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_3))))))) # label(fact_3948_monoseq__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1919 (all X_a (number_ring(X_a) -> (all Ya (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),Ya))))) <-> hAPP(int,X_a,number_number_of(X_a),Ya) = zero_zero(X_a))))) # label(fact_2182_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1920 (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_4734_scaleR__minus__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1921 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),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(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)),B_2))) & (-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),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C))))))))) # label(fact_1867_less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1922 (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_83_zadd__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1923 (all Ma all K all Na (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K),Na) -> (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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma))))) # label(fact_3314_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1924 (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(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_4521_summable__sumr__LIMSEQ__suminf) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1925 (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_2087_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1926 (all M all D_3 all R_3 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),D_3) = R_3 -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),R_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_4),D_3)) = M))) # label(fact_1574_mod__eqD) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1927 (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_3578_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1928 (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_3775_of__nat__rat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1929 (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)),M)))) # label(fact_793_one__not__neg__one__mod__m) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1930 (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_55_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1931 (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]. 7.53/7.53 1932 (all X_b all X_a (real_normed_algebra(X_a) -> (all G all A_2 all Ya 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_2)),Ya) = 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)),Ya)),A_2)))) # label(fact_4212_mult__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1933 (all X_a all X_b all B_1 all F all A_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_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_2))) <-> (exists AA (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_2)) & hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA) = ti(fun(X_a,bool),B_1))))) # label(fact_3663_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1934 (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_3435_real__of__int__div3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1935 (all Xa all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_1 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))),Xa))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),Xa))))) # label(fact_4317_suminf__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1936 (all G all F all Xa 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),Xa))),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),Xa))),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,Xa))))))) # label(fact_4950_isCont__inv__fun) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1937 (all X_a all X_b all B_1 all F all A_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_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_2))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1))))) # label(fact_3678_finite__surjI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1938 (all X_a (linordered_field(X_a) -> (all B_2 all A_3 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)),A_3)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)))))))) # label(fact_1824_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1939 (all X_a (semiring_div(X_a) -> (all A_1 all C_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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_1115_div__mult__self2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1940 (all X_a all C 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),C),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_2),B_1))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),B_1))))) # label(fact_2232_DiffE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1941 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,abs_abs(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4392_gcd__abs2__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1942 (all Xa all A_3 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_3),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_3)) -> (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),Xa),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_3),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)),Xa)),A_3),P_4)))))))) # label(fact_3960_SetS__setprod__prop) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1943 (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_3535_zero__le__dist) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1944 (all A_3 all B_2 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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),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))))) -> ((all X_1 exists D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all A_4 all 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_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_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_4),B_4))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_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_3),B_2))))))) # label(fact_3235_lemma__BOLZANO) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1945 (all X_a (linord1117847801e_zero(X_a) -> (all B_2 all C all A_3 ((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),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),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(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)),A_3))) & (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_3),C)),B_2)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)),A_3)))))) # label(fact_1868_divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1946 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_3),B_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),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_3),B_2))))) # label(fact_4066_splitI) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1947 (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_2963_complex__mod__cnj) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1948 (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_404_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1949 (all X_a (real_normed_vector(X_a) -> (all A_1 all 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)) = 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))))) # label(fact_4749_norm__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1950 (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]. 7.53/7.53 1951 (all P_1 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),P_1),semiring_1_of_nat(int))))) # label(fact_3907_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1952 (all X_a (ab_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_1960_ab__left__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1953 (all A_3 all A_2 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_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,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_3)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_4183_aux__some) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1954 (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_1322_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1955 (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_1074_div__by__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1956 (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_953_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1957 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)))) # label(fact_1084_abs__div) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1958 (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))) -> (ti(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)),A_1))))))) # label(fact_2591_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1959 (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_3102_prime__divprod__pow) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1960 (all A_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),A_3),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_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(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),A_3)))))) # label(fact_4524_summable__Leibniz_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1961 (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_536_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1962 (all X_a all X_b all Xa all Ya 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),Xa),Ya) = 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),Xa)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Ya))))) # label(fact_4170_The__split__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1963 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),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_2))) -> (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_2)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_3)) & hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3) = ti(fun(X_a,bool),B_1)))))) # label(fact_3669_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1964 (all M all K_4 all N (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))))) # label(fact_3486_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1965 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> hAPP(X_a,X_b,F,X_1) = 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),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S))))))) # label(fact_3988_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1966 (all X_a (field_inverse_zero(X_a) -> (all A_3 all B_2 all C (ti(X_a,A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C) <-> (zero_zero(X_a) = ti(X_a,C) -> zero_zero(X_a) = ti(X_a,A_3)) & (ti(X_a,C) != zero_zero(X_a) -> ti(X_a,B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)))))) # label(fact_1846_eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1967 (all Na all Q_1 all P_1 ((all X_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_1,X_1)),hAPP(nat,nat,P_1,X_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),Na))),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),Na))) = 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),Na)))) # label(fact_4353_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1968 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) = X)))) # label(fact_3431_powr__log__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1969 (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_989_abs__of__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1970 (all L all K ((zero_zero(int) != ti(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(bool,bool,hAPP(bool,fun(bool,bool),fdisj,hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),L),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)) & (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))) & (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_4090_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1971 (all X_a (real_normed_vector(X_a) -> (all X_2 all L_2 ((all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_1)) -> 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_2,N_1)),L_2))),R_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_2),L_2),sequentially)))))) # label(fact_4544_LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1972 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) -> -(all K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) -> -(all N_1 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_2,N_1))),K_2))))))))) # label(fact_3526_BseqE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1973 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))))) # label(fact_3625_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1974 (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_3796_rat__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1975 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Va (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),hAPP(int,X_a,number_number_of(X_a),Va))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),Xa)),hAPP(int,int,number_number_of(int),Va))))))) # label(fact_2911_floor__less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1976 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 all X_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))))) # label(fact_2830_of__real_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1977 (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_1490_expand__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.53 1978 (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]. 7.53/7.54 1979 (all K all Xa 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),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),K)))))) # label(fact_3848_DERIV__cos__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1980 (all Na all Xa all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 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),Diff,M_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_1)))) & zero_zero(real) != Xa & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (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),Xa))) & hAPP(real,real,F,Xa) = 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) & 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_4303_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1981 (all X_a (real_normed_vector(X_a) -> (all B_2 all F all A_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),F),A_3),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_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)),sequentially)))))) # label(fact_4503_LIMSEQ__diff__const) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1982 (all Q_3 all B all R_3 all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),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_1))),R_3))))))) # label(fact_1474_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1983 (all X_a (banach(X_a) -> (all F all N_3 all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),one_one(real))) -> ((all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_1)) -> 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_1)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_1))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4081_ratio__test) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1984 (all A_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),A_3),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,A_3,zero_zero(nat))),zero_zero(real))) -> (all N_1 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)))),A_3))),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)))),A_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),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))))),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)))),A_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),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))))))))))) # label(fact_4548_summable__Leibniz_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1985 (all A_2 all Xa (hBOOL(hAPP(int,bool,nat_is_nat,Xa)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(int,nat,nat_1,Xa)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_2)))))) # label(fact_4884_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1986 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all 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_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_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),plus_plus(X_a),A_1),B)),E_1)),C_1)))) # label(fact_381_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1987 (all D_3 all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),A_1))) # label(fact_3296_coprime__lmult__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1988 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3792_real__divide__code) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1989 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) | Xa = Ya <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))) # label(fact_352_less__eq__real__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1990 (all X all A_1 zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3349_powr__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1991 (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_3378_powr__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1992 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F 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,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_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_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_2)))))) # label(fact_4192_setsum__abs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1993 (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_134_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1994 (all A_3 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),im),A_3))) # label(fact_4933_Im_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1995 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (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),hAPP(X_a,filter(X_a),at(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),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_3))))))) # label(fact_4608_LIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1996 (all X_a (divisi14063676e_zero(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,inverse_inverse(X_a),A_1)),N) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2563_power__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1997 (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_1124_div__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1998 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all Xa 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),Xa))))))) # label(fact_4773_summable__exp__generic) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 1999 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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_2))))) # label(fact_3979_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2000 (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_3089_prime__g__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2001 (all X_a (linordered_idom(X_a) -> (all Xa all Na (-hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa),Na)))))))) # label(fact_2490_zero__le__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2002 (all P_4 all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4))))) # label(fact_1204_wset__mem__mem) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2003 (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_1596_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2004 (all N hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)) # label(fact_3596_of__int__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2005 (all Y all U_1 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_1))) -> 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_1))))))) # label(fact_2624_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2006 (all X_a (order(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C),D_1))) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) | (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),D_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)))))) # label(fact_4552_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2007 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3904_card__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2008 (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_1511_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2009 (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_2054_negative__zle) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2010 (all A_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),A_3),zero_zero(real)),sequentially)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_3,N_1)))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,hAPP(nat,nat,suc,N_1))),hAPP(nat,real,A_3,N_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(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)))),A_3))))))) # label(fact_4556_summable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2011 (exists K_2 ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) # label(fact_3045_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2012 (all X_a (ordered_ab_group_add(X_a) -> (all Xa all Ya 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),Xa),Ya)) = 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),Ya)),hAPP(X_a,X_a,uminus_uminus(X_a),Xa))))) # label(fact_3696_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2013 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N) = N) # label(fact_4990_max__0L) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2014 (all N (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),N) = one_one(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),N) = hAPP(int,int,number_number_of(int),min))) # label(fact_918_neg__one__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2015 (all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))))) # label(fact_56_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2016 (all X_a (metric_space(X_a) -> (all Ra all X_2 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_2),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ra)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_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),hAPP(nat,X_a,X_2,N_1)),L_2)),Ra))))))))) # label(fact_4546_metric__LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2017 (all X_a all F1 all F2 hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),zero_zero(code_code_numeral)) = ti(X_a,F1)) # label(fact_3574_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2018 (all Ma all Na (Ma = zero_zero(nat) & zero_zero(nat) != Na <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),Na) = zero_zero(nat))) # label(fact_337_nat__power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2019 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_1271_zero__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2020 (all F all Na zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),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))),Na))) # label(fact_4214_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2021 (all X_b all X_a (comm_monoid_mult(X_a) -> (all A_2 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_2) = one_one(X_a)))) # label(fact_3974_setprod__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2022 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),d22set,A_3))))) # label(fact_1221_d22set__le__swap) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2023 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),Xa))))) # label(fact_1786_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2024 (all Xa all Ya (hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) & hBOOL(hAPP(int,bool,even_odd_even(int),Ya)) | -hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) & -hBOOL(hAPP(int,bool,even_odd_even(int),Ya)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),Ya))))) # label(fact_1598_even__sum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2025 (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_626_mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2026 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Ya all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ya),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_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),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),Ya)),A_2))))) # label(fact_3986_setprod__constant) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2027 (all X_a all X_b (dvd(X_b) & comm_monoid_mult(X_b) -> (all F all G all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))) -> 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_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_2))))))) # label(fact_4452_setprod__dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2028 (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_1763_exp__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2029 (all L all U 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) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U)) # label(fact_4288_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2030 (all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = zero_zero(nat)))) # label(fact_2923_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2031 (all 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))))) = X) # label(fact_1806_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2032 (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_2507_fact__diff__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2033 (all X_a (ring_char_0(X_a) -> (all Z (ti(int,Z) = zero_zero(int) <-> zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3590_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2034 (all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) = one_one(int) -> (exists X_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),X_1)),one_one(int)),N)))))) # label(fact_3504_zcong__lineq__ex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2035 (all X_1 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) -> hAPP(nat,real,sin_coeff,X_1) = zero_zero(real)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) -> 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_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),X_1))) = hAPP(nat,real,sin_coeff,X_1)))) # label(fact_2533_sin__coeff__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2036 (all Na all Ma (one_one(nat) = Na & one_one(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),Ma) = one_one(nat))) # label(fact_618_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2037 (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),times_times(int),K_4),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)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)))) # label(fact_3480_zgcd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2038 (all X_a (group_add(X_a) -> (all A_1 ti(X_a,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))))) # label(fact_736_diff__0__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2039 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2042_log__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2040 (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_3091_prime__factor__lt) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2041 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1)) = hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z_1))) # label(fact_3034_Re__sgn) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2042 (all X_a (real_normed_vector(X_a) -> (all Y_2 all B_2 all X_2 all A_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_2),A_3),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_2),B_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),plus_plus(X_a)),X_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2)),sequentially))))))) # label(fact_4505_LIMSEQ__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2043 (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_2)) -> 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_2)),Y_2)))))) # label(fact_4878_vanishes__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2044 (all Ma all Na ((exists K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1) = Na) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_411_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2045 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_86_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2046 (all X_a all X_b the(product_prod(X_a,X_b)) = ti(fun(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b)),the(product_prod(X_a,X_b)))) # label(tsy_c_HOL_OThe_2_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2047 (all Va all V_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Va),hAPP(int,int,uminus_uminus(int),V_1))))),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),Va),hAPP(int,int,uminus_uminus(int),V_1))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(int,nat,number_number_of(nat),V_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls)) -> hAPP(int,nat,number_number_of(nat),Va) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_3938_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2048 (all Va all Na 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,Va)))),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))),Na))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(nat,nat,suc,Na))) # label(fact_4970_max__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2049 (all K all Xa 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),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),K))))) # label(fact_3867_DERIV__sin__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2050 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_356_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2051 (all X_a (real_normed_vector(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4778_scaleR_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2052 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),zero_zero(nat))) <-> one_one(nat) = D_1)) # label(fact_2892_coprime__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2053 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4391_gcd__abs__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2054 (all X_b all X_a (semiring_0(X_a) -> (all Ra all F all A_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ra),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_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_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),Ra)),F)),A_2)))) # label(fact_4242_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2055 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) <-> (exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists X_1 all N_1 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_2,N_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)))),K_1))))))))) # label(fact_3515_Bseq__iff2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2056 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_2 all F all A_3 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),A_3),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),B_2),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),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_3),B_2)),A_2))))))) # label(fact_4501_tendsto__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2057 (all Xa all Ya ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Ya)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),zero_zero(real)))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Ya),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa))) <-> 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),Xa),Ya))))) # label(fact_1770_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2058 (all X_a (linord1117847801e_zero(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1)))))))) # label(fact_1835_divide__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2059 (all L all U 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),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))) # label(fact_4630_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2060 (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]. 7.53/7.54 2061 (all U_1 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),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_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U_1)),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_1)),N)))) # label(fact_865_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2062 (all B all A_1 all C_1 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_1)) = 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_1))) # label(fact_4406_gcd__int_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2063 (all X_a (metric_space(X_a) -> (all X_2 hAPP(fun(nat,X_a),X_a,lim(X_a),X_2) = 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_2)),sequentially))))) # label(fact_4454_lim__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2064 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int))) # label(fact_1734_even__div__2__prop1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2065 (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,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,tan,X))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))))) # label(fact_2365_tan__double) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2066 (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_2398_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2067 (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_1554_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2068 (all Na all Ma (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,Ma))) <-> Na = Ma))) # label(fact_1331_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2069 (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_61_int__less__0__conv) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2070 (all D_1 all A_3 all B_2 (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_3),B_2)) = one_one(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),B_2) = one_one(nat) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),A_3) = one_one(nat))) # label(fact_3292_coprime__mul__eq__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2071 (all X_a all X_b (ord(X_b) -> (all Xa all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa))))))) # label(fact_500_le__funE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2072 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_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_2)),A_3)) <-> 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_3)),B_2)))))) # label(fact_1931_minus__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2073 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_765_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2074 (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_2160_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2075 (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_3533_dist__triangle__lt) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2076 (all K_4 hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4)) # label(fact_123_number__of__is__id) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2077 (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_247_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2078 (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_2338_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2079 (all X_b all X_a (order(X_b) & order(X_a) -> (all C all F all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_2)),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C),B_2)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_3)))))))) # label(fact_2841_xt4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2080 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all G all A_2 all B_1 (B_1 = A_2 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> ((all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(int,X_a,G,X_1) = hAPP(int,X_a,F,X_1))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),G),B_1) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_2))))))) # label(fact_3989_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2081 (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]. 7.53/7.54 2082 (all X_a (linord1117847801e_zero(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),one_one(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)) <-> 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),Xa))))))) # label(fact_2615_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2083 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (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_1)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1))))) -> (ti(int,X_1) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),D))))))) # label(fact_4660_bset_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2084 (all M all N -(all Q_4 all R_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),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_4),R_1))))) # label(fact_3129_divmod__nat__rel__ex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2085 (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_1057_power2__eq1__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2086 (all X_a (number_ring(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))),Z_1)))) # label(fact_1926_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2087 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Ya),hAPP(real,real,uminus_uminus(real),Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),Ya)),zero_zero(real))))) # label(fact_2021_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2088 (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_1265_StandardRes__prop4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2089 (all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),W))) # label(fact_599_real__le__refl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2090 (all A_1 all Q_3 all R_3 (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_3))) -> (zero_zero(int) != ti(int,A_1) -> one_one(int) = ti(int,Q_3)))) # label(fact_1617_self__quotient) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2091 (all A_3 all Na all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_3),hAPP(nat,nat,suc,Na))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_2),hAPP(nat,nat,suc,Na)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_3),B_2)))) # label(fact_2900_coprime__exp2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2092 (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_2446_tan__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2093 (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_3818_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2094 (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_863_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2095 (all X_a all Xa all A_2 all B_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)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),B_1))))) # label(fact_2206_in__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2096 (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_4399_gcd__red__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2097 (all X_a all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),B_1),A_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_2),B_1)) = 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_2)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_1))))) # label(fact_4287_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2098 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),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))),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D),hAPP(X_a,X_a,uminus_uminus(X_a),E_3))))))))) # label(fact_3859_DERIV__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2099 (all X_a (ring_11004092258visors(X_a) -> (all N all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> zero_zero(X_a) != hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_168_field__power__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2100 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))))))) # label(fact_3635_floor__correct) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2101 (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_711_dvd__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2102 (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_3707_Rats__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2103 (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_2336_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2104 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(int,nat,nat_1,Xa))))) # label(fact_1691_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2105 (all Xa hAPP(real,real,cos,Xa) = 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),Xa)))) # label(fact_3998_cos__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2106 (all X_a (real_n2089651433ebra_1(X_a) -> (all N hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_1938_norm__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2107 (all Xa all Ya (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)))))),Ya)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ya),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)))))),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),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,Ya)),hAPP(real,real,tan,Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ya),Xa)))))))) # label(fact_2447_tan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2108 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))))))) # label(fact_213_add__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2109 (all P_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,uminus_uminus(rat),P_4)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4055_rat__uminus__code) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2110 (all X_a (linorder(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))))) # label(fact_4859_dual__max) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2111 (all Ma all K all Na (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),Na) -> (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),Na)))))) # label(fact_4377_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2112 (all Xa hAPP(real,real,exp(real),Xa) = 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)),Xa)),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),Xa)),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_4002_exp__first__two__terms) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2113 (all K_4 pls != hAPP(int,int,bit1,K_4)) # label(fact_66_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2114 (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_4447_finite__image__set) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2115 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_823_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2116 (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_415_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2117 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = N))) # label(fact_1326_less__SucE) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2118 (exists X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),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,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_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),Y_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> ti(int,X_1) = ti(int,Y_1))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))))) # label(fact_710__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]. 7.53/7.54 2119 (all X_a (real_normed_algebra(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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),Xa)),X_2))))))) # label(fact_4028_mult__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2120 (all Ya all Xa all A_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_3),Xa)),hAPP(real,real,hAPP(real,fun(real,real),log,A_3),Ya)))))))) # label(fact_2031_log__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2121 (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(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)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))))) # label(fact_720_of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2122 (all E_1 all B all D_3 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),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_3),E_1)))))) # label(fact_2877_coprime__divisors) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2123 (all X_b all X_a (ring_1(X_a) -> (all F all 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),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_2) = 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_2))))) # label(fact_4217_of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2124 (all X hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X)) # label(fact_2373_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2125 (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_387_mult__1__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2126 (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_3043_cmod__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.54 2127 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_2051_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2128 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> 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),Ra)),X_2))))))) # label(fact_4745_scaleR__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2129 (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_2067_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2130 (all X_c all X_b all X_a all P_4 all F all G all Q_2 ((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) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_1),Y_1) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_1),Y_1))) -> (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_4796_split__cong) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2131 (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_1016_nat__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2132 (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_1077_zdiv__self) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2133 (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_253_one__le__power) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2134 (all X_a (ring(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_755_mult__diff__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2135 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))))) # label(fact_278_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2136 (all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,tan,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))) # label(fact_2449_tan__inverse) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2137 (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_2927_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2138 (all X_b all X_a (topological_space(X_a) & 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)),hAPP(X_a,filter(X_a),at(X_a),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)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4636_LIM__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2139 (all X_a (comm_ring_1(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Xa),Ya)) <-> 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),Xa)),Ya)))))) # label(fact_1919_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2140 (all X_a all X_b product_fst(X_a,X_b) = ti(fun(product_prod(X_a,X_b),X_a),product_fst(X_a,X_b))) # label(tsy_c_Product__Type_Ofst_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2141 (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_2422_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2142 (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_459_less__1__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2143 (all C all D_1 all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),B_2)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),A_3)),Ma))))) # label(fact_896_zcong__zmult__prop2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2144 (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(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),K_4)))) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)) & (-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))))))) # label(fact_3584_of__int__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2145 (all Ma all Na hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),Na) = 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),Na)))) # label(fact_4567_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2146 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1)) # label(fact_646_nat__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2147 (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 (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))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Z_2)))))) # label(fact_2456_tan__total__pi4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2148 (all Na 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),Na)) -> 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_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)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))))))))) # label(fact_4309_Maclaurin2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2149 (all Na all Ma (ti(int,Na) = ti(int,Ma) <-> hAPP(int,quickcheck_code_int,quickcheck_of_int,Na) = hAPP(int,quickcheck_code_int,quickcheck_of_int,Ma))) # label(fact_3563_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2150 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,Na))))) # label(fact_1391_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2151 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (one_one(nat) != B -> (exists X_1 exists Y_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_1)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_1))))) # label(fact_2922_coprime__bezout__strong) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2152 (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_991_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2153 (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_3400_powr__mono2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2154 (all X_a all A_3 all F all Va 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_3),F),hAPP(int,nat,number_number_of(nat),Va)) = 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,Va)))),A_3),hAPP(nat,X_a,F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) # label(fact_4152_nat__case__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2155 (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_1366_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2156 (all A_3 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),d22set,A_3)))) # label(fact_2730_d22set__fin) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2157 (all X_a (linord1117847801e_zero(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),Xa)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),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),Xa)),one_one(X_a))))))) # label(fact_2611_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2158 (all X_a (linorder(X_a) -> (all A_1 all B all C_1 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_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),A_1),B)),C_1)))) # label(fact_4837_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2159 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_1354_mod__mult__self2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2160 (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),minus_minus(real),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(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_4697_scaleR_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2161 (all X_a (real_normed_algebra(X_a) -> (all C 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))))))) # label(fact_4027_summable__mult2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2162 (all X_a (real_normed_vector(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_2)) -> 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_2)),Xa)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(nat,real),real,suminf(real),X_2)),Xa))))) # label(fact_4766_scaleR__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2163 (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_3134_div__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2164 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all 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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C_1)))) # label(fact_384_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2165 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_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),times_times(X_a),A_3),B_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3))) & (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_3),B_2)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_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_3)),hAPP(X_a,X_a,inverse_inverse(X_a),B_2))))))) # label(fact_2626_inverse__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2166 (all R_3 all A_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1)))) = hAPP(real,real,abs_abs(real),R_3)) # label(fact_2824_cmod__complex__polar) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2167 (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_598_real__le__linear) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2168 (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_4872_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2169 (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_1422_neg__mod__conj) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2170 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1))) # label(fact_4172_The__split) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2171 (all Xa (zero_zero(real) != hAPP(real,real,cos,Xa) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),tan),Xa)))) # label(fact_4906_isCont__tan) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2172 (all X_a (real_algebra(X_a) -> (all A_1 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),A_1),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4721_mult__scaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2173 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> 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)),Na))) = 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),Na)))))) # label(fact_4623_setsum__head__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2174 (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_2002_abs__of__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2175 (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_1 (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_1 (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_927_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2176 (all K_4 hAPP(int,int,bit1,hAPP(int,int,pred,hAPP(int,int,uminus_uminus(int),K_4))) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,K_4))) # label(fact_2931_minus__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2177 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2178 (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_2307_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2179 (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_1841_divide__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2180 (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_218_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2181 (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_885_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2182 (all Xa all Ya (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Xa),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),Ya),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1735_even__div__2__l) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2183 (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_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2184 (all V all W hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),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))) # label(fact_17_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2185 (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_3777_rat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2186 (all Ma all Na (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),Na))) <-> ti(int,Na) != zero_zero(int) | ti(int,Ma) != zero_zero(int))) # label(fact_4411_gcd__pos__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2187 (all Na all N_3 ((all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Na)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_3693_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2188 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),one_one(real)))))) # label(fact_2702_real__root__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2189 (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,natceiling,X))) # label(fact_1673_natceiling__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2190 (all Z all Z_3 ((hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(int,nat,nat_1,Z) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3))) & (-hBOOL(hAPP(int,bool,nat_neg,Z_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),Z_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,Z_3))))) # label(fact_3860_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2191 (all Y all X (X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,sqrt,X) = Y))) # label(fact_2169_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2192 (all K_4 hAPP(int,int,bit1,K_4) = hAPP(int,int,succ,hAPP(int,int,bit0,K_4))) # label(fact_286_succ__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2193 (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),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N))) # label(fact_3293_gcd__mult__cancel__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2194 (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_2707_real__root__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2195 (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_186_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2196 (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_2813_sgn__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2197 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_2 all C all Wa ((-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),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),hAPP(int,X_a,number_number_of(X_a),Wa)),C)),B_2))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Wa))))) & (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),B_2),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),Wa)),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),B_2),C)),hAPP(int,X_a,number_number_of(X_a),Wa))))))) # label(fact_1802_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2198 (all X_a (number_ring(X_a) -> (all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(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_316_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2199 (all T_2 all T_1 (finite_finite(T_2) & finite_finite(T_1) -> finite_finite(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2200 (all X_a (real_normed_field(X_a) -> (all F all Xa 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),Xa),D_1)) -> (hAPP(X_a,X_a,F,Xa) != 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)),Xa),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,Xa)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))))))))) # label(fact_3930_DERIV__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2201 (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_1676_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2202 (all X_a (linord1117847801e_zero(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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(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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C_1),B))))))))) # label(fact_1888_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2203 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),Xa)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),one_one(X_a))))))) # label(fact_2909_floor__less__one) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2204 (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_931_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2205 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all Wa all B_2 all C (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),Wa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),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(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),Wa)),C)),B_2))) & (-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),C),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),Wa)),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),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),Wa)),C))))))))) # label(fact_1793_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2206 (all U_1 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_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),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2039_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2207 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) -> (ti(X_a,Ya) = ti(X_a,Xa) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))))))) # label(fact_559_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2208 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) -> (exists Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),Y_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),hAPP(real,real,F,B_2)),hAPP(real,real,F,A_3)))))) # label(fact_3552_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2209 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))))))) # label(fact_3325_one__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2210 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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),Xa),one_one(int))),zEven)))) # label(fact_1727_odd__minus__one__even) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2211 (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_728_dvd__triv__right) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2212 (all X_a (semiri456707255roduct(X_a) -> (all C all D_1 all A_3 all B_2 (ti(X_a,D_1) != ti(X_a,C) & ti(X_a,A_3) != ti(X_a,B_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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_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_3),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_2),C)))))) # label(fact_383_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2213 (all N ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> 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)))) = hAPP(int,int,zfact,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)))) # label(fact_1137_zfact_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2214 (all K all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K))))) # label(fact_824_dvd__reduce) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2215 (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_4737_scaleR__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2216 (all X_a (number_ring(X_a) -> (all Xa (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),Xa),hAPP(int,int,uminus_uminus(int),pls))))) <-> hAPP(int,X_a,number_number_of(X_a),Xa) = zero_zero(X_a))))) # label(fact_2183_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2217 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_2 all A_3 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_2),A_3)) -> 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_2)),hAPP(real,X_a,of_real(X_a),A_3))))))) # label(fact_4111_of__real_Osums) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2218 (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_1255_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2219 (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_921_zcong__zprime__prod__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2220 (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_2223_arctan__ubound) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2221 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (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_1)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1) != ti(int,X_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_1)) -> 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_1),D))))))))) # label(fact_4657_bset_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2222 (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_1572_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2223 (all Q_3 all R_3 hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),Q_3),R_3) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),Q_3),hAPP(rat,rat,inverse_inverse(rat),R_3))) # label(fact_3725_divide__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2224 (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_1193_Int2_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2225 (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_978_power__abs) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2226 (all X_b all X_a all A_3 all B_2 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_3),B_2) <-> ti(X_b,B_7) = ti(X_b,B_2) & ti(X_a,A_3) = ti(X_a,A_8))) # label(fact_3154_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2227 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all Na 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),Na)) = 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,Na)))))) # label(fact_4569_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2228 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all C 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)),hAPP(X_a,filter(X_a),at(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),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)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4760_scaleR_OLIM__right__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2229 (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_1918_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2230 (all X_a all X_b all Sb all Ta (ti(product_prod(X_a,X_b),Sb) = ti(product_prod(X_a,X_b),Ta) <-> hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Sb) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Ta) & hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Sb) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Ta))) # label(fact_3161_prod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2231 (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_450_mult__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2232 (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_2308_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2233 (all Ma all Na all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),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),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),Na))))) # label(fact_862_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2234 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) <-> (exists N_2 all N_1 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_2,N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))))))))) # label(fact_3521_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2235 (all A_3 all B_2 all C (C != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_3),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_2),C) <-> B_2 = A_3))) # label(fact_610_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2236 (all X_a all X_b all X_c all X_d all Xa all P_1 ((all A_4 all B_4 all C_4 all D_2 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_2)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,Xa)))) # label(fact_3177_prod__induct4) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2237 (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,abs_abs(X_a),A_1))))) # label(fact_965_abs__idempotent) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2238 (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_2728_Suc__le__D) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2239 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(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),Ra)),X_2)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_2)))))) # label(fact_4744_scaleR__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2240 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1054_abs__power2__distrib) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2241 (all X_a all A_2 ((exists N_1 exists F_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_1))) = ti(fun(X_a,bool),A_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_4154_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2242 (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_313_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2243 (all Y all X exists R_1 exists A_4 (Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,sin,A_4)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,cos,A_4)) = X)) # label(fact_3517_polar__Ex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2244 (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_1080_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2245 (all X_a (dvd(X_a) & semiring_0(X_a) -> (all P_1 all L ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & 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_1),zero_zero(X_a)))))) <-> (exists X_1 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_1)))))))) # label(fact_771_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2246 (all X_a (real_normed_algebra(X_a) -> (all R_3 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),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),R_3),X)),Y)))) # label(fact_4723_mult__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2247 (all Xa all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),sRStar,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),Xa) = ti(int,Xa))) # label(fact_1530_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2248 (all X_a all X_b all P_1 ((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)))) <-> (all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))))) # label(fact_3153_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2249 (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_3147_prod__size__simp) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2250 (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_372_of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2251 (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_1537_mod__mult__self3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2252 (all X_a (ring_char_0(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),ring_1_Ints(X_a))) -> (zero_zero(X_a) = ti(X_a,A_3) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),A_3)))))) # label(fact_3835_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2253 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1)),hAPP(X_a,X_a,sgn_sgn(X_a),B))))) # label(fact_2264_sgn__times) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2254 (all X_a undefined(X_a) = ti(X_a,undefined(X_a))) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2255 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))))) # label(fact_2049_divide_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2256 (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))) -> (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))))) <-> (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_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(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_1))))))))) # label(fact_4448_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2257 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))) = N)) # label(fact_1465_Suc__pred_H) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2258 (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_977_abs__minus__commute) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2259 (all Xa all Ya (hBOOL(hAPP(int,bool,even_odd_even(int),Ya)) | hBOOL(hAPP(int,bool,even_odd_even(int),Xa)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Xa),Ya))))) # label(fact_1593_Parity_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2260 (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_3164_conjI__realizer) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2261 (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_2325_sin__periodic) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2262 (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_4982_max__ord__max) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2263 (all X_a (real_normed_vector(X_a) -> (all R_3 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_3)),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_3),X))))) # label(fact_4692_sgn__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2264 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all Na (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),Na),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),Na))),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),Na),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),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),Na),P_4))))))) # label(fact_4629_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2265 (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(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,hAPP(int,int,uminus_uminus(int),Z_1))),hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),Z_4))))) # label(fact_2097_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2266 (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_323_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2267 (all Na all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),Na) = one_one(int) <-> one_one(int) = ti(int,Ma) & ti(int,Na) = one_one(int)))) # label(fact_497_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2268 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1312_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2269 (all X_a all R_2 all F all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,Xa)),hAPP(X_a,nat,F,Ya))) -> (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),Xa),Ya)),R_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),Xa),Ya)),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_2)))))) # label(fact_3821_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2270 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Ya all G 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),G),L),hAPP(X_a,filter(X_a),at(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),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)),Ya)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L),Ya)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4590_mult__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2271 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),zero_zero(int))) <-> ti(int,B_2) = ti(int,A_3))) # label(fact_890_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2272 (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) <-> hBOOL(hAPP(int,bool,nat_is_nat,Xa)))) # label(fact_4865_is__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2273 (all X all Y all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C_1),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_1),hAPP(real,real,abs_abs(real),Y)))) -> X = zero_zero(real)))) # label(fact_1200_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2274 (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_2727_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2275 (all Na all Va 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,Va)))),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),Na),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,Na)),hAPP(int,nat,number_number_of(nat),Va))) # label(fact_4969_max__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2276 (all Xa all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa) = hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Ya) <-> Ya = Xa))) # label(fact_2676_real__root__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2277 (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_4389_abs__gcd__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2278 (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_1061_Int2_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2279 (all X_a (topological_space(X_a) -> (all G all L 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),L),hAPP(X_a,filter(X_a),at(X_a),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,L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4622_Im_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2280 (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_1594_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2281 (all N hAPP(nat,complex,semiring_1_of_nat(complex),N) = hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_2962_complex__cnj__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2282 (all Na all G all Xa all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),Xa),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)),Na)),Xa),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),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,G,Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),one_one(nat))))),Ma))))) # label(fact_3909_DERIV__fun__pow) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2283 (all Na all Ma (hBOOL(hAPP(int,bool,nat_is_nat,Ma)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Na)) -> 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,Na))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Ma),Na)))) # label(fact_4864_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2284 (all X_a (comple44059174attice(X_a) -> (all A_2 all B_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)),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_1))))))) # label(fact_1816_Sup__subset__mono) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2285 (all Xa (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),Xa))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)))) # label(fact_2483_even__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2286 (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_655_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption]. 7.53/7.55 2287 (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_903_zcong__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2288 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)) -> zero_zero(nat) = A_1)) # label(fact_1251_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2289 (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_3248_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2290 (all X_a all R_2 all F all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,Xa)),hAPP(X_a,nat,F,Ya))) -> 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),Xa),Ya)),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_2))))) # label(fact_3837_mlex__less) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2291 (all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_2 ((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_2)) -> 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),Xa),H_1))),hAPP(real,real,F,Xa)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2))))))) # label(fact_2664_DERIV__pos__inc__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2292 (all K all Ma all Na (Ma = Na <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Na) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma))) # label(fact_1346_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2293 (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_230_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2294 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_1))))) -> 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_2))))))) # label(fact_4178_setprod__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2295 (all Ta all A_2 all D_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1))))) -> (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_1),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_1),D)),Ta)))))))) # label(fact_4675_aset_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2296 (all V hAPP(int,real,number_number_of(real),V) = hAPP(complex,real,re,hAPP(int,complex,number_number_of(complex),V))) # label(fact_3030_complex__Re__number__of) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2297 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> 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))) # label(fact_850_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2298 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (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),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_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),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4609_LIM__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2299 (all A_1 all B all C_1 all Q_3 all R_3 (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_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_3))) -> (zero_zero(int) != ti(int,C_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,hAPP(int,fun(int,int),times_times(int),A_1),B)),C_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),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_3)),C_1))),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_3)),C_1))))))) # label(fact_1643_zmult1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2300 (all P_2 all P_1 all Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(P_2) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) <-> hBOOL(P_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa))))) # label(fact_573_conj__le__cong) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2301 (all Ma all No_1 all F ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_1)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_1))))) -> 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_1651_lemma__f__mono__add) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2302 (all P_1 ((all X1 hBOOL(hAPP(nat,bool,P_1,X1))) <-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_1))))))) # label(fact_1002_all__nat) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2303 (all X_a (comm_monoid_add(X_a) -> (all F all Na 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)),Na)) = 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)))),Na))))))) # label(fact_4647_setsum__triangle__reindex) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2304 (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_1362_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2305 (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) <-> -hBOOL(hAPP(int,bool,nat_neg,Xa)))) # label(fact_1605_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2306 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_145_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2307 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = M) # label(fact_1403_div__1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2308 (all 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) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))) # label(fact_1462_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2309 (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_1504_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2310 (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_1363_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2311 (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_1272_dvd__1__left) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2312 (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_4373_gcd__dvd2__int) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2313 (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_1327_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2314 (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_2788_complex__inverse__complex__split) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2315 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),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),Xa)),zero_zero(real)),sequentially))))) # label(fact_4520_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2316 (all Xa all Ya (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Xa),Xa)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ya),Ya)) = zero_zero(real) <-> zero_zero(real) = Xa & Ya = zero_zero(real))) # label(fact_638_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2317 (all X_a (field(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),hAPP(int,int,bit1,pls))) = ti(X_a,X)))) # label(fact_1783_divide__Numeral1) # label(axiom) # label(non_clause). [assumption]. 7.53/7.56 2318 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Xa)),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),Xa)),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_4525_zeroseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2319 (all Na all Xa ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa) = 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)),Na))),Xa)))) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) -> hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa) = zero_zero(real)) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),Na))),hAPP(real,real,uminus_uminus(real),Xa))))) = hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa))))) # label(fact_4163_root__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2320 (all X_a (real_normed_field(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_2)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_2)))))) # label(fact_4017_suminf__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2321 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B))))))) # label(fact_328_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2322 (all X_c all X_b all X_a all C all Xa 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_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C,A_4),B_4),Xa)))) -> 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),P_4),Xa)))) # label(fact_4086_splitI2_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2323 (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_3076_prime__g__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2324 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_8_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2325 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),Y)) -> hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4387_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2326 (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]. 7.58/7.56 2327 (all B_2 all A_3 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4)))))))) # label(fact_1210_wset__mem) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2328 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F all Sb (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sb)) <-> 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)))),Sb),sequentially)))))) # label(fact_4522_sums__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2329 (all X hAPP(real,real,tan,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,tan,X))) # label(fact_2369_tan__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2330 (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),plus_plus(real),A_1),B)),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))))) # label(fact_4693_real__vector_Oscale__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2331 (all X_a (semiring_div(X_a) -> (all C_1 all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))))) # label(fact_1286_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2332 (all X_a (semiring_div(X_a) -> (all B all A_1 all 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),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_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))) # label(fact_1413_div__mod__equality2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2333 (all X_a (linord20386208strict(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_475_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2334 (all N all M all R_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_3)) -> (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_3)))))) # label(fact_3313_divides__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2335 (all B_2 all A_3 all F all G all Xa all D (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,Xa)),D)) -> (D != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),B_2)) -> ((all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),B_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),Y_1)) -> Y_1 = hAPP(real,real,F,hAPP(real,real,G,Y_1)))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),Xa)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),Xa),hAPP(real,real,inverse_inverse(real),D)))))))))) # label(fact_4946_DERIV__inverse__function) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2336 (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_1856_divide__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2337 (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_1134_Euler__part2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2338 (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_1548_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2339 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 all D_3 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_1)),D_3) = 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_1),D_3))))) # label(fact_299_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2340 (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_517_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2341 (all X_a (division_ring(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> 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_2597_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2342 (all X_a (comm_monoid_add(X_a) -> (all F all Na 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_atMost(nat),Na))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,Na))) = 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_atMost(nat),hAPP(nat,nat,suc,Na)))))) # label(fact_4968_setsum__atMost__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2343 (all Xa hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),cos),Xa),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,Xa))))) # label(fact_2651_DERIV__cos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2344 (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_3770_Fract__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2345 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) -> 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)),Na)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Na)),one_one(nat)))) # label(fact_3911_card__bdd__int__set__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2346 (all P_1 all Xa all Ya ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ya),Xa)) -> 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),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) <-> 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),Xa),Ya)))))) # label(fact_884_zdiff__int__split) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2347 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)))))) # label(fact_270_semiring__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2348 (all X_2 all A_3 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_2),A_3)) -> 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_2)),hAPP(complex,real,re,A_3))))) # label(fact_4141_Re_Osums) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2349 (all X_a all X_b (minus(X_b) -> (all A_2 all B_1 all X_1 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_2),B_1),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_2,X_1)),hAPP(X_a,X_b,B_1,X_1))))) # label(fact_2989_fun__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2350 (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,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_3331_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2351 (all Z_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_5),zero_zero(int))) <-> hBOOL(hAPP(int,bool,nat_neg,Z_5)))) # label(fact_1603_neg__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2352 (all P_4 hAPP(int,fun(int,bool),sr,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)))) # label(fact_1261_SR__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2353 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),Ya)) <-> 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),Xa)),hAPP(int,X_a,number_number_of(X_a),Ya))))))) # label(fact_207_le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2354 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),int_lcm,X),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))))) # label(fact_3698_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2355 (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]. 7.58/7.56 2356 (all X_b all X_a all 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)) = ti(product_prod(X_a,X_b),P_5)) # label(fact_3149_pair__collapse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2357 (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_1280_mod__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2358 (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_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),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))))))) # label(fact_2644_ex__inverse__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2359 (all X_b all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_1)) = 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_2),B_1))))) # label(fact_3223_card__Plus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2360 (all X_a (real_vector(X_a) -> ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)) = scaleR_scaleR(X_a))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2361 (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_3644_ex__of__int__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2362 (all P_1 all Xa all Ya (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) -> hBOOL(P_1)))) # label(fact_939_dvd_Oless__imp__triv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2363 (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_2353_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2364 (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_1 all Y_1 (ti(product_prod(X_b,X_c),Z) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_1),Y_1) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,X_1),Y_1))))))) # label(fact_4795_splitE2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2365 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_1315_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2366 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_398_mult__Pls) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2367 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z_1)),W) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W))) # label(fact_2061_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2368 (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_2287_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2369 (all B all A_1 (zero_zero(nat) != A_1 -> (exists X_1 exists Y_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3338_bezout__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2370 (all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Ya)))))) # label(fact_2698_real__root__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2371 (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)))) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min)),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_687_Legendre__1mod4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2372 (all X_a ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a)) = measure(X_a)) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2373 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),times_times(X_a),A_1),B)),C_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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1))),C_1)))) # label(fact_1285_mod__mult__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2374 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arccos),Xa))))) # label(fact_4942_isCont__arccos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2375 (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_169_power__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2376 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_4830_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2377 (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_2600_field__divide__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2378 (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_3718_Rats__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2379 (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_2428_natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2380 (all X_a (real_normed_vector(X_a) -> (all R_3 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),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),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_3),A_1)),B)))) # label(fact_4710_scaleR_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2381 (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_1590_Parity_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2382 (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_2290_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2383 (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_2004_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2384 (all Ma all Na (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na) <-> one_one(nat) = Na & Ma = one_one(nat))) # label(fact_621_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2385 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arcsin),Xa))))) # label(fact_4943_isCont__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2386 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2229_arcsin__lbound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2387 (all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B_2),A_3),Ma)))) # label(fact_874_zcong__sym) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2388 (all X_a (ab_group_add(X_a) -> (all F all P_4 all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),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),Na),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),Na)))))))) # label(fact_4229_setsum__diff__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2389 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2390 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2975_mult__left__idem) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2391 (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_3131_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2392 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Ya all G 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),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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)),Ya)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4599_mult__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2393 (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_1524_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2394 (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_1237_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2395 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> zero_zero(nat) != N)) # label(fact_143_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2396 (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_1559_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2397 (all A_3 all B_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)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_3),B_2))) -> (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),B_2)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_2),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_3),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_2))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_3),B_2)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),B_2))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_3),B_2) = 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)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),B_2))))) # label(fact_1657_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2398 (all P_5 all X hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),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))))))) # label(fact_1184_MultInv__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2399 (all X_a all X_b (real_normed_algebra(X_b) -> (all Ya all G all A_3 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),A_3),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)),Ya)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_3),Ya)),A_2)))))) # label(fact_4480_mult__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2400 (all X_a (real_normed_vector(X_a) -> (all X_2 ((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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) -> 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_2,M_2)),hAPP(nat,X_a,X_2,N_1)))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)))))) # label(fact_3342_CauchyI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2401 (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_2305_cos__double) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2402 (all Xa all Na all Ya ((exists Q1 exists Q2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ya),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),Q2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Xa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),Q1))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Xa),Na) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ya),Na))) # label(fact_1575_nat__mod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2403 (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_549_cube__square) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2404 (all X_a (ordered_ring(X_a) -> (all A_3 all E_2 all C all B_2 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_3),B_2)),E_2)),C)),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_3),E_2)),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),B_2),E_2)),D_1))))))) # label(fact_773_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2405 (all M all N all K_4 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)))))) # label(fact_3497_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2406 (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_1174_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2407 (all X_b all X_a all F all Xa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> 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,Xa)),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_2))))) # label(fact_3660_imageI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2408 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_1 exists N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),X)))))) # label(fact_2464_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2409 (all X_b (number(X_b) & ring(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),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))) = 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))))) # label(fact_757_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2410 (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_2806_of__real__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2411 (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_2554_fact__mod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2412 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),A_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4740_scaleR__minus__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2413 (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)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) != one_one(int))))) # label(fact_4440_Rat__cases) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2414 (all X_a (semiring_1(X_a) -> (all Na hAPP(nat,X_a,semiring_1_of_nat(X_a),Na) = 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))),Na),zero_zero(X_a))))) # label(fact_4185_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2415 (all K all Ma all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),Na))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Na)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)))) # label(fact_3464_zgcd__greatest__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2416 (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_408_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2417 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (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),Xa),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),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) <-> ti(X_a,Xa) = zero_zero(X_a) & ti(X_a,Ya) = zero_zero(X_a))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2418 (all A_1 all B (ti(int,B) != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),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_2098_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2419 (all Ma all Na ((-(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) | Na = zero_zero(nat)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),Na) = 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),Na)),Na))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) | zero_zero(nat) = Na -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),Ma) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),Na)))) # label(fact_4079_divmod__nat__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2420 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_2)) -> 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_2))))))) # label(fact_4104_of__real_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2421 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3621_ceiling__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2422 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),one_one(real))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,Xa)),one_one(nat))))) # label(fact_1675_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2423 (all X_a (real_normed_field(X_a) -> (all C all F all Xa all D (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),Xa),D)) -> 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)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),D),C))))))) # label(fact_3872_DERIV__cdivide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2424 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),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),Na),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),Na)))) # label(fact_4637_fact__div__fact) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2425 (all Na (Na = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))))) # label(fact_396_le__0__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2426 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a))) # label(fact_3_one__power2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2427 (all X_a (ring_1(X_a) -> zero_zero(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),zero_zero(int)))) # label(fact_3589_of__int__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2428 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all 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),plus_plus(X_a),A_1),B)),C_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))))) # label(fact_297_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2429 (all R all S_5 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R),S_5) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R),hAPP(real,real,inverse_inverse(real),S_5))) # label(fact_2604_real__divide__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2430 (all Ma all Z (Ma = hAPP(int,nat,nat_1,Z) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) <-> hAPP(nat,int,semiring_1_of_nat(int),Ma) = ti(int,Z))) # label(fact_1023_int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2431 (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_550_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2432 (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_3839_Ints__cases) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2433 -(all S_1 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),S_1)))) # label(fact_709__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]. 7.58/7.56 2434 (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_2273_sin__le__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2435 (all A_1 all B hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B))) # label(fact_3056_cis__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2436 (all Xa -(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)))) # label(fact_1704_even__odd__conj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.56 2437 (all Xa all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),Xa)),A_3)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_3)),one_one(real)))))) # label(fact_3441_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2438 (all Wa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int)))))) # label(fact_779_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2439 (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_2096_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2440 (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_1897_field__le__epsilon) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2441 (all X_a (ring_1(X_a) -> (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,Z_1)))))) # label(fact_3629_of__nat__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2442 (all M all N (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> N = one_one(nat) | M = zero_zero(nat))) # label(fact_637_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2443 (all A_3 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_3),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_3),P_4)) = hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1690_MultInvPair__prop2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2444 (all X_a (semiring_div(X_a) -> (all A_1 all B all 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),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_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))) # label(fact_1414_div__mod__equality) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2445 (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_1543_mod__le__divisor) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2446 (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_2798_of__real_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2447 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1336_add__Suc__shift) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2448 (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_2394_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2449 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Xa all G 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),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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),Xa)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4601_mult__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2450 (all Xa all Na all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),hAPP(nat,nat,suc,Na))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ya),hAPP(nat,nat,suc,Na)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)))) # label(fact_1406_exp__mono__lt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2451 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) # label(fact_125_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2452 (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,bit0,L))))) # label(fact_53_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2453 (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_1177_inv__not__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2454 (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_308_number__of__succ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2455 (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_423_zero__le__square) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2456 (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_1132_zfact__prop) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2457 (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_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_1),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_2859_dense__le__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2458 (all X_a (metric_space(X_a) -> (all X_2 ((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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),hAPP(nat,X_a,X_2,M_2)),hAPP(nat,X_a,X_2,N_1))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)))))) # label(fact_3550_metric__CauchyI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2459 (all Na (Na = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_1375_less__Suc0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2460 (all Xa 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)),Xa),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,Xa))),hAPP(real,real,cos,Xa))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,Xa))),hAPP(real,real,cos,Xa)))))) # label(fact_3913_DERIV__cos__cos__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2461 (all X_a (metric_space(X_a) -> (all X_2 all L_2 ((all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_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),hAPP(nat,X_a,X_2,N_1)),L_2)),R_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_2),L_2),sequentially)))))) # label(fact_4687_metric__LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2462 (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_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all Y_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),X),Y_1))),D_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),B))))))))) # label(fact_1646_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2463 (all X_a (ring_11004092258visors(X_a) -> (all A_3 (one_one(X_a) = ti(X_a,A_3) | ti(X_a,A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) <-> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2037_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2464 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 all X_1 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_1),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))) # label(fact_2110_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2465 (all X_a (number_ring(X_a) -> (all Xa all Ya (hAPP(int,X_a,number_number_of(X_a),Ya) = hAPP(int,X_a,number_number_of(X_a),Xa) <-> 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),Xa),hAPP(int,int,uminus_uminus(int),Ya))))))))) # label(fact_2162_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2466 (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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = one_one(X_a)))) # label(fact_695_power__m1__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2467 (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),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_271_semiring__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2468 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),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),hAPP(X_a,X_b,F,A_3)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4902_isCont__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2469 (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),hAPP(X_a,X_b,Q,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)) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2470 (all Xa ((exists N_1 Xa = hAPP(int,real,real_1(int),N_1)) <-> Xa = hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),Xa)))) # label(fact_3351_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2471 (all Xa all Na (one_one(nat) = Xa | Na = zero_zero(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na) = one_one(nat))) # label(fact_195_exp__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2472 (all 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))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),N)) # label(fact_2366_sin__cos__npi) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2473 (all X_b all X_a all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) -> 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_2),B_1)))))) # label(fact_3208_finite__Plus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2474 (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]. 7.58/7.57 2475 (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_3053_cis__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2476 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa),D)) -> 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)),Xa),hAPP(X_a,X_a,uminus_uminus(X_a),D))))))) # label(fact_3891_DERIV__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2477 (all Z all P_1 ((all N_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),N_1)))) -> ((all N_1 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_1)))))) -> hBOOL(hAPP(int,bool,P_1,Z))))) # label(fact_3554_int__of__nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2478 (all X_a all A_2 all B_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_2),B_1) = 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_2))),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_1))))) # label(fact_2245_set__diff__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2479 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = ti(int,A_1)))) # label(fact_1420_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2480 (all Na 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),Na)),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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),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),Na))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),Na)) = zero_zero(real)) # label(fact_2526_lemma__STAR__sin) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2481 (all B_2 all C all A_3 all D_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_3),D_1) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B_2),C) = one_one(nat) -> (A_3 = B_2 & C = D_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_3),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_2),D_1))))) # label(fact_3295_coprime__crossproduct__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2482 (all X_a (number_ring(X_a) -> (all V all 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)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W))))) # label(fact_716_number__of__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2483 (all X_a (real_vector(X_a) -> (all A_3 all Xa (A_3 = zero_zero(real) | zero_zero(X_a) = ti(X_a,Xa) <-> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa) = zero_zero(X_a))))) # label(fact_4736_scaleR__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2484 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Z all F all Xa (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),Xa)))) -> (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),Xa))) -> 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_4051_powser__inside) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2485 (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_3771_of__int__rat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2486 (all A_2 all B_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_2),B_1)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_2)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))))) # label(fact_3676_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2487 (all Ma all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na) = one_one(nat) <-> Ma = one_one(nat) & Na = one_one(nat))) # label(fact_619_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2488 (all X one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),one_one(nat)),X)) # label(fact_3278_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2489 (all X_b (monoid_mult(X_b) & number(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_551_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2490 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)) # label(fact_1399_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2491 (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_2260_sgn0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2492 (all Xa 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),Xa)),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,Xa),zero_zero(int)),P_4))))) # label(fact_1565_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2493 (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_1799_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2494 (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]. 7.58/7.57 2495 (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_1917_minus__diff__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2496 (all 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))) = hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat_1))) # label(fact_2945_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2497 (all A_2 A_2 = 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_2))) # label(fact_3674_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2498 (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_3243_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2499 (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_3269_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2500 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) <-> Ya != Xa & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))) # label(fact_351_real__less__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2501 (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_2552_dvd__fact__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2502 (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_252_zero__le__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2503 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> 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_3)))))) # label(fact_4908_isCont__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2504 (all A_1 all B all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_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_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C_1))),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_1)))) # label(fact_1479_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2505 (all Ma all Na ((hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na))))) # label(fact_2469_even__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2506 (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_1394_diff__less__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2507 (all X_a (linord219039673up_add(X_a) -> (all A_3 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),A_3) <-> zero_zero(X_a) = ti(X_a,A_3))))) # label(fact_321_double__zero__sym) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2508 (all C_1 all D_3 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_1),D_3),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_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D_3)),M))))) # label(fact_893_zcong__zmult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2509 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na))))) # label(fact_630_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2510 (all X_a all X_b (order(X_b) & order(X_a) -> (all C all A_3 all F all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_b,X_a,F,B_2))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_2),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_b,X_a,F,C))))))))) # label(fact_2854_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2511 (all X hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_2965_complex__cnj__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2512 (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),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2620_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2513 (all A_1 all B all C_1 all D_3 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D_3)) = 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_1),D_3))) # label(fact_2763_complex__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2514 (all R_3 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_3),hAPP(complex,real,im,X))) # label(fact_4707_Im_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2515 (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_3362_power__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2516 (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_1825_divide__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2517 (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_4393_gcd__abs1__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2518 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N)))) # label(fact_2465_lemma__STAR__cos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2519 (all X_a (archim1727834104eiling(X_a) -> archim2085082626_floor(X_a) = ti(fun(X_a,int),archim2085082626_floor(X_a)))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2520 (all Na all Xa all Diff all F ((all M_2 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),Diff,M_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_1)))) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> (exists T_4 (hAPP(real,real,F,Xa) = 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) & 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),Xa))))))) # label(fact_4313_Maclaurin__all__le__objl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2521 (all X all Y (hAPP(complex,real,re,X) = hAPP(complex,real,re,Y) -> (hAPP(complex,real,im,Y) = hAPP(complex,real,im,X) -> X = Y))) # label(fact_3021_complex__eqI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2522 (all X_a (linorder(X_a) -> (all Xa all Ya all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Ya),Z))))))) # label(fact_4846_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2523 (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 = P_4 | one_one(nat) = M_2)) <-> hBOOL(hAPP(nat,bool,prime,P_4)))) # label(fact_3092_prime__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2524 (all X_b all X_a all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (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_2))) -> (exists X_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),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_2))),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_1)))))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2))))))) # label(fact_4358_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2525 (all P_5 all Q_3 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3))) -> Q_3 = one_one(nat) | one_one(nat) = P_5)) # label(fact_3080_prime__product) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2526 (all R_3 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3)) # label(fact_2802_complex__of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2527 (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]. 7.58/7.57 2528 (all N all A_1 hAPP(complex,real,re,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N)) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3050_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2529 (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_1133_Euler_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2530 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),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),Xa)),Z)))))) # label(fact_3617_floor__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2531 (all Va all Na ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> 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,Va)))),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(nat,nat,suc,Na))))) # label(fact_3925_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2532 (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_1788_exp__gt__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2533 (all K_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4)) # label(fact_79_add__Pls) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2534 (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_260_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2535 (all X_a (real_normed_field(X_a) -> (all C all F all Xa all D (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),Xa),D)) -> 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)),F)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))))))) # label(fact_3887_DERIV__cmult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2536 (all Ma all Na all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na))))) # label(fact_657_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2537 (all X_a collect(X_a) = ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2538 (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_3789_real__plus__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2539 (all X_a (real_normed_vector(X_a) -> (all X_2 all L_2 ((all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_1)) -> 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_2,N_1)),L_2))),R_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_2),L_2),sequentially)))))) # label(fact_4684_LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2540 (all Ma all Na 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),Na)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),Na)) # label(fact_4171_divmod__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2541 (all X_a (linord1117847801e_zero(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C_1)))))))) # label(fact_1836_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2542 (all X_a (field(X_a) -> (all X all Y all Z_1 (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1))))) # label(fact_1883_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2543 (all Xa (zero_zero(real) != hAPP(real,real,cos,Xa) -> 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)),Xa),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,Xa)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3943_lemma__DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2544 (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]. 7.58/7.57 2545 (all X_a (division_ring(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_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),times_times(X_a),A_1),B)),C_1)))) # label(fact_1827_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2546 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,Xa)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))) # label(fact_2122_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2547 (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 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2) = X))))) # label(fact_3112_prime__power__exp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2548 (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_4784_scaleR_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2549 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) | Na = zero_zero(nat))) # label(fact_150_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2550 (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_1212_d22set__eq__wset) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2551 (all X_a (ring_1(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = one_one(X_a)))) # label(fact_2044_power__minus1__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2552 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)))) # label(fact_1392_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2553 (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_1345_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2554 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),Ya)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ya),hAPP(real,real,uminus_uminus(real),Xa))))) # label(fact_2023_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2555 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),d22set,A_3))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)))) # label(fact_1222_d22set__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2556 (all G all F all Xa 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),Xa))),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),Xa))),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,Xa)),hAPP(real,real,F,Z_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),Xa))),D_1)))))))) # label(fact_4955_lemma__isCont__inj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2557 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,exp(X_a),X)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2606_exp__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2558 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),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),Xa)),Z)))))) # label(fact_3634_floor__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2559 (all A_1 all R_3 all B all M all C_1 all D_3 all N hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_3),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_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_3),D_3))),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_1),N))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_3),N))))) # label(fact_906_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2560 (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_114_zero__less__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2561 (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_3271_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2562 (all X_a (linord219039673up_add(X_a) -> (all A_3 (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_3),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)))))) # label(fact_197_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2563 (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_3531_dist__triangle2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2564 (all X_a all X_c all X_b all Z all C 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),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C,A_3),B_2))) -> 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),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_3),B_2)))))) # label(fact_4065_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2565 (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_47_zadd__commute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2566 (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_2427_log__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2567 (all A_1 all B hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),B)) # label(fact_3758_minus__rat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2568 (all Ma all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,Ma))))) # label(fact_1334_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2569 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2527_lemma__not__even__div2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2570 (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_1353_mod__by__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2571 (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_538_power__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2572 (all P_1 all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> (all N_1 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_3),B_2),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_3),B_2),hAPP(nat,nat,suc,N_1)))))))) # label(fact_3167_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2573 (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_4401_dvd__gcd__D2__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2574 (all K 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),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)) = 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))) # label(fact_4566_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2575 (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_800_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2576 (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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N)) # label(fact_4385_gcd__add1__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2577 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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)),A_2),B_1)))) # label(fact_2208_equalityD1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2578 (all M all N ((hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),one_one(nat)))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) & (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) -> one_one(nat) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_2536_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2579 (all X_a all X_b (real_normed_vector(X_b) -> (all Xa all G all A_3 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),A_3),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)),Xa)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_3),Xa)),A_2)))))) # label(fact_4752_scaleR__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2580 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ya),Xa)) -> Xa = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),Ya),Xa)))) # label(fact_4280_Sup__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2581 (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,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,inverse_inverse(real),X)))))) # label(fact_2639_log__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2582 (all X_2 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_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)))),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_3926_SR__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2583 (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_1430_power__gt1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2584 (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_3711_Rats__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2585 (all A_3 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_3),Ma) -> (exists X_1 ((all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),Y_1),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),hAPP(int,fun(int,bool),norRRset,Ma))) -> ti(int,X_1) = ti(int,Y_1))) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),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_3),X_1),Ma))))))) # label(fact_3639_norR__mem__unique) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2586 (all X_a all R_2 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_2),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_2)),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_4366_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2587 (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_3474_zgcd__1__power__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2588 (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 (zero_zero(X_a) != ti(X_a,H_1) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,F,H_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),K_3),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4651_lemma__termdiff4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2589 (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_3333_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2590 (all X_a (real_normed_vector(X_a) -> (all X_2 all A_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_2),A_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,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_2)),hAPP(X_a,real,norm_norm(X_a),A_3)),sequentially)))))) # label(fact_4496_LIMSEQ__norm) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2591 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)) = ti(int,A_1)))))) # label(fact_1141_inv__inv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.57 2592 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_2 all A_3 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_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),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_3))),B_2)),zero_zero(X_b))),S) = hAPP(X_a,X_b,B_2,A_3)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3))),B_2)),zero_zero(X_b))),S)))))) # label(fact_4236_setsum__delta) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2593 (all X_a (linordered_idom(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3)),zero_zero(X_a))))))) # label(fact_2279_sgn__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2594 (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,uminus_uminus(rat),Q_3) = hAPP(rat,rat,abs_abs(rat),Q_3)))) # label(fact_3734_abs__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2595 (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_2901_floor__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2596 (all F all G ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_1))),hAPP(nat,real,G,N_1))))) -> (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_4045_summable__rabs__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2597 (all X_a (power(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) -> (all A_3 all Wa (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),hAPP(int,nat,number_number_of(nat),Wa)) = zero_zero(X_a) <-> ti(X_a,A_3) = zero_zero(X_a) & hAPP(int,nat,number_number_of(nat),Wa) != zero_zero(nat))))) # label(fact_89_power__eq__0__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2598 (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_2399_real__natfloor__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2599 (all A_3 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_3)),Xa)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_3),hAPP(real,nat,natfloor,Xa)))))) # label(fact_2410_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2600 (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_2550_of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2601 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> 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_2694_real__root__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2602 (all Na all Va (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va))) = Na) <-> hAPP(nat,nat,suc,Na) = hAPP(int,nat,number_number_of(nat),Va))) # label(fact_3915_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2603 (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)) -> Q_3 = P_5)))) # label(fact_3071_primes__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2604 (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]. 7.58/7.58 2605 (all B all 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)))) = 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)) # label(fact_1812_real__average__minus__second) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2606 (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_2321_sin__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2607 (all K_4 hAPP(int,int,uminus_uminus(int),K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min),K_4)) # label(fact_2079_mult__Min) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2608 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)))) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),zero_zero(real))))) -> hAPP(real,real,F,A_3) = hAPP(real,real,F,B_2))))) # label(fact_4953_DERIV__isconst__end) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2609 (all X_a (linorder(X_a) -> (all Xa all Ya (hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Xa) = hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Ya) <-> ti(X_a,Ya) = ti(X_a,Xa))))) # label(fact_4343_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2610 (all Xa all Na all Ya (Xa = Ya <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ya),hAPP(nat,nat,suc,Na)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),hAPP(nat,nat,suc,Na)))) # label(fact_1349_exp__mono__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2611 (all Xa all A_3 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_3),zero_zero(int)),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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_3),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),Xa)))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1518_SRStar__mult__prop2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2612 (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_3488_zrelprime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2613 (all Na all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,Na)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),Na)) & (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))))))))) # label(fact_578_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2614 (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_461_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2615 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> hAPP(complex,complex,cnj,hAPP(fun(nat,complex),complex,suminf(complex),X_2)) = 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_2)))) # label(fact_4068_cnj_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2616 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) -> (Xa = Ya <-> hAPP(real,real,ln,Xa) = hAPP(real,real,ln,Ya))))) # label(fact_1706_ln__inj__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2617 (all X hAPP(complex,complex,sgn_sgn(complex),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)) # label(fact_4767_complex__sgn__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2618 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_1)) -> 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_1),D)))))))) # label(fact_4662_aset_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2619 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)))))) # label(fact_376_no__zero__divisors) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2620 (all Q_3 all B all R_3 all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),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_1))),R_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C_1))))))) # label(fact_1475_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2621 (all X_a (semiring_div(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),A_1))))) # label(fact_1090_div__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2622 (all X_a all X_b (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)),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)),A_2)))))) # label(fact_4473_tendsto__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2623 (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_140_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2624 (all X_b all X_a (topological_space(X_b) & metric_space(X_a) -> (all L all F all G all A_3 all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> ((all X_1 (ti(X_a,A_3) != ti(X_a,X_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_1),A_3)),R_2)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,X_1)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(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),hAPP(X_a,filter(X_a),at(X_a),A_3))))))))) # label(fact_4677_metric__LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2625 (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_3123_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2626 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_3),B_2)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_2)),one_one(rat)))))) # label(fact_3816_Fract__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2627 (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_4118_sums__summable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2628 (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_251_power__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2629 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),X) = X) # label(fact_3251_gcd__idem__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2630 (all X_a (real_vector(X_a) -> (all A_3 all Xa all B_2 (zero_zero(X_a) = ti(X_a,Xa) | A_3 = B_2 <-> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B_2),Xa))))) # label(fact_4732_scaleR__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2631 (all F all L all 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),F),L),hAPP(real,filter(real),at(real),C))) -> (L != zero_zero(real) -> (exists R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) & (all 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),C),X_1))),R_1)) & X_1 != C -> zero_zero(real) != hAPP(real,real,F,X_1)))))))) # label(fact_4654_LIM__fun__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2632 (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_946_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2633 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> (all D_1 all Sb exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_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_1),Sb))) <-> -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_1),Sb)))))))) # label(fact_1215_pinf_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2634 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_2)) -> 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_2))))) # label(fact_3879_cnj_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2635 (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]. 7.58/7.58 2636 (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_2269_cos__diff2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2637 (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_2697_real__root__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2638 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_1)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1) != ti(int,X_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_1)) -> 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_1),D))))))))) # label(fact_4665_bset_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2639 (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_1083_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2640 (all X_a all X_b all B_2 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),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_2))) -> -(all X_1 (hAPP(X_b,X_a,F,X_1) = ti(X_a,B_2) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_2)))))) # label(fact_3991_imageE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2641 (all M all N hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_4991_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2642 (all X_a (linorder(X_a) -> (all Xa all Ya all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),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),Xa),Ya)),Z)))))) # label(fact_4983_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2643 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hAPP(X_a,X_b,G,X_1) = 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_2) = one_one(X_b)))))) # label(fact_4175_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2644 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2955_complex__cnj__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2645 (all X_a (linord893533164strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_454_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2646 (all Ra all X_2 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Ra)) -> (exists K_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_2,N_1))),Ra))))))) # label(fact_4888_vanishesD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2647 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all C_1 all D_3 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_1),D_3)))),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_1))),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_3)))))))) # label(fact_2029_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2648 (all X_a all X_b ti(fun(product_prod(X_a,X_b),X_b),product_snd(X_a,X_b)) = product_snd(X_a,X_b)) # label(tsy_c_Product__Type_Osnd_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2649 (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_447_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2650 (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_2 ((all Y_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),X),Y_1))),D_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),B)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_1)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2))))))) # label(fact_1584_lemma__interval) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2651 (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_1863_frac__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2652 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),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_2359_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2653 (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_3423_floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2654 (all Xa 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)),Xa),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))),hAPP(real,real,cos,Xa))),hAPP(real,real,sin,Xa))))) # label(fact_3921_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2655 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),Na)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),Ma)),one_one(real)))))) # label(fact_2407_nat__le__real__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2656 (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]. 7.58/7.58 2657 (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_554_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2658 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) <-> 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_3))))))) # label(fact_2583_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2659 (all X_a all A_2 all B_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)),A_2),B_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)),B_1),A_2)) -> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_1)))) # label(fact_2190_equalityI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2660 (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_1765_power__one__over) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2661 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_2837_le__funI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2662 (all W hAPP(complex,complex,cnj,hAPP(int,complex,number_number_of(complex),W)) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_2968_complex__cnj__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2663 (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_2344_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2664 (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_1497_le__div__geq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2665 (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_1744_ln__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2666 (all X_a (real_algebra_1(X_a) -> (all R_3 all 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_3)),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),X)))) # label(fact_4715_scaleR__conv__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2667 (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_3539_dist__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2668 (all Xa all Na (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Na))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),Na)),hAPP(real,nat,natfloor,Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),Na)),Xa)))))) # label(fact_1679_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2669 (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_2495_power__mono__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2670 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3270_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2671 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_2 all Wa all A_3 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),hAPP(int,X_a,number_number_of(X_a),Wa)) = ti(X_a,A_3) <-> (hAPP(int,X_a,number_number_of(X_a),Wa) != zero_zero(X_a) -> ti(X_a,B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa))) & (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),Wa) -> ti(X_a,A_3) = zero_zero(X_a)))))) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2672 (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_54_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2673 (all X_a (comm_semiring_1(X_a) -> (all Na 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)),Na))) = 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),Na)),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),Na)),one_one(X_a)))))) # label(fact_4642_gauss__sum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2674 (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_3037_cnj__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2675 (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_180_not__one__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2676 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (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),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> (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_3)))))))) # label(fact_4615_LIM__sgn) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2677 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),K)))) # label(fact_680_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2678 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_2 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_2)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),A_2)))) # label(fact_4291_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2679 (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]. 7.58/7.58 2680 (all L all U hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U),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))) # label(fact_4227_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2681 (all X_a all F all G all Ma all S ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_1)),hAPP(X_a,int,G,X_1)),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_4444_setprod__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2682 (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_378_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2683 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) # label(fact_4384_gcd__mult__distrib__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2684 (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_2124_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2685 (all A_1 all B all C_1 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_1)) = 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_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B))) # label(fact_1546_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2686 (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_3119_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2687 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> (exists N_1 (hAPP(nat,int,semiring_1_of_nat(int),N_1) = ti(int,K_4) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))))) # label(fact_193_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2688 (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_468_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2689 (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_4424_gcd__le2__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2690 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all Ma all F all L all Xa (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa)))))))) # label(fact_4612_LIM__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2691 (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),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),X)))) # label(fact_1369_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2692 (all X_a (one(X_a) -> (all Xa (ti(X_a,Xa) = one_one(X_a) <-> ti(X_a,Xa) = one_one(X_a))))) # label(fact_302_one__reorient) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2693 (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]. 7.58/7.58 2694 (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)) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2303_sgn__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2695 (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_1545_SRStar__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2696 (all X_a all A_2 all B_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)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2742_finite__subset) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2697 (all X all Y all R_3 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),R_3)),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_3))) # label(fact_2818_Complex__add__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2698 (all P_5 all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))))) & (zero_zero(nat) = M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = one_one(nat)))) # label(fact_881_power__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2699 (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_2421_less__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2700 (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),A_1),M) = 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)))) # label(fact_1427_zmod__zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2701 (all M all N hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)),N))) # label(fact_1436_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2702 (all S ((all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),S)) -> 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,S)))) # label(fact_3684_nat__set__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2703 (all X_a (metric_space(X_a) -> (all Xa all Ya (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),Xa),Ya)),zero_zero(real))) <-> ti(X_a,Xa) = ti(X_a,Ya))))) # label(fact_3534_dist__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2704 (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_1 all Y_1 -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1))))) # label(fact_3171_exE__realizer_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2705 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N) # label(fact_1401_diff__Suc__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2706 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_389_mult__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2707 (all X_a (metric_space(X_a) -> (all X_2 all L_2 ((all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),No)) & (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_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),hAPP(nat,X_a,X_2,N_1)),L_2)),R_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_2),L_2),sequentially)))))) # label(fact_4542_LIMSEQ__iff__nz) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2708 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_3)) -> 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_3))))))) # label(fact_4911_mult_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2709 (all Xa all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)))) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),zero_zero(real))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),B_2)) -> hAPP(real,real,F,Xa) = hAPP(real,real,F,A_3))))))) # label(fact_4952_DERIV__isconst2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2710 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) | Y = X)) # label(fact_954_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2711 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_1520_mod__div__decomp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2712 (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,bit1,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(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)))))) # label(fact_348_zadd__power3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2713 (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_2154_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2714 (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_1192_MultInv__zcong__prop3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2715 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,X)) = hAPP(real,real,ln,hAPP(real,real,inverse_inverse(real),X)))) # label(fact_2637_ln__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2716 (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_1729_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2717 (all X_a (semiring_div(X_a) & number(X_a) -> (all Xa all Ya (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),Ya)),hAPP(int,X_a,number_number_of(X_a),Xa)) = zero_zero(X_a) <-> 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),Xa)),hAPP(int,X_a,number_number_of(X_a),Ya))))))) # label(fact_1409_dvd__eq__mod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2718 (all J all A_3 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_3),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_3)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J),zero_zero(int)),P_4)) -> 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_3),P_4),J)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1682_MultInvPair__card__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2719 (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]. 7.58/7.58 2720 (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]. 7.58/7.58 2721 (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_175_of__nat__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2722 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_476_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2723 (all X_a (ordere236663937imp_le(X_a) -> (all A_3 all C all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C))))))) # label(fact_215_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2724 (all X_a (linordered_field(X_a) -> (all B_2 all A_3 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)),A_3)) <-> 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_3),C)),B_2))))))) # label(fact_1874_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2725 (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_1750_divide_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2726 (all X_a (real_n1866405975lgebra(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)))))) # label(fact_2580_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2727 (all D_3 all C_1 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (ti(int,B) = ti(int,C_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),D_3),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),D_3),M)))))) # label(fact_872_zcong__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2728 (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_1903_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2729 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2228_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2730 (all A_1 all B all C_1 (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = ti(int,C_1) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C_1),B) = ti(int,A_1))) # label(fact_891_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2731 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> 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)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_2397_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2732 (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_1004_nat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2733 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Ya))))))) # label(fact_241_le__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2734 (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_2982_compl__le__swap1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2735 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all 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)) = 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)),X)))) # label(fact_2032_minus1__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2736 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C_1 (ti(X_a,C_1) != 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))) # label(fact_1851_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2737 (all Na all Va ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Na)),hAPP(int,nat,number_number_of(nat),Va))))) # label(fact_3922_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2738 (all X_a (divisi14063676e_zero(X_a) & real_n1866405975lgebra(X_a) -> (all A_1 hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1))))) # label(fact_2581_norm__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2739 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> hAPP(X_a,X_b,F,X_1) = 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_3987_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2740 (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)),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)))) # label(fact_1513_power__m1__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2741 (all N exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)))) # label(fact_3130_euclid) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2742 (all Xa 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),Xa)))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,Xa))) # label(fact_4001_lemma__sin__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2743 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2744 (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_2590_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2745 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 ((all X_1 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_1),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4779_scaleR__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2746 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2710_real__root__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2747 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_158_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2748 (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_3831_Ints__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2749 (all Na 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),Na)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K) <-> Ma = Na)))) # label(fact_817_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2750 (all X_b all X_a (real_normed_vector(X_a) -> (all F all A_2 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_2))),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_2)))))) # label(fact_4206_norm__setsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.58 2751 (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),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_1),zero_zero(real)))) # label(fact_3841_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2752 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Ya))))))) # label(fact_63_less__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2753 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))) # label(fact_2017_number__of__Min) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2754 (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_399_mult__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2755 (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_3572_fact__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2756 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2957_cnj_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2757 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2758 (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_1718_ln__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2759 (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_949_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2760 (all A_3 all B_2 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_3),B_2) <-> (all D_2 (D_2 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B_2)))))) # label(fact_3290_coprime__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2761 (all X_b all X_a all X_c (real_normed_vector(X_c) -> (all F all A_3 all A_2 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_3,I_2)),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),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_3),S)),A_2)))))) # label(fact_4788_tendsto__setsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2762 (all X_a (linordered_semiring(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_477_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2763 (all X_a all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) # label(fact_2745_card__infinite) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2764 (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_3532_dist__triangle3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2765 (all X_b all X_a (topological_space(X_a) & 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)),hAPP(X_a,filter(X_a),at(X_a),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)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4635_LIM__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2766 (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_2448_tan__monotone) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2767 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_1913_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2768 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,K_4),L_4)))) # label(fact_1637_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2769 (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_979_dvd__if__abs__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2770 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,H,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),H),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),G),A_2)))))) # label(fact_4799_setsum_Ocong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2771 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2502_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2772 (all X_a all A_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_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)))) # label(fact_2846_Pow__top) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2773 (all X all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),K_4) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)))) # label(fact_2688_real__root__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2774 (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_4826_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2775 (all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),hAPP(int,int,bit1,L_4))) # label(fact_781_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2776 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M_2 ti(int,Z_1) != hAPP(nat,int,semiring_1_of_nat(int),M_2)))) # label(fact_343_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2777 (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),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,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)) # label(fact_1348_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2778 (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_3401_powr__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2779 (all X_a (boolean_algebra(X_a) -> (all Xa all Ya (hAPP(X_a,X_a,uminus_uminus(X_a),Ya) = hAPP(X_a,X_a,uminus_uminus(X_a),Xa) <-> ti(X_a,Xa) = ti(X_a,Ya))))) # label(fact_2978_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2780 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_1))))) -> 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_3990_setprod__pos__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2781 (all X_a (number_ring(X_a) -> (all 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),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,uminus_uminus(int),hAPP(int,int,bit1,pls))))))) # label(fact_2103_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2782 (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_3833_Ints__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2783 (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_1894_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2784 (all A_1 all B all C_1 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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C_1))),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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C_1))),C_1)) = 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_1)) # label(fact_1539_div__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2785 (all F all A_2 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_2)) -> ((all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_2)) -> (all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),A_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,F,X_1)),hAPP(int,int,F,Xa_1)),Ma)) -> ti(int,X_1) = ti(int,Xa_1)))))) -> 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_2))))))) # label(fact_3668_ResSet__image) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2786 (all B_2 all A_3 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)))) # label(fact_3231_Bnor__mem__zle) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2787 (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_4976_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2788 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_1030_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2789 (all P_1 all A0 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),zero_zero(int))) -> (ti(int,I_2) != zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) -> hBOOL(hAPP(int,bool,P_1,A0))))) # label(fact_3202_around__zero_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2790 (all Sb (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Sb)) -> 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),Sb))),zero_zero(real)),sequentially)))) # label(fact_4513_LIMSEQ__neg__powr) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2791 (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_820_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2792 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zOdd))))) # label(fact_1219_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2793 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K)))) # label(fact_4340_finite__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2794 (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_2337_cos__double__less__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2795 (all X_a (ring_1(X_a) -> (all C all 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),hAPP(nat,nat,suc,X_1))),hAPP(nat,X_a,C,hAPP(nat,nat,suc,X_1))) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C),X_1)))) # label(fact_4145_diffs__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2796 (all N all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),B) = one_one(int))) # label(fact_3475_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2797 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_3360_real__of__int__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2798 (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),B)),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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_1915_minus__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2799 (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_2578_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2800 (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_1774_mult__exp__exp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2801 -(all R_1 all V_3 -(hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),x),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) = ti(int,V_3) & 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),V_3))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))))) # label(fact_925__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An_) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2802 (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_2917_le__mult__floor) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2803 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))))) # label(fact_2992_cnj_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2804 (all R_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_3),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_3))),one_one(real))))) # label(fact_3421_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2805 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),zero_zero(nat))) # label(fact_4827_min__0R) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2806 (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_1446_Suc__pred) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2807 (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_4963_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2808 (all K all L (L = K <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,K) = hAPP(quickcheck_code_int,int,quickcheck_int_of,L))) # label(fact_3187_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2809 (all X_a (linordered_idom(X_a) -> (all Xa all Wa (zero_zero(X_a) != ti(X_a,Xa) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),Wa) <-> 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),Xa),hAPP(int,nat,number_number_of(nat),Wa)))))))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2810 (all X_b all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all G all A_2 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_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_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_2)))) # label(fact_4211_of__real_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2811 (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_555_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2812 (all X all N_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),N),N_4)) -> (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_4),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2703_real__root__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2813 (all N all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M) -> N = M))) # label(fact_661_mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2814 (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]. 7.58/7.59 2815 (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_1707_ln__less__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2816 (all X hAPP(int,real,ring_1_of_int(real),X) = hAPP(int,real,number_number_of(real),X)) # label(fact_3592_number__of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2817 (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_1081_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2818 (all A_3 all Xa (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_3)),one_one(real))),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_3),hAPP(real,int,archimedean_ceiling(real),Xa))))) # label(fact_3442_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2819 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I) = K <-> J = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I)))) # label(fact_851_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2820 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_4)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4)) # label(fact_801_diff__commute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2821 (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_3159_fst__eqD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2822 (all X_a all X_b all F all A_2 all B_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_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_2)),B_1)) -> 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_2))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_3662_image__Pow__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2823 (all A_3 all B_2 all Na (zero_zero(nat) != Na -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_3),Na)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_2),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_3),B_2))))) # label(fact_1236_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2824 (all Na (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),Na))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Na)))) # label(fact_3409_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2825 (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_1 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_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(nat,bool,even_odd_even(nat),N_1))))))) # label(fact_2530_sin__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2826 (all Xa all Na all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (Xa != zero_zero(real) -> ((all M_2 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),Diff,M_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_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),Xa))) & hAPP(real,real,F,Xa) = 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) & 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_4304_Maclaurin__all__lt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2827 (all A_1 all B 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)) = ti(int,A_1)) # label(fact_1431_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2828 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),zero_zero(nat)),X) = X) # label(fact_3279_gcd__0__left__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2829 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (Q_3 != P_5 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),Q_3)))))) # label(fact_3074_distinct__prime__coprime) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2830 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_3133_div__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2831 (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_1944_mod__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2832 (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_1941_minus__divide__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2833 (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_1563_mod2__gr__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2834 (all X_a (real_normed_vector(X_a) -> (all R_3 exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_1 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_3),X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))))) # label(fact_4782_scaleR__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2835 (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_3784_number__of__real__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2836 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all C all B_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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3))) & (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_3),B_2))))))) # label(fact_1859_divide__le__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2837 (all N one_one(int) = 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)) # label(fact_4395_coprime__minus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2838 (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),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_358_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2839 (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_3031_Re_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2840 (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_3299_gcd__diff1__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2841 (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]. 7.58/7.59 2842 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) -> 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)),Na)) = hAPP(int,int,fact_fact(int),Na))) # label(fact_4639_fact__altdef__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2843 (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_1051_abs__power2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2844 (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]. 7.58/7.59 2845 (all A_2 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_2),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_2)))) # label(fact_3665_RsetR__fin) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2846 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Na),zero_zero(int))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Na)),zero_zero(real))))) # label(fact_3411_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2847 (all X_a (real_normed_vector(X_a) -> (all Y_2 all B_2 all X_2 all A_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_2),A_3),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_2),B_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),plus_plus(X_a)),X_2)),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_2))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,uminus_uminus(X_a),B_2))),sequentially))))))) # label(fact_4509_LIMSEQ__add__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2848 (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_962_dvd_Oless__irrefl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2849 (all V_2 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_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = 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_2)))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> 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_2)) = zero_zero(nat)))) # label(fact_1633_div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2850 (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_135_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2851 (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_1),B) = 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),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_6)),B))))) # label(fact_1945_mod__minus__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2852 (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_2500_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2853 (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_3765_inverse__rat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2854 (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_1109_zdiv__mono2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2855 (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_1766_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2856 (all X_a (real_vector(X_a) -> (all X all Y all Xa_2 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_2)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_2)) = 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_2)))) # label(fact_4696_scaleR__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2857 (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]. 7.58/7.59 2858 (all X_a (real_normed_field(X_a) -> (all Ya all A_3 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)),Ya)),A_3))))) # label(fact_4922_divide_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2859 (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_4400_gcd__exp__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2860 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) = one_one(int))) # label(fact_2732_neg__one__special) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2861 (all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) = one_one(real)) # label(fact_2767_cmod__unit__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2862 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3273_gcd__add1__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2863 (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_4807_Eps__split) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2864 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> (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_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2743_finite__Diff2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2865 (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_3530_dist__triangle) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2866 (all X_a (ordered_semiring(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_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_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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_431_mult__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2867 (all X_a (real_normed_vector(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_2)) -> 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_2)),Xa))))))) # label(fact_4748_scaleR__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2868 (all P_2 all P_1 all Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(P_2) <-> hBOOL(P_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hBOOL(P_2))))) # label(fact_574_imp__le__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2869 (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_3069_prime__dvd__power__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2870 (all Xa all A_2 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_2),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,Xa),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)),Xa)),A_2)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))))) # label(fact_3929_RsetR__zmult__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2871 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,abs_abs(X_a),Ma)),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)))))) # label(fact_980_abs__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2872 (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_1 L_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_1)))) # label(fact_1692_le__Suc__ex) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2873 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,Ma))))) # label(fact_1342_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2874 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N)) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N)))))) # label(fact_1658_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.59 2875 (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_1191_MultInv__zcong__prop2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2876 (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_758_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2877 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all Wa all B_2 all C ((zero_zero(X_a) = ti(X_a,C) -> hAPP(int,X_a,number_number_of(X_a),Wa) = zero_zero(X_a)) & (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),hAPP(int,X_a,number_number_of(X_a),Wa)),C) = ti(X_a,B_2)) <-> hAPP(int,X_a,number_number_of(X_a),Wa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C))))) # label(fact_1777_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2878 (all X_a (linord581940658strict(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) & 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_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2))))))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2879 (all X_a (group_add(X_a) -> (all A_3 all B_2 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2) <-> ti(X_a,B_2) = ti(X_a,A_3))))) # label(fact_733_right__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2880 (all A_3 all B_2 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_3),Ma) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_2),Ma) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma))))) # label(fact_1426_zcong__zmod__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2881 (all B_1 all P_2 all P_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> ((exists Z_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Z_2)) -> (hBOOL(hAPP(int,bool,P_2,X_1)) <-> hBOOL(hAPP(int,bool,P_1,X_1))))) -> ((all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1))))) -> (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),D)))))) -> ((all X_1 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D)))) <-> hBOOL(hAPP(int,bool,P_2,X_1)))) -> ((exists X_1 (hBOOL(hAPP(int,bool,P_2,X_1)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))))) | (exists X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) & (exists Xa_1 (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa_1),X_1))) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),B_1)))))) <-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))))) # label(fact_4957_cpmi) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2882 (all X_a (real_algebra_1(X_a) -> (all R_3 hAPP(real,X_a,of_real(X_a),R_3) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),one_one(X_a))))) # label(fact_4705_of__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2883 (all X_a (order(X_a) -> (all X all Least ((all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_1))) -> 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_4860_min__leastR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2884 (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_1538_le__mod__geq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2885 (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_3588_of__int__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2886 (all Xa all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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,Xa),zero_zero(int)),P_4)))) # label(fact_1551_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2887 (all X_a (semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M))))) # label(fact_1437_of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2888 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),zero_zero(real)))))) # label(fact_2699_real__root__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2889 (all X all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) -> (one_one(real) != B -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,B)),hAPP(real,real,ln,A_1))),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))))))) # label(fact_2046_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2890 (all Z_1 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W),Z_1)) # label(fact_663_real__mult__commute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2891 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2316_sgn__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2892 (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]. 7.58/7.60 2893 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,N_1)))) -> 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_4098_suminf__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2894 (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(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(nat,real,real_1(nat),Y))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(real,nat,natfloor,X)),Y)))) # label(fact_2438_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2895 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> ti(int,A_1) = one_one(int) | ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))))))) # label(fact_796_zcong__square__zless) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2896 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C_1 all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C_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),A_1),B)),C_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),A_6),B_5)),C_1)))))) # label(fact_1290_mod__add__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2897 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)))) # label(fact_462_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2898 (all X_a all X_b (real_normed_vector(X_b) & real_algebra_1(X_b) -> (all G all A_3 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),A_3),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),A_3)),A_2)))))) # label(fact_4488_of__real_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2899 (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)) -> 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_4849_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2900 (all C_1 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_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C_1))))) # label(fact_827_divides__mul__r) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2901 (all Y all X (zero_zero(real) != hAPP(real,real,cos,X) -> (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)) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y)))) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)))))) # label(fact_2442_tan__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2902 (all X_a (monoid_mult(X_a) -> (all Z_1 all W hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3881_power__number__of__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2903 (all Ma all Wa ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> Ma = zero_zero(nat)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> ti(int,Wa) = hAPP(nat,int,semiring_1_of_nat(int),Ma)) <-> Ma = hAPP(int,nat,nat_1,Wa))) # label(fact_1038_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2904 (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_834_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2905 (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_2424_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2906 (all L all F ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_1)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_1))))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_1)),L))) -> ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_1 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_1)),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_4898_increasing__LIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2907 (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_1592_even__times__anything) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2908 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> 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,Na)),Xa),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2672_DERIV__real__root) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2909 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) -> 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)),Na)))) = hAPP(int,nat,nat_1,Na))) # label(fact_3855_card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2910 (all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),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_3),Ma)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_2),Ma)),Ma)))) # label(fact_1321_zcong__zmod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2911 (all K_4 ((zero_zero(quickcheck_code_int) = K_4 -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = zero_zero(int)) & (zero_zero(quickcheck_code_int) != K_4 -> (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & (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))))) # label(fact_3182_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2912 (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_1274_StandardRes__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2913 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),min)),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)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) # label(fact_1636_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2914 (all J all K all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)))) # label(fact_845_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2915 (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_3820_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2916 (all C_1 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_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C_1)),M)))) # label(fact_900_zcong__shift) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2917 (all Va all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(nat,nat,suc,Na))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> 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,Va)))),Na))))) # label(fact_3923_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2918 (all Z_1 hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real)) # label(fact_2999_Im__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2919 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_813_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2920 (all X_a (group_add(X_a) -> (all A_3 all B_2 (ti(X_a,B_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_3) <-> ti(X_a,A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),B_2))))) # label(fact_1922_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2921 (all X_a (semiri456707255roduct(X_a) -> (all Wa all Ya all Xa all Z (ti(X_a,Wa) = ti(X_a,Xa) | ti(X_a,Z) = ti(X_a,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),Wa),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),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),Wa),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Ya)))))) # label(fact_386_crossproduct__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2922 (all M all N hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_639_int__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2923 (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)),N)) # label(fact_2433_cos__npi) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2924 (all X_a (number_semiring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_84_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2925 (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)) -> hAPP(int,int,sgn_sgn(int),I_1) = hAPP(int,int,uminus_uminus(int),one_one(int))) & (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) = one_one(int))) & (zero_zero(int) = ti(int,I_1) -> hAPP(int,int,sgn_sgn(int),I_1) = zero_zero(int)))) # label(fact_2351_zsgn__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2926 (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_2385_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2927 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_2)) -> 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_2))))))) # label(fact_4031_of__real_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2928 (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_4840_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2929 (all C all D_1 all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_3),D_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_2),D_1)),Ma))))) # label(fact_897_zcong__zmult__prop1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2930 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),one_one(real)),X) = ti(X_a,X)))) # label(fact_4703_real__vector_Oscale__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2931 (all X_a (ab_group_add(X_a) -> (all A_3 all B_2 (ti(X_a,A_3) = ti(X_a,B_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2))))) # label(fact_734_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2932 (all X hAPP(real,real,sgn_sgn(real),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,abs_abs(real),X))) # label(fact_2281_real__sgn__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2933 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> hAPP(complex,real,im,hAPP(fun(nat,complex),complex,suminf(complex),X_2)) = 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_2)))) # label(fact_4076_Im_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2934 (all Xa (one_one(int) = hAPP(int,int,abs_abs(int),Xa) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Xa),one_one(int))))) # label(fact_1008_zdvd1__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2935 (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_2712_real__root__pos2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2936 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)))))) # label(fact_2748_card__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2937 (all X_a (real_normed_field(X_a) -> (all R_3 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_3),X)),Y) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y))))) # label(fact_4704_divide_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2938 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(nat,nat,suc,zero_zero(nat)))) <-> hAPP(nat,nat,suc,zero_zero(nat)) = Ma)) # label(fact_1377_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2939 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_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),minus_minus(X_a),A_3),B_2)),zero_zero(X_a))))))) # label(fact_751_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2940 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all L_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),L_2),hAPP(X_a,filter(X_a),at(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),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_3))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4605_LIM__offset__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2941 (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_2476_power__mono__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2942 (all R_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_3),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_3))))) # label(fact_3370_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2943 (all X_a (real_normed_algebra(X_a) & power(X_a) -> (all Ma all X_2 all A_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_2),A_3),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_2)),Ma)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_3),Ma)),sequentially)))))) # label(fact_4490_LIMSEQ__pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2944 (all X_a all P all X (hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)) | -hBOOL(hAPP(X_a,bool,P,X)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2945 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_3)) -> 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_3))))))) # label(fact_4924_isCont__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2946 (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]. 7.58/7.60 2947 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_80_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2948 (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_645_power__even__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2949 (all X_a combi(X_a) = ti(fun(X_a,X_a),combi(X_a))) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2950 (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_3087_prime__coprime__strong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2951 (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_4494_LIMSEQ__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2952 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),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),Xa)),zero_zero(int))))))) # label(fact_2908_floor__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2953 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3406_powr__minus__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2954 (all X_a (number_ring(X_a) & linord1117847801e_zero(X_a) -> (all Ra (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),Ra),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Ra)))))) # label(fact_1807_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2955 (all A_1 ((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,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(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))) & (zero_zero(real) = A_1 -> zero_zero(real) = hAPP(real,real,sgn_sgn(real),A_1)))) # label(fact_2313_sgn__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2956 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_3 hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(real,X_a,of_real(X_a),R_3)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,sgn_sgn(real),R_3))))) # label(fact_2812_sgn__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2957 (all D_3 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),D_3)),D_3))) # label(fact_1227_zdvd__self__abs2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2958 (all M all 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)))) = 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))) # label(fact_1494_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2959 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C_1)))) # label(fact_1287_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2960 (all X all N all Y (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y),X)) -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),Q_4)) = X)))) # label(fact_1568_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2961 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2355_cos__arccos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2962 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat)) = N) # label(fact_620_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2963 (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_1439_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2964 (all X_a all C 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),C),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_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)))) # label(fact_2242_DiffD1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2965 (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_2891_floor__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2966 (all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_3)) -> (exists N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(nat,real,real_1(nat),N_1))) & 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_1),one_one(nat)))),R_3)))))) # label(fact_2461_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2967 (all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,P_1,N_1)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_2834_zero__induct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2968 (all K all Ma all Na (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),Na))) <-> 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),Na)))) # label(fact_4404_gcd__greatest__iff__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2969 (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),A_1),zero_zero(X_a))))) # label(fact_320_add__0__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2970 (all X ((zero_zero(real) = X -> zero_zero(real) = hAPP(real,real,sgn_sgn(real),X)) & (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) = hAPP(real,real,uminus_uminus(real),one_one(real))) & (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_2312_real__sgn__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2971 (all X_a (order(X_a) -> (all X_2 ((all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,N_1)),hAPP(nat,X_a,X_2,M_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_4157_monoI2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2972 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2973 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),pi)) & hAPP(real,real,cos,X_1) = Y & (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)) & Y = hAPP(real,real,cos,Y_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),pi)) -> Y_1 = X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1))))))) # label(fact_2348_cos__total) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2974 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1)))) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_514_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2975 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) -> (exists K_2 ((all N_1 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_2,N_1))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))))) # label(fact_3522_BseqD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2976 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_1907_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2977 (all X_a (linordered_semidom(X_a) -> (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na))))))) # label(fact_110_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2978 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all A_3 all B_2 all Wa ((-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),Wa))) -> (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),Wa)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa))))) & (-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),Wa)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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),Wa))) -> 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_3),hAPP(int,X_a,number_number_of(X_a),Wa))),B_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),hAPP(int,X_a,number_number_of(X_a),Wa)))))))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2979 (all A_3 all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_3),hAPP(int,nat,nat_1,Xa)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_3)),hAPP(int,nat,nat_1,Xa))))) # label(fact_2100_neg__even__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2980 (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_4102_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2981 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))))) # label(fact_3013_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2982 (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_2390_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2983 (all Xa (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Xa),field_char_0_Rats(real))) -> -(all M_2 all N_1 (N_1 != zero_zero(nat) -> (hAPP(real,real,abs_abs(real),Xa) = 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_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_2),N_1) != one_one(nat)))))) # label(fact_3697_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2984 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa),D)) -> 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),Xa)))),hAPP(X_a,X_a,F,Xa)))),combi(X_a))),D),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4644_DERIV__D) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2985 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))))) # label(fact_151_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2986 (all D_3 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),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_3),A_1)))) # label(fact_2879_coprime__rmul2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2987 (all M 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),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4386_gcd__add2__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2988 (all X_a (real_normed_field(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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_2))))))) # label(fact_4025_summable__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2989 (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_275_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2990 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_326_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2991 (all D_3 all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),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_3),B))) # label(fact_3297_coprime__rmult__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2992 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = K_4 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),K_4))))))) # label(fact_1442_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2993 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_2516_even__nat__div__two__times__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2994 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Ya))))) # label(fact_2141_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2995 (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_3612_of__int__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2996 (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_31_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2997 (all X_a (linordered_field(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C_1),B))))))))) # label(fact_1889_divide__left__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2998 (all R_3 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_3),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_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),one_one(int))))))) # label(fact_576_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 2999 (all B all D_3 all A_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),A_1) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int)))) # label(fact_4414_coprime__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3000 (all N all M all R_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_3)) -> (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_3)))))) # label(fact_2894_divides__mul) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3001 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,one_one(int)),hAPP(int,int,number_number_of(int),K_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3755_Fract__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3002 (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_1108_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3003 (all Va all V_1 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Va))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),zero_zero(int)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Va))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> zero_zero(int) = hAPP(int,int,number_number_of(int),Va)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> ti(int,Va) = ti(int,V_1))) <-> hAPP(int,nat,number_number_of(nat),V_1) = hAPP(int,nat,number_number_of(nat),Va))) # label(fact_1620_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3004 (all Xa ((exists A_4 exists B_4 ti(int,Xa) = 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,Xa)))) # label(fact_1067_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3005 (all Y (Y != zero_zero(nat) -> -(all Nat_2 Y != hAPP(nat,nat,suc,Nat_2)))) # label(fact_2833_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3006 (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),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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)))))) # label(fact_1882_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3007 (all Xa all Ra (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Xa)),Ra)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ra)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),Ra)),Xa)))) # label(fact_1991_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3008 (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_7_add__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3009 (all X_a all X_b (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)),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)),A_2)))))) # label(fact_4474_tendsto__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3010 (all X_a all Xa all A_2 (hBOOL(hAPP(X_a,bool,A_2,Xa)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)))) # label(fact_74_mem__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3011 (all X_a (linord1117847801e_zero(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),one_one(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Xa)) <-> 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),Xa))))))) # label(fact_2630_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3012 (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_1840_divide__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3013 (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_642_is__mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3014 (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_1188_inv__is__inv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3015 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1)))) # label(fact_88_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3016 (all X hAPP(real,nat,natfloor,X) = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))) # label(fact_2886_natfloor__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.60 3017 (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_115_int__gr__induct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3018 (all X_a all X_b (topological_space(X_b) -> (all K 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)),K),A_2))))) # label(fact_4486_tendsto__const) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3019 (all X_a all X_b all Z all F all A_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_2))) <-> (exists X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_2)) & hAPP(X_b,X_a,F,X_1) = ti(X_a,Z))))) # label(fact_3659_image__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3020 (all D_3 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),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_3),B)))) # label(fact_2878_coprime__lmul2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3021 (all X_a (idom(X_a) -> (all A_3 all B_2 (ti(X_a,B_2) = ti(X_a,A_3) | hAPP(X_a,X_a,uminus_uminus(X_a),B_2) = ti(X_a,A_3) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_2),B_2))))) # label(fact_1904_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3022 (all A_3 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_3),zero_zero(int)),P_4)) -> hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_3),P_4))))))) # label(fact_3962_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3023 (all Xa (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,uminus_uminus(int),Xa))) <-> hBOOL(hAPP(int,bool,even_odd_even(int),Xa)))) # label(fact_2072_even__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3024 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_2913_floor__add__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3025 (all D_1 all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_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),Xa),Y_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Xa)),hAPP(real,real,F,Y_1))))) -> L = zero_zero(real))))) # label(fact_2660_DERIV__local__min) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3026 (all X_a (ring_div(X_a) -> (all B all B_5 all A_1 all C_1 all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C_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),minus_minus(X_a),A_1),B)),C_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),minus_minus(X_a),A_6),B_5)),C_1)))))) # label(fact_1298_mod__diff__cong) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3027 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> hAPP(fun(int,bool),nat,finite_card(int),A_2) = 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_2)))) # label(fact_3690_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3028 (all P_5 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) -> (hAPP(product_prod(int,int),int,product_snd(int,int),P_5) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5)) & (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))) & (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)))) # label(fact_4371_normalize__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3029 (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_2094_power3__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3030 (all A_1 all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)) # label(fact_1365_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3031 (all X_a (semiring_div(X_a) -> (all A_1 all B 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),div_div(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))) # label(fact_1086_div__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3032 (all Wa all Z ((exists N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1))) = ti(int,Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)))) # label(fact_1451_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3033 (all X_a (number_ring(X_a) -> (all Xa (hAPP(int,X_a,number_number_of(X_a),Xa) = one_one(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),Xa),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))))))) # label(fact_2118_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3034 (all Na 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),Na)),one_one(real))),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Na),Ma)))) # label(fact_3416_int__less__real__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3035 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all 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),times_times(X_a),A_1),B)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C_1)))))) # label(fact_722_dvd__mult__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3036 (all X_a (comm_ring(X_a) & monoid_mult(X_a) -> (all Xa all Na all Ya 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),Xa),hAPP(nat,nat,suc,Na))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Ya),hAPP(nat,nat,suc,Na))) = 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),Xa),Ya)),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),Xa))),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),Ya)),hAPP(nat,fun(nat,nat),minus_minus(nat),Na)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,Na))))))) # label(fact_4254_lemma__realpow__diff__sumr2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3037 (all X_c all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) & topological_space(X_c) -> (all G all C all F all B_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),B_2),hAPP(X_a,filter(X_a),at(X_a),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),G),C),hAPP(X_b,filter(X_b),at(X_b),B_2))) -> ((exists D_2 ((all X_1 (ti(X_a,A_3) != ti(X_a,X_1) & 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_1),A_3))),D_2)) -> hAPP(X_a,X_b,F,X_1) != ti(X_b,B_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C),hAPP(X_a,filter(X_a),at(X_a),A_3))))))))) # label(fact_4633_LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3038 (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_983_abs__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3039 (all K all L (hAPP(int,int,bit0,L) = hAPP(int,int,bit0,K) <-> ti(int,K) = ti(int,L))) # label(fact_43_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3040 (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_3006_Im_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3041 (all P_1 all Na ((exists M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),Na)) & hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (exists X_1 (hBOOL(hAPP(nat,bool,P_1,X_1)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),Na))))))) # label(fact_4560_ex__nat__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3042 (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_1602_odd__pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3043 (all X (X != zero_zero(real) -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),X)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,arctan,X)))) # label(fact_2248_arctan__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3044 (all B_2 all Q_2 all Ra 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),Ra),B_2))),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),Ra),B_2))),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)),Ra)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_2),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),Ra))) # label(fact_3840_adjust__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3045 (all X_a (real_n2089651433ebra_1(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_2266_sgn__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3046 (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_1672_natfloor__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3047 (all Na 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))),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,Na))) = one_one(real)) # label(fact_4267_sumr__cos__zero__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3048 (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_3095_prime__coprime__lt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3049 (all X_a (linordered_idom(X_a) -> (all A_3 (zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),A_3) <-> zero_zero(X_a) = ti(X_a,A_3))))) # label(fact_2261_sgn__0__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3050 (all 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)))) = hAPP(fun(nat,bool),fun(nat,bool),collect(nat),P_1)) # label(fact_3850_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3051 (all X_a (real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))) # label(fact_1939_divide_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3052 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))))) # label(fact_3046_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3053 (all X_a all X_b (uminus(X_b) -> (all A_2 all X_1 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_2),X_1) = hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_2,X_1))))) # label(fact_2953_fun__Compl__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3054 (all X_a (linord20386208strict(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_452_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3055 (all A_9 all B_8 all Y all R_5 (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_5) -> ((-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_5)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_5),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_5)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),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_1125_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3056 (all X_a (real_normed_vector(X_a) -> (all X_2 all K_3 all N_3 ((all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_1)) -> 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_2,N_1))),K_3)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)))))) # label(fact_3524_BseqI2_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3057 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Ya all G 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),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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)),Ya)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4611_divide_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3058 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3059 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Z all F all Xa (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),Xa)))) -> (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),Xa))) -> 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_4024_powser__insidea) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3060 (all S ((all M_2 exists N_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_1),S)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3681_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3061 (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_1892_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3062 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),hAPP(real,real,uminus_uminus(real),B)) = hAPP(complex,complex,cnj,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_2973_complex__cnj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3063 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),Ya)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,Xa)),hAPP(int,nat,nat_1,Ya))))))) # label(fact_1021_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3064 (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_1171_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3065 (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_2059_minus__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3066 (all X_b all X_a (ord(X_b) & order(X_a) -> (all C all F all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B_2)),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),B_2)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_3)))))))) # label(fact_2840_xt6) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3067 (all K 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),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)) = 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))) # label(fact_4250_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3068 (all A_3 (zero_zero(nat) = A_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_3)))) # label(fact_1252_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3069 (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_920_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3070 (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_304_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3071 (all X0 all F all R_2 ((all X_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),hAPP(real,real,uminus_uminus(real),R_2)),R_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(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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_1)))))) -> (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_2)),R_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> 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_4063_DERIV__power__series_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3072 (all F all G ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_1)),hAPP(nat,real,G,N_1)))) -> (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_4156_summable__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3073 (all Ma all K all F ((all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,Ma)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)))))) # label(fact_658_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3074 (all A_3 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_3),P_4)))) # label(fact_2729_wset__fin) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3075 (all B_2 all P_4 all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3)) -> (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),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_3),one_one(int))),P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_3) = ti(int,B_2) | ti(int,A_3) = ti(int,B_2))))) # label(fact_1208_wset__mem__imp__or) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3076 (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_393_power__commutes) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3077 (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_1789_exp__ge__add__one__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3078 (all A_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),A_3),zero_zero(real)),sequentially)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_3,N_1)))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,hAPP(nat,nat,suc,N_1))),hAPP(nat,real,A_3,N_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,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)))),A_3))),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)))),A_3))),sequentially)))))) # label(fact_4529_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3079 (all X_a all C all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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)),F)),A_2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_2)))) # label(fact_4276_setsum__const__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3080 (all X_a (banach(X_a) & real_normed_field(X_a) -> one_one(X_a) = hAPP(X_a,X_a,exp(X_a),zero_zero(X_a)))) # label(fact_1773_exp__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3081 (all X_a (comm_monoid_add(X_a) & power(X_a) -> (all Xa all Ya all Na 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),Xa)),hAPP(nat,fun(nat,nat),minus_minus(nat),Na)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Ya))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,Na))) = 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),Xa))),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),Ya)),hAPP(nat,fun(nat,nat),minus_minus(nat),Na)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,Na)))))) # label(fact_4201_lemma__realpow__rev__sumr) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3082 (all X_a (topological_space(X_a) -> (all G 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),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> ((all X_1 (ti(X_a,X_1) != ti(X_a,A_3) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,G,X_1))))) -> ((all X_1 (ti(X_a,X_1) != ti(X_a,A_3) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,G,X_1)),hAPP(X_a,real,F,X_1))))) -> 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_3))))))))) # label(fact_4801_real__LIM__sandwich__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3083 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) -> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Ya)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),X_1)) & hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))))))) # label(fact_3719_Rats__dense__in__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3084 (all X_a (linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> ti(X_a,B_2) = ti(X_a,D_1))))))) # label(fact_4222_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3085 (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_2086_nat__zminus__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3086 (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_1104_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3087 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_3)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_3),B_2)),zero_zero(int)))))) # label(fact_1079_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3088 (all X_a (linord581940658strict(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,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),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya))),zero_zero(X_a))) <-> ti(X_a,Xa) = zero_zero(X_a) & ti(X_a,Ya) = zero_zero(X_a))))) # label(fact_487_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3089 (all X_a (order(X_a) -> (all Xa all Ya (ti(X_a,Xa) = ti(X_a,Ya) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_567_order__le__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3090 (all B_2 all D_1 all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_2)) & (all E (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),D_1)))) <-> D_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_3),B_2))) # label(fact_3258_gcd__unique__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3091 (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_3023_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3092 (all X all N hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),N)),pi))) = hAPP(real,real,tan,X)) # label(fact_2416_tan__periodic__n) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3093 (all Ma all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_2)) <-> (all Y1 all Y2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y1),Y2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y2),X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y1),X_2)) -> ti(int,Y2) = ti(int,Y1))))) # label(fact_2941_ResSet__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3094 (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_1164_aux______1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3095 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),one_one(nat)))) # label(fact_2883_coprime__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3096 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1) != ti(int,X_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),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_1),D)),Ta))))))) # label(fact_4658_bset_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3097 (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),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)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N))) # label(fact_3476_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3098 (all Na all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),Na)),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),Na)),hAPP(int,real,real_1(int),Ma))))) # label(fact_3414_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3099 (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_1677_natfloor__add__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3100 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,Xa)),hAPP(real,real,ln,Ya))))))) # label(fact_1705_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3101 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_1)))))))) # label(fact_3966_setprod__pos__nat__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3102 (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_2092_neg__zminus__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3103 (all X_a (ordere779506340up_add(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_3)) -> 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3)))))))) # label(fact_211_add__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3104 (all A_1 all B all C_1 all D_3 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_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_3),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) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),C_1) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_1),A_1) -> (exists K_1 exists L_3 exists M_2 (hAPP(int,int,abs_abs(int),C_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),N) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),N) = hAPP(int,int,abs_abs(int),B) & hAPP(int,int,abs_abs(int),A_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N))))))))) # label(fact_3508_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3105 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_165_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3106 (all X_b all X_a (comm_monoid_mult(X_a) -> (all H all G all S all R_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,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_2,Y1),Y2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X1),X2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,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_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,hAPP(X_b,X_a,H,X_1)),hAPP(X_b,X_a,G,X_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,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_4804_setprod_Orelated) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3107 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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),Xa),Ya)),zEven)))) # label(fact_1696_even__times__either) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3108 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_3242_gcd__mult__distrib__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3109 (all X_a all A_3 all P_1 ((exists X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) & (all Y_1 (hBOOL(hAPP(X_a,bool,P_1,Y_1)) -> ti(X_a,Y_1) = ti(X_a,X_1))))) -> (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,A_3)))) # label(fact_4893_some1__equality) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3110 (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_993_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3111 (all X_a (real_normed_field(X_a) -> (all G all Db all F all Xa 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),Xa),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),Xa),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)),Xa),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,Xa))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Db),hAPP(X_a,X_a,F,Xa)))))))))) # label(fact_3858_DERIV__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3112 (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_1440_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3113 (all Na 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)),Na)))))) # label(fact_3851_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3114 (all A_3 all B_2 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Xa),A_3)),hAPP(real,real,hAPP(real,fun(real,real),powr,Xa),B_2)))))) # label(fact_3379_powr__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3115 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2272_sgn__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3116 (all X_1 hAPP(nat,fun(nat,bool),ord_less(nat),X_1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_1))) # label(fact_3856_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3117 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) & real_algebra_1(X_b) -> (all G 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),zero_zero(real)),hAPP(X_a,filter(X_a),at(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),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_3))))))) # label(fact_4638_of__real_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3118 (all X_a (banach(X_a) -> (all F all G ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> 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_1))),hAPP(nat,real,G,N_1))))) -> (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_4044_summable__norm__comparison__test) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3119 (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_892_zcong__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3120 (all X_a (real_algebra(X_a) -> (all X all A_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4719_mult__scaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3121 (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_883_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3122 (all B_2 all P_4 all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),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_3),one_one(int))),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_3),P_4)))))) # label(fact_1205_wset__subset) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3123 (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_2045_power__minus1__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3124 (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_4735_scaleR_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3125 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N)) # label(fact_2388_power__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3126 (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(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)),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))) | 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(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))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))) # label(fact_1638_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3127 (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_2577_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3128 (all I_1 all U_1 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_1)),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_1)),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_1)),K_4)) # label(fact_694_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3129 (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_3268_dvd__gcd__D2__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3130 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3131 (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_888_diff__square) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3132 (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_3650_ex__less__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3133 (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_1655_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3134 (all X_a (ring_char_0(X_a) -> (all Z (zero_zero(int) = ti(int,Z) <-> hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a))))) # label(fact_3591_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3135 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_373_mult__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3136 (all A_1 all B all P_5 all Q_3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3))) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),P_5)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),P_5))))) # label(fact_1009_mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3137 (all R_3 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_3) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3740_quotient__of__denom__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3138 (all Ma all Na ((exists K_1 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1)) = Na) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_1383_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3139 (all Z_1 Z_1 = hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1))) # label(fact_3018_Re__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3140 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C_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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),B)),C_1)))) # label(fact_1288_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3141 (all X_a all C_2 all A_2 all B_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)),A_2),B_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)),B_1),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_2),C_2))))) # label(fact_2247_psubset__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3142 (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)),posDivAlg,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))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))))) # label(fact_1649_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3143 (all A_3 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),abs_abs(real)),A_3))) # label(fact_4907_isCont__abs) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3144 (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_5_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3145 (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)) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2014_mult__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3146 (all A_3 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_3)),hAPP(complex,filter(complex),at(complex),A_3)))) # label(fact_4572_Im_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3147 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,uminus_uminus(int),Ta))))) # label(fact_2066_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3148 (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_242_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3149 (all A_3 all X_2 all Xa (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_2),Xa),sequentially)) -> ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),hAPP(nat,real,X_2,N_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),Xa))))) # label(fact_4517_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3150 (all B all A_1 all C_1 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_1)) = 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_1))) # label(fact_3246_gcd__left__commute__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3151 (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),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),Y)))))) # label(fact_3111_coprime__prime__dvd__ex) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3152 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3153 (all X_a (ordere216010020id_add(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))))))) # label(fact_245_add__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3154 (all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) | hAPP(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))))) # label(fact_1562_mod__exhaust__less__4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.61 3155 (all B_2 all C all A_3 all D_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),D_1) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B_2),C) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A_3)),hAPP(int,int,abs_abs(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B_2)),hAPP(int,int,abs_abs(int),D_1)) <-> hAPP(int,int,abs_abs(int),B_2) = hAPP(int,int,abs_abs(int),A_3) & hAPP(int,int,abs_abs(int),D_1) = hAPP(int,int,abs_abs(int),C))))) # label(fact_4421_coprime__crossproduct__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3156 (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_2412_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3157 (all F all A_3 all B_2 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_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_2)),hAPP(real,real,F,A_3))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3))),B_2)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,A_3)),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_2)),hAPP(real,real,F,A_3))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3))),A_3))) # label(fact_1772_lemma__MVT) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3158 (all X_a (order(X_a) -> (all X_2 ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,X_2,N_1)))) | (all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,N_1)),hAPP(nat,X_a,X_2,hAPP(nat,nat,suc,N_1))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_3949_monoseq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3159 (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_2942_ResSet__SRStar__prop) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3160 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_2415_natceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3161 (all X_a all X_b (real_normed_vector(X_b) -> (all Ra all G all A_3 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),A_3),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),Ra)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),Ra),A_3)),A_2)))))) # label(fact_4751_scaleR__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3162 (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),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))) # label(fact_4419_gcd__non__0__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3163 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),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))) # label(fact_1162_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3164 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_3 hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),R_3)) = hAPP(real,real,abs_abs(real),R_3)))) # label(fact_2808_norm__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3165 (all U all Ma all Na 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)),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)),Na))) <-> 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)),Na)))))) # label(fact_866_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3166 (all X_a (real_normed_vector(X_a) -> (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),Xa)),zero_zero(real))) <-> zero_zero(X_a) = ti(X_a,Xa))))) # label(fact_1997_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3167 (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_4352_finite__nat__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3168 (all Na hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,Na)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),Na)) # label(fact_4149_cos__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3169 (all Va all Na 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,Va)))),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,Va)))),Na))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(nat,nat,suc,Na))) # label(fact_4822_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3170 (all X_a all X_b (metric_space(X_b) & real_n2089651433ebra_1(X_a) -> (all K all L_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(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_3))) -> ti(X_b,K) = ti(X_b,L_2))))) # label(fact_4584_LIM__const__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3171 (all X_a (divisi14063676e_zero(X_a) -> (all A_3 (ti(X_a,A_3) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),A_3))))) # label(fact_2574_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3172 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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_3),Ma))),Ma))) # label(fact_3958_Bnor__prod__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3173 (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_732_dvd__power__same) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3174 (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_1668_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3175 (all X_b all X_a (real_n1866405975lgebra(X_b) & topological_space(X_a) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (zero_zero(X_b) != hAPP(X_a,X_b,F,A_3) -> 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_3))))))) # label(fact_4910_isCont__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3176 (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_2571_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3177 (all A_3 all B_2 ((all D_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_3)) <-> one_one(nat) = D_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_3),B_2)))) # label(fact_2897_coprime) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3178 (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_3440_ceiling__eq3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3179 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all 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),plus_plus(X_a),A_1),B)),C_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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))))) # label(fact_298_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3180 (all X_b all X_a all A_2 all B_1 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_2),B_1) = 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_2)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1))))) # label(fact_4186_Nitpick_Oprod__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3181 (all X_a (linord1117847801e_zero(X_a) -> (all B_2 all C all A_3 ((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),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),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(X_a),C),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_3))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)),B_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_2),C)),A_3)))))) # label(fact_1822_divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3182 (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_2899_coprime__plus1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3183 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all A_3 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_3)),hAPP(real,filter(real),at(real),A_3)))))) # label(fact_4586_of__real_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3184 (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_3461_zgcd__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3185 (all Ma all D_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),D_1) <-> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_1),Q_4) = Ma))) # label(fact_1534_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3186 (all P_1 all Na ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))) -> hBOOL(hAPP(nat,bool,P_1,X_1)))))) # label(fact_4226_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3187 (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_3424_tan__periodic__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3188 (all X_a all X_b (ordere216010020id_add(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> ((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_1),A_2))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_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_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),B_1))))))))) # label(fact_4320_setsum__mono2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3189 (all F all F_2 all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),hAPP(real,real,F_2,X_1))))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),B_2)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3)),hAPP(real,real,F_2,Z_2)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_2)),hAPP(real,real,F,A_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),Z_2))))))) # label(fact_2673_MVT2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3190 (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_226_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3191 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1549_mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3192 (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_3064_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3193 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),X),Y) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_3544_dist__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3194 (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_762_zcong__zpower__zmult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3195 (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_2437_fact__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3196 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_464_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3197 (all X_a all A_2 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),X_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)),X_3),C_2)))))) # label(fact_2113_UnionE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3198 (all X_a all X_b all X_c all X_d all F all 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),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)) = 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))) # label(fact_4042_split__comp__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3199 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,Na)),zero_zero(real))))) # label(fact_4938_isCont__root__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3200 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_397_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3201 (all X_a (real_n2089651433ebra_1(X_a) -> (all Z_1 hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),Z_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3599_norm__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3202 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))) # label(fact_3355_powr__powr) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3203 (all U_1 all X (hAPP(real,real,exp(real),U_1) = X -> hAPP(real,real,ln,X) = U_1)) # label(fact_1760_exp__ln__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3204 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> (exists R_1 exists A_4 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,cos,A_4)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_1),hAPP(real,real,sin,A_4)))))) # label(fact_2559_polar__ex2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3205 (all Xa all Ya (zero_zero(nat) = Ya & zero_zero(nat) = Xa <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Xa),Ya))) # label(fact_3282_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3206 (all Xa (zero_zero(real) = hAPP(real,real,sin,Xa) <-> (exists N_1 (Xa = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_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(nat,bool,even_odd_even(nat),N_1)))) | (exists N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & Xa = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_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)))))))))) # label(fact_2466_sin__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3207 (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_4169_split__paired__The) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3208 (all X_a (linordered_idom(X_a) -> (all Xa all Wa ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),zero_zero(X_a))) | ti(X_a,Xa) = zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa)))) & zero_zero(nat) != hAPP(int,nat,number_number_of(nat),Wa) <-> 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),Xa),hAPP(int,nat,number_number_of(nat),Wa))),zero_zero(X_a))))))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3209 (all L (ti(int,L) = pls <-> pls = hAPP(int,int,bit0,L))) # label(fact_71_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3210 (all V_2 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> 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_2)) = hAPP(nat,nat,suc,zero_zero(nat))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> 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_2)) = 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_2)))))) # label(fact_1582_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3211 (all X_a (order(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,C_1) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1))))))) # label(fact_519_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3212 (all X_a (linordered_field(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1)))))))) # label(fact_1837_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3213 (all T_2 all T_1 (finite_finite(T_2) & finite_finite(T_1) -> finite_finite(sum_sum(T_2,T_1)))) # label(arity_sum___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3214 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> 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),Ra)),X_2)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),A_3))))))) # label(fact_4746_scaleR__right_Osums) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3215 (all Ya 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)),Ya)))) = hAPP(real,real,arccos,Ya)) # label(fact_4164_arccos__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3216 (all Y all X all U_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U_1)) -> (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_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),Y),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U_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_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_1)))))))) # label(fact_2116_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3217 (all Na all N_6 all F ((all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_6)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Na)),hAPP(nat,nat,F,N_6)))))) # label(fact_1522_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3218 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3))))))) # label(fact_484_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3219 (all Na all Ma (zero_zero(nat) = Na & Ma = zero_zero(nat) <-> hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Na)) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_2074_negative__eq__positive) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3220 (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_248_zero__le__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3221 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> isCont(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(X_a,bool)),isCont(X_a,X_b)))) # label(tsy_c_Lim_OisCont_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3222 (all P (fTrue = ti(bool,P) | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3223 (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_2768_complex__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3224 (all X_a all C 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),C),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),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_2),B_1))))) # label(fact_2244_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3225 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_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),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))) <-> (all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 ((all X_1 (ti(X_a,X_1) != ti(X_a,A_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),minus_minus(X_a),X_1),A_3))),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_1)),L_2))),R_1)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))))))) # label(fact_4669_LIM__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3226 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),min),K_4)) # label(fact_2933_add__Min) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3227 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) <-> Xa = hAPP(real,real,exp(real),hAPP(real,real,ln,Xa)))) # label(fact_1791_exp__ln__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3228 (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))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(int)))) # label(fact_1622_int__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3229 (all X_a (linordered_idom(X_a) -> (all X all W (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_2499_power__even__abs__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3230 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_23_zadd__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3231 (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),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_838_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3232 (all X_a all X_b all S all R_2 (ti(fun(product_prod(X_a,X_b),bool),R_2) = ti(fun(product_prod(X_a,X_b),bool),S) <-> (all X_1 all Xa_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),Xa_1)),R_2)) <-> 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),Xa_1)),S)))))) # label(fact_4365_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3233 (all K_4 all 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) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K_4)),L_4)) # label(fact_496_mult__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3234 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_2 all A_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),X_2),A_3),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_2)),hAPP(real,X_a,of_real(X_a),A_3)),sequentially)))))) # label(fact_4489_of__real_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3235 (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_3494_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3236 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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),Ra)),X_2))))))) # label(fact_4743_scaleR__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3237 (all R_3 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X))) # label(fact_4708_cnj_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3238 (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_322_add__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3239 (all N N != hAPP(nat,nat,suc,N)) # label(fact_1277_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3240 (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_729_dvd__triv__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3241 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),Xa)),hAPP(int,X_a,number_number_of(X_a),Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)))))) # label(fact_18_less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3242 (all X_a (real_normed_algebra(X_a) -> (all Xa all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_2)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(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),Xa)),X_2)))))) # label(fact_4014_mult__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3243 (all X_a (real_normed_vector(X_a) -> (all R_3 all X all Xa_2 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_2)) = 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_3),X)),Xa_2)))) # label(fact_4709_scaleR__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3244 (all X_a all X_b (comm_monoid_mult(X_b) -> ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co302546470etprod(X_a,X_b)) = big_co302546470etprod(X_a,X_b))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3245 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (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_2)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1) != ti(int,X_1))))) -> (ti(int,X_1) = ti(int,Ta) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),D) = ti(int,Ta))))))) # label(fact_4661_aset_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3246 (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_1121_zdiv__leq__prop) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3247 (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_3743_quotient__of__number_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3248 (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]. 7.58/7.62 3249 (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_3158_fst__conv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3250 (all X_a all A_2 all B_1 (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_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_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)),A_2),B_1)))) # label(fact_2843_PowD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3251 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F 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(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_2)))))) # label(fact_4193_setsum__abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3252 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M) # label(fact_810_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3253 (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_1324_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3254 (all R_3 all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(complex,real,re,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(complex,real,im,X))) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X)) # label(fact_4769_complex__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3255 (all X_a (linordered_idom(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_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_3)),B_2)) <-> 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_3)),B_2)))))) # label(fact_1981_abs__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3256 (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_137_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3257 (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_3769_floor__Fract) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3258 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z_1),X))))) # label(fact_4979_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3259 (all Code_numeral_2 hAPP(code_code_numeral,nat,code_c271388182l_size,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,code_c271388182l_size,Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2951_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3260 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1)))) # label(fact_2534_even__square) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3261 (all Na 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))),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)),Na)) = zero_zero(real)) # label(fact_4266_lemma__STAR__cos2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3262 (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_972_abs__le__D1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3263 (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_4032_summable__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3264 (all X hAPP(real,real,tan,X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,X))) # label(fact_2404_tan__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3265 (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_986_abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3266 (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_246_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3267 (all Ya all Xa all A_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_3),Xa)),hAPP(real,real,hAPP(real,fun(real,real),log,A_3),Ya)))))))) # label(fact_2036_log__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3268 (all X_a (linordered_field(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1)))))))) # label(fact_1838_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3269 (all X_2 ((all R_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_2,N_1))),R_1)))))) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)))) # label(fact_4890_vanishesI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3270 (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_3094_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3271 (all R_3 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_3),A_1)),N) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_3),N)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3183_DeMoivre2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3272 (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_3237_bezw__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3273 (all X_a (archim1727834104eiling(X_a) -> zero_zero(int) = hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)))) # label(fact_3304_ceiling__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3274 (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_548_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3275 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) -> hAPP(int,nat,nat_1,Na) = 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)),Na)))))) # label(fact_3854_card__bdd__int__set__l) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3276 (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_307_le__imp__0__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3277 (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_1541_zmod__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3278 (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_2797_of__real__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3279 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_103_number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3280 (all X_a (real_algebra_1(X_a) -> (all N hAPP(real,X_a,of_real(X_a),hAPP(nat,real,semiring_1_of_nat(real),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_2811_of__real__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3281 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_1800_ln__div) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3282 (all X_a (comple44059174attice(X_a) -> (all Xa all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_2))))))) # label(fact_1815_complete__lattice__class_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3283 (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_3128_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3284 (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_2364_tan__half) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3285 (all Xa all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Xa),Ma) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),Xa))))) # label(fact_3640_card__nor__eq__noX) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3286 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Xa all C 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)))),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),Xa)),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))),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),Xa))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa))))),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),Xa)),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_4557_termdiffs__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3287 (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),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))))) # label(fact_539_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3288 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_2889_floor__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3289 (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_2429_natceiling__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3290 (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_16_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3291 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,Z_1)))) # label(fact_1491_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.62 3292 (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) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = X))) # label(fact_3747_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3293 (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_3437_floor__eq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3294 (all X_a (real_normed_vector(X_a) -> (all B_2 all F all A_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),F),A_3),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_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2)),sequentially)))))) # label(fact_4506_LIMSEQ__add__const) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3295 (all X_a (metric_space(X_a) -> (all X_2 all L_2 all A_3 ((all S_2 ((all N_1 A_3 != hAPP(nat,real,S_2,N_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),S_2),A_3),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_2),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_2),L_2),hAPP(real,filter(real),at(real),A_3))))))) # label(fact_4659_LIMSEQ__SEQ__conv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3296 (all N (zero_zero(nat) != N -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,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_1508_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3297 (all X all A_1 all 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)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3383_powr__divide2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3298 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_766_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3299 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),min)))) # label(fact_679_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3300 (all M hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3283_gcd__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3301 (all X_a (number_ring(X_a) -> (all V all W all C_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),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C_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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C_1)))) # label(fact_777_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3302 (all X_a (order(X_a) -> (all F ((all X_1 all Y_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_eq(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1))))) -> 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_4819_dvd_OmonoI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3303 (all Xa ((exists Y_1 ti(int,Xa) = 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_1)),one_one(int))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),Xa)))) # label(fact_1639_odd__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3304 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),d22set,A_3)))))) # label(fact_1225_d22set__mem) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3305 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y))))) # label(fact_2360_arccos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3306 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) & Ma != Na <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_400_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3307 (all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) -> (exists N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1))) & -hBOOL(hAPP(nat,bool,P_1,N_1))))))) # label(fact_2756_exists__least__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3308 (all N hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N)) = N) # label(fact_2374_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3309 (all X_a (ab_group_add(X_a) -> (all F all Ma all Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> 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),Na)) = 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),Na),one_one(nat))))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) -> 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),Na))))))) # label(fact_4643_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3310 (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_940_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3311 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Va (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),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),Va)),one_one(X_a)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),hAPP(int,int,number_number_of(int),Va))))))) # label(fact_3336_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3312 (all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_202_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3313 (all A_1 all C_1 all B all D_3 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_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),plus_plus(real),B),D_3)),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_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),D_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2174_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3314 (all F all K all A_3 all B_2 (B_2 != A_3 -> ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),K))) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3)),K) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_2)),hAPP(real,real,F,A_3))))) # label(fact_2669_DERIV__const__ratio__const) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3315 (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_139_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3316 (all Xa ((exists Y_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_1) = ti(int,Xa)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),Xa)))) # label(fact_1625_even__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3317 (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_2689_real__root__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3318 (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_1580_pdivmod__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3319 (all G all F all Xa 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),Xa))),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),Xa))),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),Xa))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Z_2)),hAPP(real,real,F,Xa))))))))) # label(fact_4956_lemma__isCont__inj2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3320 (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),inverse_divide(real),X),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))))))) # label(fact_2043_log__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3321 (all X_a all X_b (comm_ring_1(X_b) & real_normed_algebra(X_b) -> (all X_2 all L_2 all S ((all N_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_1),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_2,N_1)),hAPP(X_a,X_b,L_2,N_1)),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_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),L_2),S)),sequentially)))))) # label(fact_4682_LIMSEQ__setprod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3322 (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_1034_abs__power3__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3323 (all X_a (linord219039673up_add(X_a) -> (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,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),A_3)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))))))) # label(fact_231_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3324 (all Y all X (zero_zero(real) != hAPP(real,real,cos,X) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_2443_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3325 (all X_a (order(X_a) -> (all X_2 ((all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,N_1)),hAPP(nat,X_a,X_2,M_2))))) | (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,M_2)),hAPP(nat,X_a,X_2,N_1))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_3950_monoseq__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3326 (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_526_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3327 (all X_a all F all C all H ((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),C),H),N_1) = hAPP(nat,X_a,F,N_1)) -> ti(X_a,C) = hAPP(nat,X_a,F,zero_zero(nat)))) # label(fact_4359_def__nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3328 (all X_a (order(X_a) -> (all X_2 ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,X_2,N_1)))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_4168_mono__SucI2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3329 (all X_a all A_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_2)) -> ((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_2)) -> 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_2)))))) # label(fact_2750_finite__Union) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3330 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1314_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3331 (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_3405_powr__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3332 (all X_a (division_ring(X_a) -> (all A_3 all B_2 (ti(X_a,B_2) != zero_zero(X_a) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),B_2) = one_one(X_a) <-> ti(X_a,A_3) = ti(X_a,B_2)))))) # label(fact_1855_right__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3333 (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_1161_zdiv__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3334 (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]. 7.58/7.63 3335 (all Xa all Ya (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Xa),Ya))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Ya)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)))) # label(fact_2474_even__product__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3336 (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_3898_finite__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3337 (all A_1 all B all C_1 all N (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C_1),N) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> (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_3501_int__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3338 (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(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)))) # label(fact_1041_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3339 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zOdd))))) # label(fact_1714_odd__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3340 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_3)) -> 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_3))))))) # label(fact_4935_isCont__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3341 (all 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)))) = 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)))) # label(fact_2952_complex__mod__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3342 (all N (hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2529_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3343 (all X_a (metric_space(X_a) -> (all Xa all Ya (ti(X_a,Ya) != ti(X_a,Xa) <-> 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),Xa),Ya))))))) # label(fact_3537_zero__less__dist__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3344 (all X all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,cnj,X)),N) = hAPP(complex,complex,cnj,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),X),N))) # label(fact_2956_complex__cnj__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3345 (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_3139_bezw__non__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3346 (all X_b all X_a all F1 all A_3 all B_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,A_3),B_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),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_3),B_2))))) # label(fact_4067_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3347 (all Na (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Na),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)))) # label(fact_2523_even__even__mod__4__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3348 (all U hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),U)) = hAPP(nat,nat,suc,U)) # label(fact_4966_card__atMost) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3349 (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_3565_times__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3350 (all X_a (real_normed_vector(X_a) -> (all E_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> (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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) -> 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_2,M_2)),hAPP(nat,X_a,X_2,N_1)))),E_2))))))))))) # label(fact_3341_CauchyD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3351 (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]. 7.58/7.63 3352 (all Ta all B_1 all D_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1))))) -> (-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_1),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_1),D)),Ta)))))))) # label(fact_4673_bset_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3353 (all A_3 all D_1 all Na 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_3)),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),Na))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_3),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),Na),one_one(nat)))),D_1))))) # label(fact_4338_arith__series__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3354 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hAPP(real,real,sqrt,X) = zero_zero(real) -> zero_zero(real) = X))) # label(fact_2137_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3355 (all B all Q_3 all R_3 all B_5 all Q_5 all 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_4) = 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_3) -> (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_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_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_584_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3356 (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_364_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3357 (all X_a (comm_semiring_1(X_a) -> (all X all N (ti(X_a,X) = one_one(X_a) | 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_785_dvd__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3358 (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)),N)) # label(fact_2434_cos__npi2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3359 (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_3785_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3360 (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]. 7.58/7.63 3361 (all V_2 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_2))) -> 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_2)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> 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_2))) = 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_2)))) & (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_2)) = zero_zero(nat)))) # label(fact_1634_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3362 (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_2557_Ln_Oaux1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3363 (all X_a all A_2 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_2)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_2)) # label(fact_2845_Pow__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3364 (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_1319_Residues_Oaux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3365 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_1)))))) # label(fact_2851_minf_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3366 (all X_a all X_b all P_1 all Q_1 all X_1 (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_1)) <-> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,P_1))),Q_1)),X_1)))) # label(fact_4071_split__part) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3367 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M)) -> ti(int,X) = zero_zero(int))))) # label(fact_914_Int2_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3368 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all Xa 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)),Xa),hAPP(X_a,X_a,exp(X_a),Xa)))))) # label(fact_2645_DERIV__exp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3369 (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_1048_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3370 (all X_a all X_b all R_2 all 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_2)),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))) <-> 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_2),S)))) # label(fact_4362_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3371 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) # label(fact_1402_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3372 (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_2073_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3373 (all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,cis,A_1)) = hAPP(real,complex,cis,hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3055_cis__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3374 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,im,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_3017_complex__Im__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3375 (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_1653_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3376 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(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)))))))) # label(fact_4195_suminf__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3377 (all X all N_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),N),N_4)) -> (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_4),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2706_real__root__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3378 (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_1467_StandardRes__lbound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3379 (all X_a (cancel_semigroup_add(X_a) -> (all A_3 all B_2 all C (ti(X_a,B_2) = ti(X_a,C) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2))))) # label(fact_295_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3380 (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_3779_abs__rat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3381 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_210_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3382 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists 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),hAPP(real,real,tan,X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))))) # label(fact_2460_lemma__tan__total) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3383 (all A_3 all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_3),Ma)))) # label(fact_3645_RRset__gcd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3384 (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),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1))))) # label(fact_3078_prime__divprod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3385 (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_3239_gcd__dvd2__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3386 (all X all Y (Y != X -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_131_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3387 (all P_4 (hBOOL(hAPP(int,bool,zprime,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)) -> ti(int,M_2) = one_one(int) | ti(int,M_2) = ti(int,P_4))))) # label(fact_798_zprime__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3388 (all Diff all Na all Xa (zero_zero(real) = Xa -> (zero_zero(nat) != Na -> 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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na)) = hAPP(real,real,hAPP(nat,fun(real,real),Diff,zero_zero(nat)),zero_zero(real))))) # label(fact_4257_Maclaurin__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3389 (all X_a (real_normed_algebra(X_a) -> (all Xa all X_2 all A_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_2),A_3),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),Xa)),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),A_3)),sequentially)))))) # label(fact_4482_mult__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3390 (all K_4 all N all M 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) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N)) # label(fact_1544_mod__mult__self4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3391 (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_2368_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3392 (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_122_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3393 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_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_3),B_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_2),A_3))))) # label(fact_3815_one__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3394 (all B_5 all Q_5 all R_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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),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_581_q__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.63 3395 (all X_a all X_b (real_normed_algebra(X_b) -> (all Xa all G all A_3 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),A_3),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),Xa)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Xa),A_3)),A_2)))))) # label(fact_4479_mult__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3396 (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_4694_scaleR_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3397 (all Y_2 all X_2 ((exists A_4 ((all N_1 hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_2,N_1))),A_4))) & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A_4)))) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_2)) -> 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_2)),Y_2)))))) # label(fact_4863_vanishes__mult__bounded) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3398 (all A_2 all P_2 all P_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> ((exists Z_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_1)) -> (hBOOL(hAPP(int,bool,P_1,X_1)) <-> hBOOL(hAPP(int,bool,P_2,X_1))))) -> ((all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1))))) -> (hBOOL(hAPP(int,bool,P_1,X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),D)))))) -> ((all X_1 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D)))) <-> hBOOL(hAPP(int,bool,P_2,X_1)))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_1 ((exists Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),A_2)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa_1),X_1))))) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))))) | (exists X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) & hBOOL(hAPP(int,bool,P_2,X_1)))))))))) # label(fact_4958_cppi) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3399 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> the(X_a) = ti(fun(fun(X_a,bool),X_a),the(X_a)))) # label(tsy_c_HOL_OThe_3_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3400 (all X_a all A_2 all B_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)),A_2),B_1)) -> 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_2)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_2848_Pow__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3401 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (ti(X_a,Y) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),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),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))))))) # label(fact_1877_add__frac__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3402 (all X_a all X_b (real_normed_vector(X_b) -> (all X_2 all L_2 all S ((all N_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_1),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_2,N_1)),hAPP(X_a,X_b,L_2,N_1)),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_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),L_2),S)),sequentially)))))) # label(fact_4683_LIMSEQ__setsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3403 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_3)) <-> 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_3),B_2)))))) # label(fact_3804_zero__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3404 (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_444_mult__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3405 (all F ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_1)))) -> (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_4099_suminf__0__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3406 (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_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1)) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),F,X_1),Y_1))))) -> 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_4153_exE__realizer) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3407 (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_4182_nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3408 (all X_a (real_normed_field(X_a) & field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))) # label(fact_1984_norm__divide) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3409 (all X_a (linordered_idom(X_a) -> (all Xa all Wa (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa),hAPP(int,nat,number_number_of(nat),Wa)))))))) # label(fact_2510_zero__le__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3410 (all X_a (ordered_ring_abs(X_a) -> (all B all A_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | 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)),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,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_1011_abs__eq__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3411 (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_1359_neg__mod__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3412 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_1281_mod__by__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3413 (all X_a (real_normed_field(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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_2)),Ya)) = 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_2)),Ya))))) # label(fact_4011_divide_Osuminf) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3414 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_1339_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3415 (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_174_of__nat__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3416 (all X_a (real_normed_field(X_a) -> (all H_2 all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_2638_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3417 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) <-> Ya = Xa)) # label(fact_961_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3418 (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_486_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3419 (all D_1 all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_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),Xa),Y_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Y_1)),hAPP(real,real,F,Xa))))) -> zero_zero(real) = L)))) # label(fact_2659_DERIV__local__max) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3420 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3136_div__pos__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3421 (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_2632_inv__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3422 (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_15_zless__linear) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3423 (all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_3)) -> (exists N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),R_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)))))))) # label(fact_2463_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3424 (all Na (Na = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,Na),Na)))) # label(fact_2884_coprime__refl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3425 (all X_a all G all A_3 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),A_3),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,A_3)),A_2)))) # label(fact_4533_Im_Otendsto) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3426 (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_2539_fact__mono__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3427 (all R_3 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_3)) -> -(all S_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),S_1)) -> (all T_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),T_4)) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),S_1),T_4) != R_3)))))) # label(fact_3736_obtain__pos__sum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3428 (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,int,hAPP(int,fun(nat,int),power_power(int),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,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)))) & (-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_3931_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3429 (all X_a (real_normed_algebra(X_a) -> (all Xa all A_3 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),Xa)),A_3))))) # label(fact_4914_mult__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3430 (all X_a (ring_11004092258visors(X_a) -> (all Xa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa) = one_one(X_a) <-> ti(X_a,Xa) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) | one_one(X_a) = ti(X_a,Xa))))) # label(fact_1965_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3431 (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_205_zle__linear) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3432 (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))))) -> zero_zero(nat) = N | hAPP(nat,nat,suc,zero_zero(nat)) = N)) # label(fact_1502_less__2__cases) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3433 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_844_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3434 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min_1(X_a)) = min_1(X_a))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3435 (all X_a (metric_space(X_a) -> (all X_2 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_2),L_2),sequentially)) -> hAPP(fun(nat,X_a),X_a,lim(X_a),X_2) = ti(X_a,L_2))))) # label(fact_4455_limI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3436 (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_2088_zabs__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3437 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_217_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3438 (all X_a (linorder(X_a) -> (all Xa all Ya (ti(X_a,Ya) = ti(X_a,Xa) <-> hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Ya) = hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Xa))))) # label(fact_4965_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3439 (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_917_zpower__zdvd__prop1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3440 (all X_a all B_1 all A_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)),B_1),A_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_1),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2))))) # label(fact_1796_Union__upper) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3441 (all Ma all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na) = hAPP(nat,nat,suc,zero_zero(nat)) <-> Ma = zero_zero(nat) & Na = hAPP(nat,nat,suc,zero_zero(nat)) | Na = zero_zero(nat) & Ma = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1379_one__is__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3442 (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_4843_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3443 (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_3238_gcd__dvd1__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3444 (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(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_4))))) # label(fact_1046_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3445 (all X_a (linordered_field(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)))))))) # label(fact_1891_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3446 (all Xa (-hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Xa),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2504_odd__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3447 (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_491_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3448 (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_4493_LIMSEQ__imp__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3449 (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_448_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3450 (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_1595_odd__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3451 (all X_a (linord626643107strict(X_a) -> (all V all U_1 all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_542_convex__bound__lt) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3452 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (exists N_1 ti(int,K_4) = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_345_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3453 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_1 (ti(X_a,C_1) != 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_1085_div__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3454 (all X_a (metric_space(X_a) -> (all B_2 all X_2 all A_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_2),A_3),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_2),B_2),sequentially)) -> ti(X_a,B_2) = ti(X_a,A_3)))))) # label(fact_4464_LIMSEQ__unique) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3455 (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_3039_complex__add__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3456 (all X_a (ordered_ring(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))))))) # label(fact_435_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3457 (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_429_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3458 (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_3083_prime__divexp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3459 (all B all D_3 all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),A_1) = one_one(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),B) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat)))) # label(fact_3294_coprime__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3460 (all X_a (linordered_field(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),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_3),C)),B_2))))))) # label(fact_1869_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3461 (all R_3 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_3)),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_3),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),Y))) # label(fact_2816_complex__of__real__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3462 (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_1097_div__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3463 (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_35_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3464 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),W)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),W))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min)),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_1585_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3465 (all X_a (linordered_idom(X_a) -> (all Wa 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),Wa)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z)))))) # label(fact_3604_of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3466 (all N zero_zero(real) = hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_3007_complex__Im__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3467 (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_3444_ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3468 (all X_a (linordered_semidom(X_a) -> (all B all C_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))))))) # label(fact_179_pos__add__strict) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3469 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),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,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,twoSqu1091635170sum2sq,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))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))))) # label(fact_580_smaller_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3470 (all X_a (semiring_div(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_2),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),div_div(X_a),B_2),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),C),A_3))))))))) # label(fact_1076_div__dvd__div) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3471 (all X_a (field_inverse_zero(X_a) -> (all Xa (ti(X_a,Xa) = one_one(X_a) <-> hAPP(X_a,X_a,inverse_inverse(X_a),Xa) = one_one(X_a))))) # label(fact_2566_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3472 (all X_a (linord581940658strict(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,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),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya)))) <-> zero_zero(X_a) != ti(X_a,Xa) | ti(X_a,Ya) != zero_zero(X_a))))) # label(fact_489_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3473 (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_3609_of__int__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3474 (all X_a (archim1727834104eiling(X_a) -> (all X all 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))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),Z_1)))) # label(fact_3623_floor__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3475 (all X hAPP(int,nat,nat_1,hAPP(real,int,archimedean_ceiling(real),X)) = hAPP(real,nat,natceiling,X)) # label(fact_3309_natceiling__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3476 (all B all A_1 (ti(int,B) != zero_zero(int) | 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_4379_div__gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3477 (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_1337_add__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3478 (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)))) # label(fact_858_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3479 (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_3385_real__of__int__div4) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3480 (all X all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),B)) -> hAPP(int,int,abs_abs(int),X) = one_one(int))))) # label(fact_4429_coprime__common__divisor__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3481 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_85_number__of__Pls) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3482 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> 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_2)) = 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_2)))) # label(fact_2839_card__Pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3483 (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_1062_Int2_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3484 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Xa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,Xa)))))) # label(fact_1723_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3485 (all X_a (topological_space(X_a) -> (all F all L 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),L),hAPP(X_a,filter(X_a),at(X_a),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,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_3))))))) # label(fact_4577_LIM__rabs) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3486 (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_2259_sin__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3487 (all X_4 all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_4)) -> 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_5),X_4)))))) # label(fact_2708_real__root__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3488 (all Ya 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)),Ya)))) = hAPP(real,real,arcsin,Ya)) # label(fact_4160_arcsin__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3489 (all K all F all Na ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),Na)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_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,Na))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),Na)) & ti(int,K) = hAPP(nat,int,F,I_2))))))) # label(fact_1066_int__val__lemma) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3490 (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_353_le__antisym) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3491 (all P_1 all A_3 all B_2 (-(-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2)) | (exists D_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_2),D_2) = A_3 & -hBOOL(hAPP(nat,bool,P_1,D_2))))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_3),B_2))))) # label(fact_859_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3492 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C_1 all D_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_3)) = 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_1),D_3))))) # label(fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3493 (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_3196_rcis__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3494 (all Xa 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),Xa))),hAPP(real,real,sin,Xa)))) # label(fact_4123_sin__converges) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3495 (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_3901_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3496 (all X_a (real_normed_algebra(X_a) -> (all A_1 all R_3 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),B))))) # label(fact_4718_mult_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3497 (all X_a (archim1727834104eiling(X_a) -> archimedean_ceiling(X_a) = ti(fun(X_a,int),archimedean_ceiling(X_a)))) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3498 (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))))) != zero_zero(nat))) # label(fact_3903_card__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3499 (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),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4)))) # label(fact_2187_z3mod__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3500 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_831_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3501 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_1957_right__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3502 (all Ma all Na hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),Na)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),hAPP(nat,nat,suc,Na))) # label(fact_4150_diff__Suc) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3503 (all X_a all X_b all F all A_2 all B_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,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_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),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),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_2),B_1))))) # label(fact_3657_image__diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3504 (all X_a (ring(X_a) -> (all A_3 all E_2 all C all B_2 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)),E_2)),C) = ti(X_a,D_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),E_2)),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),B_2),E_2)),D_1))))) # label(fact_753_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3505 (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,N) = ti(int,M)))))) # label(fact_761_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3506 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3507 (all X_a all X_b all A_2 all B_1 (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_2),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_3207_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3508 (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_3214_fact__less__mono__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3509 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),one_one(nat)) = one_one(nat)) # label(fact_3277_gcd__1__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3510 (all N all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),D_3)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),D_3))))) # label(fact_2419_real__of__nat__div) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3511 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all I all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),A_2)) -> 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_2)))))))) # label(fact_3980_dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3512 (all D_1 hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than2,D_1) = hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(fun(int,bool),fun(int,bool)),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combb(fun(int,bool),fun(int,bool),int),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int))))) # label(fact_4101_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3513 (all Na all S (hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),S)) -> ((all X_1 (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),S)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_1)))) -> ((all X_1 (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),S)) -> Na = hAPP(fun(int,bool),nat,finite_card(int),X_1))) -> 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)),Na)),S))))) # label(fact_4443_card__setsum__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3514 (all A_3 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Xa)) -> 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_3)),hAPP(real,fun(nat,real),power_power(real),Xa))),zero_zero(real)),sequentially)))) # label(fact_4461_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3515 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)) # label(fact_807_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3516 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1)))) # label(fact_3624_ceiling__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3517 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))) # label(fact_932_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3518 (all W hAPP(int,complex,ring_1_of_int(complex),W) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_3595_complex__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3519 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),Xa)),hAPP(real,real,exp(real),Ya))))) # label(fact_1754_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3520 (all G all Xa all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),Xa),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)),Xa),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,hAPP(real,real,G,Xa))),Ma))))) # label(fact_3883_DERIV__fun__sin) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3521 (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_948_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3522 (all X_a (real_normed_algebra(X_a) -> (all C 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)),F)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))) # label(fact_4016_suminf__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3523 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)) -> (K_4 != hAPP(nat,nat,suc,I_1) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> hAPP(nat,nat,suc,J_1) != K_4))))) # label(fact_2753_lessE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3524 (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_1325_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3525 (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_3491_zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3526 (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_2711_real__root__pos__mult__exp) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3527 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_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_3)),B_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_2)),A_3)))))) # label(fact_1901_minus__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3528 (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_99_power2__less__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3529 (all X_a all P_1 all A_3 (hBOOL(hAPP(X_a,bool,P_1,A_3)) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> ti(X_a,A_3) = ti(X_a,X_1))) -> ti(X_a,A_3) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))) # label(fact_4814_some__equality) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3530 (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_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_2),hAPP(X_a,filter(X_a),at(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),G),M_1),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4575_LIM__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3531 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X))))) # label(fact_3319_ceiling__minus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3532 (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_2565_inverse__1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3533 (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_2147_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3534 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),Xa)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),hAPP(int,int,bit1,pls))))))) # label(fact_62_less__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3535 (all X_a (real_div_algebra(X_a) -> (all X (X != zero_zero(real) -> 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_2815_nonzero__of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3536 (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_2296_sin__cos__squared__add) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3537 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y)) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y))) # label(fact_3027_Re_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3538 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)),B_2))) & (-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),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C))))))))) # label(fact_1821_le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3539 (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_778_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3540 (all X_a (real_normed_algebra(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> 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_2)),Ya))))))) # label(fact_4128_mult__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3541 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,Na)),Xa))))) # label(fact_4939_isCont__root__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3542 (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_2679_odd__real__root__pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3543 (all X_a (group_add(X_a) -> (all A_3 (hAPP(X_a,X_a,uminus_uminus(X_a),A_3) = zero_zero(X_a) <-> ti(X_a,A_3) = zero_zero(X_a))))) # label(fact_1934_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3544 (all A_2 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_2),Ma)) -> hAPP(int,fun(int,bool),norRRset,Ma) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),Ma)),A_2)))) # label(fact_3653_RRset2norRR__eq__norR) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3545 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Xa),Ya)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))) # label(fact_830_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3546 (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_4730_scaleR__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3547 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all Xa all G 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),G),L),hAPP(X_a,filter(X_a),at(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),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),Xa)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Xa),L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4589_mult__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3548 (all X_a (comm_semiring_1(X_a) -> (all B all A_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C_1)) -> 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_1))))))) # label(fact_726_dvd__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3549 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all Ra all F all L_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),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ra)) -> (exists S_1 ((all X_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_1),A_3)),S_1)) & ti(X_a,X_1) != ti(X_a,A_3) -> 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_1)),L_2)),Ra)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1))))))))) # label(fact_4678_metric__LIM__D) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3550 (all Xa all Na all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Na),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),Ya))) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ya),Na) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Xa),Na))) # label(fact_1378_zmod__eq__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3551 (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_1010_abs__mult__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3552 (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_2618_right__inverse) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3553 (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_1912_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3554 (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_3398_floor__minus__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3555 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_4)) -> (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_4)))))))) # label(fact_187_power__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3556 (all X_a all P_1 all Xa (hBOOL(hAPP(X_a,bool,P_1,Xa)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4808_someI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3557 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K all Xa hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,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),Xa)))))) # label(fact_4580_LIM__const) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3558 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,X))))) # label(fact_2350_sin__arccos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.64 3559 (all X_a all F all A_2 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_2)) = 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_2)) # label(fact_4278_int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3560 (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_2168_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3561 (all Xa all Ya 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Xa)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya))))) # label(fact_635_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3562 (all C_1 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_1),N) -> (exists R_1 exists S_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),R_1),N) = A_1 & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),S_1),N) = B))))) # label(fact_3450_coprime__pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3563 (all A_3 all Ma all Xa (ti(int,Xa) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),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)),Xa)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),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_3),Ma))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Xa),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma))))))) # label(fact_3959_Bnor__prod__power) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3564 (all X_b all X_c all X_a (comm_monoid_add(X_a) -> (all F all B_1 all 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),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_1)),A_2) = 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_2)),B_1)))) # label(fact_4243_setsum__commute) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3565 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,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),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3))))))) # label(fact_4322_setsum__mono__zero__right) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3566 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),min)))) # label(fact_688_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3567 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y)) -> (exists X_1 (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),Y),one_one(real)))) & hAPP(real,real,exp(real),X_1) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))))) # label(fact_1820_lemma__exp__total) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3568 (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_616_mult__le__mono2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3569 (all Xa 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))),Xa))),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),Xa)),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),Xa)) # label(fact_4173_floor__real__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3570 (all X_a (divisi14063676e_zero(X_a) -> (all A_3 all B_2 (ti(X_a,B_2) = ti(X_a,A_3) <-> hAPP(X_a,X_a,inverse_inverse(X_a),B_2) = hAPP(X_a,X_a,inverse_inverse(X_a),A_3))))) # label(fact_2569_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3571 (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_2776_complex_Orecs) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3572 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3573 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2384_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3574 (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_2 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_2)) -> (all N_1 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_1)))),E))))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4314_summable__Cauchy) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3575 (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(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_1624_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3576 (all X_a (linord581940658strict(X_a) -> (all A_3 all C all B_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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_2),C))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) & 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),C),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)))))) # label(fact_441_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3577 (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_3033_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3578 (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)) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_2018_divide__minus1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3579 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B_2)),C)) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_3)),C)))))))) # label(fact_2860_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3580 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all Xa all Ya (hAPP(int,X_a,number_number_of(X_a),Ya) = hAPP(int,X_a,number_number_of(X_a),Xa) <-> ti(int,Ya) = ti(int,Xa))))) # label(fact_40_eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3581 (all Na all Xa 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)),Na)),Xa),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3920_DERIV__pow) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3582 (all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) & hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(X_a,nat,F,X_1) & (all Xa_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa_1),A_2)) -> (ti(X_a,X_1) != ti(X_a,Xa_1) -> hAPP(X_a,nat,F,Xa_1) = 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_2) = hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_4283_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3583 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,suc,zero_zero(nat))),A_1))) # label(fact_2888_coprime__Suc0_H) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3584 (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_440_not__square__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3585 (all Xa 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),Xa),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),Xa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_4130_Ln_Oaux2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3586 (all Xa 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))))),Xa),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,Xa))),hAPP(real,real,sin,Xa))))) # label(fact_3937_DERIV__sin__realpow2a) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3587 (all X X = hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,zero_zero(nat))),X)) # label(fact_2675_real__root__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3588 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),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_1732_ln__add__one__self__le__self2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3589 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),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)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),Z)))))) # label(fact_3636_ceiling__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3590 (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_1896_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3591 (all X_a (linord581940658strict(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2)))))))) # label(fact_485_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3592 (all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> A_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)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_2)))) # label(fact_3688_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3593 (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_3844_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3594 (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_945_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3595 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B all C_1 all D_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(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_1),D_3)))),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_1))),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_3)))))))) # label(fact_1014_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3596 (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_3066_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3597 (all Z_1 zero_zero(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_1)),Z_1)) # label(fact_96_odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3598 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1267_inv__inv__aux) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3599 (all N 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) = one_one(int)) # label(fact_4394_coprime__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3600 (all X_a all C all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)))) # label(fact_2235_ComplE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3601 (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_3262_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3602 (all X one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),zero_zero(real))) # label(fact_3376_powr__zero__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3603 (all G all F all Xa 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),Xa))),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),Xa))),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_1 (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_1),hAPP(real,real,F,Xa))))) & 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_1),hAPP(real,real,F,Xa)))),E)) -> Y_1 = hAPP(real,real,F,hAPP(real,real,G,Y_1)))))))))) # label(fact_4954_isCont__inv__fun__inv) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3604 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_209_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3605 (all N -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1600_not__neg__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3606 (all X_a (linord20386208strict(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_481_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3607 (all X_a (real_n2089651433ebra_1(X_a) -> (all F hAPP(nat,X_a,F,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)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a))))))) # label(fact_4000_powser__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3608 (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_802_dvd__diffD) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3609 (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_3141_mod__int__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3610 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (N != hAPP(nat,nat,suc,M) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))))) # label(fact_1328_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3611 (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_430_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3612 (all X_a (order(X_a) -> (all C_1 all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1))))))) # label(fact_521_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3613 (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_1987_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3614 (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_2048_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3615 (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_2080_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3616 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)) != zero_zero(real)) # label(fact_2475_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3617 (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_2838_dvdE) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3618 (all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min),hAPP(int,int,bit0,L_4))) # label(fact_782_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3619 (all X_a all A_3 all F all Va all Na 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_3),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),Va)),Na)) = 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,Va)))),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_3),F),Na)),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,Va)))),Na)))) # label(fact_4135_nat__case__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3620 (all X_a (semiring_div(X_a) -> (all C_1 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_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),C_1)),A_1))))) # label(fact_1094_dvd__div__mult) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3621 (all S ((all M_2 exists N_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_1),S)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3680_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3622 (all X_a (metric_space(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) <-> (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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),hAPP(nat,X_a,X_2,M_2)),hAPP(nat,X_a,X_2,N_1))),E)))))))))))) # label(fact_3548_Cauchy__def) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3623 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = ti(int,K_4))) # label(fact_3481_zgcd__zmult__eq__self) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3624 (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_1864_frac__le) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3625 (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_2033_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3626 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),zero_zero(real)))))) # label(fact_2696_real__root__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3627 (all X hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X)) # label(fact_2954_complex__cnj__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3628 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all Na 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),Na),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),Na))))) # label(fact_4570_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3629 (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_463_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3630 (all X_a (archim1804426504_field(X_a) -> (all X exists N_1 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_1)))))) # label(fact_2835_ex__less__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3631 (all K_4 ((K_4 != zero_zero(code_code_numeral) -> (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(code_code_numeral) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)) = hAPP(code_code_numeral,int,code_int_of,K_4)) & (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)))))))) & (zero_zero(code_code_numeral) = K_4 -> zero_zero(int) = hAPP(code_code_numeral,int,code_int_of,K_4)))) # label(fact_1684_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3632 (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)) -> zero_zero(X_a) = ti(X_a,A_1))))) # label(fact_721_dvd__0__left) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3633 (all A_1 all B ((zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) & (hAPP(int,int,hAPP(int,fun(int,int),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)))) # label(fact_2089_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3634 (all N hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,quickcheck_of_int,N)) = ti(int,N)) # label(fact_3560_int__of__of__int) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3635 (all X_a (linordered_idom(X_a) -> (all A_3 all Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) <-> 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_3),Na))))))) # label(fact_2488_zero__le__power__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3636 (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_797_zcong__square) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3637 (all Wa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)) | ti(int,Z) = ti(int,Wa) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))))) # label(fact_60_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3638 (all Xa all Ya (hAPP(complex,real,im,Xa) = hAPP(complex,real,im,Ya) & hAPP(complex,real,re,Xa) = hAPP(complex,real,re,Ya) <-> Xa = Ya)) # label(fact_3022_complex__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3639 (all Xa 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)))),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),Xa)),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,Xa)))) # label(fact_4133_cos__paired) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3640 (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_418_add__leD1) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3641 (all X_b all X_a (real_normed_vector(X_a) & real_normed_vector(X_b) -> (all F all L_2 all A_3 ((all R_1 (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_1 (ti(X_a,X_1) != ti(X_a,A_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),minus_minus(X_a),X_1),A_3))),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_1)),L_2))),R_1)))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4688_LIM__I) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3642 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_357_le__refl) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3643 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ((zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = 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_1857_divide__self__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3644 (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_4040_summable__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3645 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,inverse_inverse(X_a),A_1) != zero_zero(X_a))))) # label(fact_2575_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3646 (all Xa (zero_zero(real) = hAPP(real,real,cos,Xa) <-> (exists N_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_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)))))) = Xa & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))) | (exists N_1 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_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))))) = Xa & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))))) # label(fact_2467_cos__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3647 (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_499_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3648 (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_354_le__trans) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3649 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1368_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3650 (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_2003_abs__if) # label(axiom) # label(non_clause). [assumption]. 7.58/7.65 3651 (all F all Ya all G all Xa (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),F),Ya)) -> 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),Xa),Ya)))))) # label(fact_4132_sums__if) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3652 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)) # label(fact_159_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3653 (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_4981_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3654 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> -(all N_1 hAPP(nat,int,semiring_1_of_nat(int),N_1) != ti(int,K_4)))) # label(fact_344_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3655 (all X_a (field_char_0(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3)),field_char_0_Rats(X_a))))))) # label(fact_3714_Rats__minus) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3656 (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_516_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3657 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),B)),C_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),times_times(X_a),A_1),B)),C_1)))) # label(fact_1284_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3658 (all Ma all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),Ma)))) # label(fact_1340_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3659 (all Y_2 all Ya all X_2 all Xa (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_2),Xa),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_2),Ya),sequentially)) -> ((exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_2,N_1)),hAPP(nat,real,Y_2,N_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya)))))) # label(fact_4519_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3660 (all A_3 all B_2 ((all D_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_2),B_2)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = D_2)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_3),B_2) = one_one(nat))) # label(fact_3321_coprime__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3661 (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))) -> 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)))) & (-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_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))) = one_one(X_b)))))) # label(fact_3934_power__number__of__odd__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3662 (all Xa 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)),Xa))))) # label(fact_3870_bdd__nat__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3663 (all X hAPP(rat,real,ratreal,hAPP(rat,rat,inverse_inverse(rat),X)) = hAPP(real,real,inverse_inverse(real),hAPP(rat,real,ratreal,X))) # label(fact_3794_real__inverse__code) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3664 (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_199_add__pos__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3665 (all L all U hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U)),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))) # label(fact_4563_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3666 (all X_a (ordered_ab_group_add(X_a) -> (all B_2 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,uminus_uminus(X_a),B_2)),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)))))) # label(fact_1900_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3667 (all N all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_1 (A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_1),hAPP(nat,nat,suc,N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)))))) # label(fact_1519_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3668 (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(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)) = 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))))) # label(fact_1463_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3669 (all X_a all C all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)) -> 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)),X_2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_2))))) # label(fact_4290_setsum__const2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3670 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)) & hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_595_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3671 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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),Xa),Na)),zEven))))) # label(fact_1726_power__preserves__even) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3672 (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> ((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)),hAPP(int,int,F,X_1))))) -> 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_2)))))) # label(fact_4332_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3673 (all B all A_1 (ti(int,B) != zero_zero(int) | ti(int,A_1) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))) = one_one(int))) # label(fact_3483_div__zgcd__relprime) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3674 (all A_3 all B_2 all Wa (hAPP(int,real,number_number_of(real),Wa) = A_3 & B_2 = zero_zero(real) <-> hAPP(int,complex,number_number_of(complex),Wa) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2))) # label(fact_2760_Complex__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3675 (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_6),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) -> -(ti(X_a,A_6) = ti(X_a,A_1) -> ti(X_b,B) != ti(X_b,B_5)))) # label(fact_3155_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3676 (all X_a (linordered_idom(X_a) -> (all Xa all Wa (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),Wa))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),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),Xa),hAPP(int,nat,number_number_of(nat),Wa))),zero_zero(X_a))))))) # label(fact_2511_power__less__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3677 (all X_a (real_normed_vector(X_a) -> (all Xa all X_2 all A_3 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_2),A_3)) -> 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_2)),Xa)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa))))))) # label(fact_4747_scaleR__left_Osums) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3678 (all X_a all X_b all F all A_2 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_2))) # label(fact_1268_transfer__morphismI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3679 (all R_3 all S_3 all T_5 all R_4 all S_4 all M all T_6 all 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_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_3) -> 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_4),R_3)),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_4),R_3)),T_5))),N)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_4),R_3)))) # label(fact_1458_xzgcda__linear__aux2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3680 (all X_a (real_normed_field(X_a) -> (all C all Xa 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)),Xa),C))))) # label(fact_2649_DERIV__cmult__Id) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3681 (all P_1 all A_3 all B_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_3),B_2))) <-> (all D_2 (A_3 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_2),D_2) -> hBOOL(hAPP(nat,bool,P_1,D_2)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_860_nat__diff__split) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3682 (all Ma all Na (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na))) <-> -(-hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma))))) # label(fact_2468_odd__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3683 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_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_1355_mod__mult__self1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3684 (all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2528_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3685 (all Na all Va (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(int,nat,number_number_of(nat),Va))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) # label(fact_3924_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.65 3686 (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_4871_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3687 (all A_3 all B_2 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Xa),A_3)),hAPP(real,real,hAPP(real,fun(real,real),powr,Xa),B_2))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2))))) # label(fact_3403_powr__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3688 (all X_a (order(X_a) -> (all Na all N_6 all F ((all N_1 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,hAPP(nat,nat,suc,N_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_6)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,Na)),hAPP(nat,X_a,F,N_6)))))))) # label(fact_1579_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3689 (all L all K ((ti(int,K) = 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)),zero_zero(int))) & (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)),product_Pair(int,int),zero_zero(int)),K) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)) & (ti(int,L) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(int,int,sgn_sgn(int),K)),hAPP(int,int,sgn_sgn(int),L))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))))))) # label(fact_4096_divmod__int__code) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3690 (all X_a (dist_norm(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_0_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3691 (all X_b all X_a (banach(X_b) & real_normed_field(X_a) -> (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_1 (zero_zero(X_a) != ti(X_a,H_1) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(nat,X_b,hAPP(X_a,fun(nat,X_b),G,H_1),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,F,N_1)),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_4650_lemma__termdiff5) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3692 (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_4832_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3693 (all X_a all X_b all F all A_3 all B_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),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_3),B_2))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_3),B_2)))) # label(fact_4069_splitD) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3694 (all T_1 comple44059174attice(filter(T_1))) # label(arity_Limits_Ofilter___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3695 (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)),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)) = 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)) # label(fact_3106_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3696 (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_1664_natfloor__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3697 (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_2541_of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3698 (all A_1 all Q_3 all R_3 (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_3))) -> (zero_zero(int) != ti(int,A_1) -> zero_zero(int) = ti(int,R_3)))) # label(fact_1614_self__remainder) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3699 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),B_1),A_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_2),B_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1))))) # label(fact_2736_card__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3700 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_1263_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3701 (all D_3 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),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_3),B) = one_one(int))) # label(fact_4416_coprime__rmult__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3702 (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]. 7.70/7.66 3703 (all X_a all X_b all C 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,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),P_4)))) # label(fact_4089_splitI2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3704 (all X_a (linordered_field(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2601_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3705 (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_2038_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3706 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zEven))))) # label(fact_1698_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3707 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),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)),Xa),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,Xa)),E_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D),hAPP(X_a,X_a,G,Xa)))))))))) # label(fact_3857_DERIV__mult_H) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3708 (all X_b all X_a (real_normed_vector(X_b) & metric_space(X_a) -> (all G 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),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(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),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4770_scaleR_OLIM__prod__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3709 (all X_a (dense_linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1))))))) # label(fact_4553_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3710 (all X_a (comple1803745165norder(X_a) -> (all A_3 all S ((exists X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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),S)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),S))))))) # label(fact_1818_less__Sup__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3711 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Xa),Ya)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))))) # label(fact_470_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3712 (all Xa all Ya all Z (Ya = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),Z) <-> Xa = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Ya),Z))) # label(fact_1211_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3713 (all A_3 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_3),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_3),P_4))),one_one(int)),P_4)))))) # label(fact_3961_wset__zcong__prod__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3714 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),zero_zero(nat))) # label(fact_3280_gcd__0__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3715 (all X_a (cancel_semigroup_add(X_a) -> (all B_2 all A_3 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_3) <-> ti(X_a,C) = ti(X_a,B_2))))) # label(fact_294_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3716 (all X_a (real_normed_field(X_a) -> (all K all Xa 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)),Xa),zero_zero(X_a)))))) # label(fact_3889_DERIV__const) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3717 (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_3118_divmod__nat__base) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3718 (all M all N hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_20_zpower__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3719 (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_1135_Euler__Criterion) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3720 (all X_a (number_semiring(X_a) -> (all V_2 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_2)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)) = 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_2))))))) # label(fact_305_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3721 (all X_a (real_n1866405975lgebra(X_a) -> (all R_3 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_3),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_3)) -> 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_3)))))))) # label(fact_2582_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3722 (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_3387_le__floor) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3723 (all Na hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),Na)) # label(fact_4345_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3724 (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_3375_powr__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3725 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_2 all A_3 (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_3))) -> (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_2))) -> 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_3))),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_2)),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_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_2))))))))) # label(fact_4648_Cauchy__product__sums) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3726 (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_1975_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3727 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = P_5 | -hBOOL(hAPP(nat,bool,even_odd_even(nat),P_5)))) # label(fact_3104_prime__odd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3728 (all X hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_650_four__x__squared) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3729 (all P_5 hAPP(product_prod(int,int),rat,frct,P_5) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) # label(fact_3800_Frct__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3730 (all N all D_3 all A_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),A_1) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_3),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)) = one_one(int))) # label(fact_4398_coprime__exp__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3731 (all X all N_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),N),N_4)) -> (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_4),X)))))))) # label(fact_2717_real__root__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3732 (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_3529_dist__triangle__alt) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3733 (all R_3 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_3))),R_3))) # label(fact_3369_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3734 (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_1769_exp__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3735 (all A_2 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_2),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) & hAPP(fun(int,bool),nat,finite_card(int),A_2) = hAPP(int,nat,phi,Ma) <-> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_2),Ma)))) # label(fact_3652_is__RRset__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3736 (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_1591_anything__times__even) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3737 (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_1384_less__add__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3738 (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_2396_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3739 (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,abs_abs(real),X)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))) # label(fact_2693_real__root__abs) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3740 (all X_a (semiring_div(X_a) -> (all A_1 all B 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),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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))) & (zero_zero(X_a) = ti(X_a,C_1) -> 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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))))))) # label(fact_1089_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3741 (all B all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),M) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),M))))) # label(fact_3493_zgcd__zcong__zgcd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3742 (all X_a (division_ring(X_a) -> (all B_2 all A_3 all C (zero_zero(X_a) != ti(X_a,C) -> (ti(X_a,B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C) = ti(X_a,A_3)))))) # label(fact_1849_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3743 (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_2 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_2),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_3173_prod__cases6) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3744 (all Na hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),Na)),ring_1_Ints(real)))) # label(fact_3826_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3745 (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_490_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3746 (all X_b all X_a (comm_monoid_add(X_a) -> (all F all G all 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),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_2) = 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_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_2))))) # label(fact_4248_setsum__addf) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3747 (all X_a all A_2 all B_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)),A_2),B_1)) -> 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_2)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_1))))) # label(fact_4895_Powp__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3748 (all X_a ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a)) = finite_psubset(X_a)) # label(tsy_c_Wellfounded_Ofinite__psubset_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3749 (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_2608_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3750 (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_1175_inv__less__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3751 (all K_4 all 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)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),L_4)) # label(fact_3772_Fract__of__int__quotient) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3752 (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) = 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)),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)),X)))))) # label(fact_2512_neg__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3753 (all X_b all X_c all X_a all P_1 all Z hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Z)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Z)) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z)) # label(fact_4043_split__beta) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3754 (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_mod(int),A_1),B) = ti(int,A_1)))) # label(fact_1423_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3755 (all X_a (real_normed_vector(X_a) & inverse(X_a) -> (all F all A_3 all D (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_3)))),hAPP(X_a,X_a,F,A_3)))),combi(X_a))),D),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_3)))),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_3))),D),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4632_DERIV__LIM__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3756 (all N (zero_zero(nat) != N -> 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_2902_coprime__minus1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3757 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_52_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3758 (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_102_number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3759 (all I (ti(int,I) != zero_zero(int) -> 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_3897_finite__divisors__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3760 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3761 (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_3222_dvd__fact__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3762 (all X_a all C_2 all A_2 all B_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)),A_2),B_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)),B_1),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_2),C_2))))) # label(fact_2203_subset__trans) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3763 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Xa),Ya))))) # label(fact_4562_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3764 (all A_3 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),hAPP(real,int,archimedean_ceiling(real),Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),A_3)),Xa)))) # label(fact_3391_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3765 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))) # label(fact_3429_powr__realpow) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3766 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),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)))) # label(fact_3407_powr__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3767 (all X_a (real_normed_vector(X_a) -> (all Xa all X_2 all A_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),X_2),A_3),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_2)),Xa)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_3),Xa)),sequentially)))))) # label(fact_4764_scaleR__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3768 (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_3453_zgcd__zdvd2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3769 (all X_a (semiring_1(X_a) -> (all Z (ti(X_a,Z) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),Z)))))) # label(fact_2146_iszero__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3770 (all X_a (linordered_field(X_a) -> (all A_3 all B_2 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)))))))) # label(fact_1873_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3771 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),zero_zero(int)) = zero_zero(rat)) # label(fact_3763_rat__number__collapse_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3772 (all X_a (linordered_idom(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))))))) # label(fact_1952_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3773 (all X_a (comple44059174attice(X_a) -> (all A_2 all B_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),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_2)),B_2)))))) # label(fact_1814_Sup__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3774 (all X hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,suc,X)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_2546_Fact_Ofact__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3775 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1))),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_2),B_1)))))) # label(fact_2735_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3776 (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_181_zero__less__one) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3777 (all A_1 all B all C_1 all D_3 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_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D_3))),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_3)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C_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)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C_1),D_3))) # label(fact_2766_complex__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3778 (all X_a all X_b (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)),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)),A_2)))))) # label(fact_4475_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3779 (all X_a (real_normed_vector(X_a) -> (all X_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,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_2)),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_2),zero_zero(X_a)),sequentially)))))) # label(fact_4472_LIMSEQ__norm__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3780 (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(hAPP(int,bool,P_1,X_1)) <-> hBOOL(hAPP(int,bool,P_2,X_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)) = 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_4361_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3781 (all Xa all Ya all Xaa (Ya = zero_zero(real) & Xaa = Xa <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Xa),Ya) = hAPP(real,complex,of_real(complex),Xaa))) # label(fact_2801_complex__eq__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3782 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_1279_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3783 (all X_b all X_a all F all B_1 all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> 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)),B_1)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_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_2)),B_1)))) # label(fact_3679_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3784 (all X_a (ord(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min_1(X_a),ord_less_eq(X_a)) = ord_min(X_a))) # label(fact_4862_min__ord__min) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3785 (all X_a (field(X_a) -> (all Xa all Wa all Z all Ya (ti(X_a,Ya) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,Z) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Wa),Ya) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Xa),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Wa),Z))))))) # label(fact_1852_frac__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3786 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_3)) -> 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3)))))))) # label(fact_234_add__less__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3787 (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_2785_i__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3788 (all X_a (ordere142940540dd_abs(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_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_3)),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_3)),B_2)))))) # label(fact_1977_abs__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3789 (all X_a (ring_1(X_a) -> hAPP(int,X_a,ring_1_of_int(X_a),one_one(int)) = one_one(X_a))) # label(fact_3603_of__int__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3790 (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_547_power2__eq__square) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3791 (all X_a (real_normed_field(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_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,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_2)),Y_2)) = 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_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_2))))))) # label(fact_4009_suminf__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3792 (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_848_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3793 (all L all U 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)))) # label(fact_3695_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3794 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(real,nat,natceiling,X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))) # label(fact_2439_natceiling__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3795 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 all X_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))) # label(fact_2111_mult__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3796 (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_1725_ln__le__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3797 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),Xa))))))) # label(fact_3326_one__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3798 (all R_3 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_3)),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_3)),hAPP(int,rat,number_number_of(rat),S_3)))) # label(fact_3756_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3799 (all X_a (field(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1))))) # label(fact_2617_field__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3800 (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_238_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3801 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arcsin),Xa),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),Xa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))))) # label(fact_2643_DERIV__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3802 (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_min(X_a),X),Y)),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_4838_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3803 (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_1768_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3804 (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_407_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3805 (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_3622_ceiling__add__of__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3806 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X)))) # label(fact_4842_Min_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3807 (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_2890_floor__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3808 (all B_5 all Q_5 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_4)),zero_zero(int))) -> (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),Q_5),zero_zero(int))))))) # label(fact_582_q__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3809 (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_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_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)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,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),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3))))))) # label(fact_4321_setsum__mono__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3810 (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_268_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3811 (all X_a all F all G all Ma all S ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_1)),hAPP(X_a,int,G,X_1)),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_4360_setsum__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3812 (all Ma all Na 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_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),P_1,N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_2),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),N_1))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Ma),Na))))) # label(fact_3555_gcd__nat__induct) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3813 (all X_a (real_normed_vector(X_a) -> (all Ra all A_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(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),Ra),A_3)),hAPP(X_a,filter(X_a),at(X_a),A_3)))))) # label(fact_4759_scaleR__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3814 (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_2686_real__root__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3815 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_1))))) -> 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_2))))))) # label(fact_4336_setsum__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3816 (all A_1 one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,one_one(real)),A_1)) # label(fact_3350_powr__one__eq__one) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3817 (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_2170_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3818 (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_1404_power__Suc__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3819 (all X_b all X_a (comm_monoid_mult(X_a) -> (all F all G all A_2 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_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_co302546470etprod(X_b,X_a),F),A_2)),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_2))))) # label(fact_3973_setprod__timesf) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3820 (all X_a (order(X_a) -> (all X_2 ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_2,N_1)),hAPP(nat,X_a,X_2,hAPP(nat,nat,suc,N_1))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_2)))))) # label(fact_4167_mono__SucI1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3821 (all A_3 all B_2 ((all P_6 -(hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),B_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),A_3)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_3),B_2)))) # label(fact_3088_coprime__prime__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3822 (all R_3 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3)) # label(fact_3190_rcis__zero__arg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3823 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_2 all Wa all A_3 (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_2),hAPP(int,X_a,number_number_of(X_a),Wa))),A_3)) <-> (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),Wa))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),hAPP(int,X_a,number_number_of(X_a),Wa))))) & (-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),Wa))) -> (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),Wa)),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_3),hAPP(int,X_a,number_number_of(X_a),Wa))),B_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),Wa)),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_3)))))))) # label(fact_1795_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3824 (all X_a (linordered_semiring(X_a) -> (all A_1 all C_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_479_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3825 (all Xa all Ya all Z (Xa = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Ya),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z)) <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Xa) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Ya),Z))) # label(fact_1805_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3826 (all Z_1 all 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))) = 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)))) # label(fact_3880_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3827 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),B_1) = ti(fun(X_a,bool),A_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_1),A_2)))) # label(fact_2207_equalityD2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3828 (all Wa all Ma (Ma = hAPP(int,nat,nat_1,Wa) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> zero_zero(nat) = Ma) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Wa)) -> ti(int,Wa) = hAPP(nat,int,semiring_1_of_nat(int),Ma)))) # label(fact_1037_nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3829 (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_3063_infinite__super) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3830 (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_1489_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3831 (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_1959_left__minus) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3832 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Na)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Na),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)),Na))))))) # label(fact_3910_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3833 (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_894_zcong__scalar2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.66 3834 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B_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)),A_2),B_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)),B_1),A_2))))) # label(fact_2202_equalityE) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3835 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = ti(int,Z_1)))) # label(fact_3597_floor__of__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3836 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> zero_zero(nat) = hAPP(int,nat,nat_1,Z_1))) # label(fact_1017_nat__le__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3837 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_206_zle__refl) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3838 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,Na))) <-> (exists J_1 (Ma = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),Na)))) | zero_zero(nat) = Ma)) # label(fact_1374_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3839 (all X_a all F all A_2 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_2)) = 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_2)) # label(fact_4271_real__of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3840 (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_1344_le__SucE) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3841 (all Xa all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),Ya))))) # label(fact_2681_real__root__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3842 (all X_a (real_normed_algebra(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_1241_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3843 (all X_a (ordered_semiring(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_436_mult__mono_H) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3844 (all L all U 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)))) # label(fact_4191_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3845 (all X_a (real_normed_field(X_a) -> (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Xa)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),Xa))))))) # label(fact_4052_summable__geometric) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3846 (all X_a (real_normed_vector(X_a) -> (all Y_2 all B_2 all X_2 all A_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_2),A_3),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_2),B_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)),X_2)),Y_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)),sequentially))))))) # label(fact_4502_LIMSEQ__diff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3847 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na))))) # label(fact_644_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3848 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(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)))))) & (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(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)))))) & Y = hAPP(real,real,sin,Y_1) & 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_1)) -> Y_1 = X_1)) & Y = hAPP(real,real,sin,X_1) & 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_1))))))) # label(fact_2347_sin__total) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3849 (all A_2 all K (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_2),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_2))))) -> 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_2))) = A_2)) # label(fact_4259_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3850 (all Xa hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_atMost(real),Xa)) = Xa) # label(fact_4971_Sup__atMost) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3851 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_1914_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3852 (all A_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),zero_zero(int)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),one_one(int))) # label(fact_3759_eq__rat_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3853 (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_1400_Suc__diff__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3854 (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_4741_scaleR_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3855 (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_4716_real__vector_Oscale__scale) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3856 (all Wa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Wa),one_one(int))),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)))) # label(fact_288_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3857 (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_502_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3858 (all B_2 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_2))))),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_2))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_2)) # label(fact_4062_adjust__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3859 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ya)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,Xa)),hAPP(int,nat,nat_1,Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)))))) # label(fact_1033_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3860 (all 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))) = hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,Nat_1))) # label(fact_2946_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3861 (all X_a all X_b (real_n2089651433ebra_1(X_b) & metric_space(X_a) -> (all A_3 all K all L_2 (ti(X_a,L_2) != ti(X_a,K) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),L_2),hAPP(X_b,filter(X_b),at(X_b),A_3))))))) # label(fact_4582_LIM__const__not__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3862 (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_335_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3863 (all X_a (semiring_div(X_a) -> (all A_1 all C_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),B)),C_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),A_1),B)),C_1)))) # label(fact_1291_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3864 (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_1143_int__le__induct) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3865 (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_3467_zgcd__assoc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3866 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),K_4)) # label(fact_601_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3867 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),T_5)))))) # label(fact_2857_pinf_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3868 (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_4428_gcd__code__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3869 (all X_a (metric_space(X_a) -> (all K 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(X_a,fun(nat,X_a),combk(X_a,nat),K)),L),sequentially)) <-> ti(X_a,K) = ti(X_a,L))))) # label(fact_4491_LIMSEQ__const__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3870 (all A_3 all B_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),A_3),B_2)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),zEven))))) # label(fact_1710_even__plus__odd__prop1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3871 (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)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = X))) # label(fact_2352_arccos__cos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3872 (all X_a (real_normed_vector(X_a) -> (all X_2 ((exists K_2 ((all N_1 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_2,N_1))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)))))) # label(fact_3519_Bseq__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3873 (all Ma all K all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),K))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na))))) # label(fact_643_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3874 (all A_1 all B all C_1 (zero_zero(int) != ti(int,C_1) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B)))) # label(fact_3761_mult__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3875 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_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)),A_2),B_1)))))) # label(fact_2734_card__psubset) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3876 (all X_b all X_a (semiring_1(X_a) -> (all Ya all 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(fun(X_b,bool),nat,finite_card(X_b),A_2))),Ya) = 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),Ya)),A_2)))) # label(fact_4255_setsum__constant) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3877 (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_257_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3878 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),abs_abs(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,abs_abs(rat),P_4))) # label(fact_4057_rat__abs__code) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3879 (all X_a (zero(X_a) -> (all Xa (zero_zero(X_a) = ti(X_a,Xa) <-> ti(X_a,Xa) = zero_zero(X_a))))) # label(fact_281_zero__reorient) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3880 (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_3201_nat__of__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3881 (all X_a (real_normed_vector(X_a) -> (all Xa (zero_zero(X_a) = ti(X_a,Xa) <-> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),Xa))))) # label(fact_2263_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3882 (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_127_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3883 (all X_a (comm_ring_1(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Xa),hAPP(X_a,X_a,uminus_uminus(X_a),Ya))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Xa),Ya)))))) # label(fact_1920_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3884 (all X_a (ordere216010020id_add(X_a) -> (all Ya all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ya)) -> (ti(X_a,Ya) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Xa) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Xa),Ya))))))) # label(fact_229_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3885 (all U 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)))) # label(fact_4279_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3886 (all Xa 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))))),Xa),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))),hAPP(real,real,cos,Xa))),hAPP(real,real,sin,Xa))))) # label(fact_3940_DERIV__cos__realpow2a) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3887 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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)),Na))))) # label(fact_1397_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3888 (all X_a (metric_space(X_a) -> (all Xa all Ya (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),Xa),Ya))) <-> ti(X_a,Xa) != ti(X_a,Ya))))) # label(fact_3538_dist__nz) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3889 (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]. 7.70/7.67 3890 (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_2553_fact__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3891 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = zero_zero(nat))) # label(fact_1159_div__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3892 (all A_1 all C_1 all D_3 all B (zero_zero(int) != ti(int,B) -> (zero_zero(int) != ti(int,D_3) -> 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_1),D_3)) = 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_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D_3))))) # label(fact_3808_diff__rat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3893 (all A_1 all B all C_1 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_1) = 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_1))) # label(fact_4407_gcd__assoc__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3894 (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_1063_of__nat__double) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3895 (all U all Ma all Na 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)),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U)),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)),Na)))))) # label(fact_878_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3896 (all A_1 all 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)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_2070_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3897 (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_2614_one__less__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3898 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)))) # label(fact_2151_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3899 (all Ma all Na (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),Na))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ma),hAPP(int,int,number_number_of(int),Na))))) # label(fact_3412_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3900 (all Na all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (one_one(nat) = Na <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),Ma)),Ma))))) # label(fact_880_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3901 (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_1330_less__antisym) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3902 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),X)) # label(fact_3249_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3903 (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_1186_MultInv__prop4) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3904 (all X_a (ordere223160158up_add(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C_1))))))) # label(fact_329_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3905 (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_1 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_2,X_1)))) -> ((exists Z_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_1)) -> (hBOOL(hAPP(int,bool,P_2,X_1)) <-> hBOOL(hAPP(int,bool,P_1,X_1))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2870_plusinfinity) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3906 (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_530_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3907 (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_4023_split__eta) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3908 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) <-> (exists N_2 all N_1 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_2,N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))))))))) # label(fact_3520_Bseq__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3909 (all D_1 all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),B_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),A_3)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_3),B_2))))) # label(fact_2881_coprime__mul__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3910 (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_822_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3911 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_2))) -> ti(fun(X_a,bool),B_1) = ti(fun(X_a,bool),A_2))))) # label(fact_2747_card__seteq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3912 (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_1096_div__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3913 (all P_1 ((all X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1)))) <-> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(int,bool,P_1,X_1)))))) # label(fact_265_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3914 (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_1775_exp__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3915 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N)) = ti(int,N)) # label(fact_3352_floor__real__of__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3916 (all Ya all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Xa)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (exists N_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,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),Ya),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),Xa))))),Xa)))))) # label(fact_1232_best__odd__division__abs) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3917 (all X_a (ordered_ab_group_add(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),hAPP(X_a,X_a,uminus_uminus(X_a),B_2))))))) # label(fact_1930_less__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3918 (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_426_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3919 (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]. 7.70/7.67 3920 (all W hAPP(int,int,ring_1_of_int(int),W) = hAPP(int,int,number_number_of(int),W)) # label(fact_3593_int__number__of__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3921 (all X all 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))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_3399_ceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3922 (all Xa all K (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) = ti(int,Xa) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)))) # label(fact_1733_zEvenI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3923 (all X_a (real_n1866405975lgebra(X_a) -> (all X_2 all A_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_2),A_3),sequentially)) -> (ti(X_a,A_3) != zero_zero(X_a) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_2)),hAPP(X_a,X_a,inverse_inverse(X_a),A_3)),sequentially))))))) # label(fact_4471_LIMSEQ__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3924 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_1297_mod__add__self2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3925 (all Q_3 all B all R_3 all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),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_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_mod(int),Q_3),C_1))),R_3))))))) # label(fact_1476_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3926 (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_3536_dist__pos__lt) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3927 (all X_a (ordered_ring(X_a) -> (all A_3 all E_2 all C all B_2 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),E_2)),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),B_2),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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),minus_minus(X_a),B_2),A_3)),E_2)),D_1))))))) # label(fact_774_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3928 (all Diff all F all Na 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)),Na)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),Na)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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,Na),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),Na))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H))))))))) # label(fact_4311_Maclaurin) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3929 (all Na all A_3 all B_2 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_3),B_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_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_3),B_2),Na))),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_3),B_2),Na))))))))) # label(fact_3169_not__P__Bolzano__bisect) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3930 (all X_a all Xa all A_2 all B_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)),A_2),B_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),B_1))))) # label(fact_2204_set__mp) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3931 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_2))))))) # label(fact_214_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3932 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),Na) = zero_zero(nat))) # label(fact_835_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3933 (all M all K_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) != M -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))))) # label(fact_1443_one__less__k) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3934 (all R_3 all A_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(real,real,sin,A_1)) = hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1))) # label(fact_3195_Im__rcis) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3935 (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_1385_less__add__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3936 (all X_a (real_normed_algebra(X_a) -> (all C 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)),F))))))) # label(fact_4026_summable__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3937 (all Ma all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Xa),zero_zero(int)),Ma)) <-> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),Xa))) # label(fact_1417_StandardRes__eq__zcong) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3938 (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_4374_gcd__dvd1__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3939 (all X_a (topological_space(X_a) -> (all G 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),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),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)),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4624_cnj_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3940 (all Va all V_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),V_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Va),pls))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),Va)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_498_le__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3941 (all X_a (ordered_semiring(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_3)) -> (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_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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_437_mult__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3942 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K_4)) = zero_zero(rat)) # label(fact_3727_Frct__code__post_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3943 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)))) # label(fact_629_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3944 (all Wa all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,Wa)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_1019_zless__nat__conj) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3945 (all Na 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,Na)),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),Na))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,Na)),Ma)) # label(fact_4988_max__Suc1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3946 (all Xa all Ya (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),Xa),Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),Xa)),Ya)))) # label(fact_2020_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3947 (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_531_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3948 (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_1111_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3949 (all A_1 all B all Q_3 all R_3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_3) = ti(int,A_1) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),zero_zero(int)))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_3)))))) # label(fact_1640_divmod__int__relI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3950 (all Ma all Na (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na) <-> Ma = hAPP(nat,nat,suc,zero_zero(nat)) & zero_zero(nat) = Na | hAPP(nat,nat,suc,zero_zero(nat)) = Na & zero_zero(nat) = Ma)) # label(fact_1380_add__is__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3951 (all A_1 all B (zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) -> (exists A_5 exists B_3 (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)) = A_1 & 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)))) # label(fact_3337_gcd__coprime__exists__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3952 (all M hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),one_one(int)) = one_one(int)) # label(fact_4396_gcd__1__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3953 (all X_a all Y_2 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_2) = ti(fun(X_a,bool),Y_2)) # label(fact_3874_image__ident) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3954 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3746_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3955 (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_3487_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3956 (all X_b all X_a (ab_group_add(X_a) -> (all F all G all A_2 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_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_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_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_2)))) # label(fact_4247_setsum__subtractf) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3957 (all X_a (topological_space(X_a) -> (all G all L 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),L),hAPP(X_a,filter(X_a),at(X_a),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,L)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4621_Re_OLIM) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3958 (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,Z_1) = ti(int,W)))) # label(fact_203_zle__antisym) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3959 (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_2715_real__root__pow__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3960 (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)) & (Y = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = X))) # label(fact_3300_gcd__nat_Osimps) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3961 (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]. 7.70/7.67 3962 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3963 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C_1))))))) # label(fact_508_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3964 (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_3890_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3965 (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_2585_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3966 (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) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),min)),B))) # label(fact_1122_div__eq__minus1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3967 (all Z all Wa (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)),Wa)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,Wa)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1039_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3968 (all X_a (semiring_div(X_a) -> (all A_1 all C_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),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_1116_div__mult__self1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3969 (all Xa all Na 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))),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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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),Na))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) = hAPP(real,real,sin,Xa)) # label(fact_4294_Maclaurin__sin__expansion) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3970 (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_2444_sin__2npi) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3971 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_3842_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3972 (all Xa all Ya (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),Xa),Ya)),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),zEven)))) # label(fact_1697_EvenOdd_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3973 (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_3388_real__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3974 (all X_a (semiri456707255roduct(X_a) -> (all B_2 all A_3 (ti(X_a,A_3) = zero_zero(X_a) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),A_3) = ti(X_a,B_2))))) # label(fact_317_add__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3975 (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_3367_real__of__int__minus) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3976 (all X_a (real_normed_field(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_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,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_2)),Y_2)) = 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_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_2))))))) # label(fact_4010_suminf__diff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3977 (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_2278_sin__double) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3978 (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_2267_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3979 (all Wa all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,Wa)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1020_nat__mono__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3980 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),hAPP(real,real,inverse_inverse(real),Y))) # label(fact_2605_divide__real__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3981 (all X one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),one_one(nat))) # label(fact_3276_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3982 (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_2056_complex__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3983 (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_3219_fact__ge__one__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3984 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),pi),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2291_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3985 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (exists 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)))))) & hAPP(real,real,tan,X_1) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))))) # label(fact_2457_tan__total__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3986 (all X_a (real_normed_field(X_a) -> (all Db all F all G all Xa 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,Xa)),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),Xa),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)),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),Db)))))))) # label(fact_3885_DERIV__chain2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3987 (all X_a (order(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,C_1) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_1))))))) # label(fact_505_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3988 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)))) # label(fact_689_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3989 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Ya),Xa)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Ya),Xa)) = Xa)) # label(fact_3720_Sup__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3990 (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_1974_norm__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3991 (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),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)) = 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))))) # label(fact_1118_div__add__self1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3992 (all Q_3 all R_3 hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),Q_3),hAPP(rat,rat,uminus_uminus(rat),R_3)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),Q_3),R_3)) # label(fact_3733_diff__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3993 (all X_a (metric_space(X_a) -> (all X_2 all L_2 ((all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_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),hAPP(nat,X_a,X_2,N_1)),L_2)),R_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_2),L_2),sequentially)))))) # label(fact_4545_LIMSEQ__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.67 3994 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),hAPP(int,X_a,number_number_of(X_a),min))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),Xa)),zero_zero(int))))))) # label(fact_3334_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 3995 (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_1351_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 3996 (all Ta all A_2 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_2)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1) != ti(int,X_1))))) -> (ti(int,Ta) != ti(int,X_1) -> ti(int,Ta) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),D))))))) # label(fact_4666_aset_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 3997 (all A_3 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_3),P_4))))) # label(fact_2740_SetS__finite) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 3998 (all X_a (power(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))))) # label(fact_1371_power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 3999 (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_528_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4000 (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(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),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_349_zadd__power2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4001 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_118_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4002 (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_4344_finite__nat__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4003 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)))) # label(fact_674_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4004 (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_3843_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4005 (all K_4 hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),min)) # label(fact_770_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4006 (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_3291_coprime__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4007 (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_138_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4008 (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_4738_scaleR_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4009 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Na)) -> 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)),Na)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Na)),one_one(nat)))) # label(fact_3912_card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4010 (all P_1 all A_3 all B_2 all Na 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_3),B_2),Na)) = 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_3),B_2),hAPP(nat,nat,suc,Na))) # label(fact_4080_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4011 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_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_3),B_2))))))) # label(fact_1845_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4012 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_133_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4013 (all M all K_4 (M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) -> (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_1444_one__less__m) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4014 (all Xa all Ya (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),Xa),Ya))) -> (zero_zero(nat) != Ya -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Ya),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Xa),Ya)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Xa),Ya)) & (Ya = zero_zero(nat) -> Xa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Xa),Ya)))) # label(fact_3751_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4015 (all K_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),pls)) # label(fact_742_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4016 (all X_a (order(X_a) -> (all F ((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(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))))) -> 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_4816_dvd_Ostrict__monoI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4017 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 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),A_3),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),A_3)),A_2)))))) # label(fact_4487_tendsto__norm) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4018 (all X_a (linordered_semidom(X_a) -> (all Xa all Ya all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_2),Xa)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_2),Ya)))))))) # label(fact_185_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4019 (all X_a (real_normed_algebra(X_a) -> (all Ya all A_3 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)),Ya)),A_3))))) # label(fact_4913_mult__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4020 (all P_1 all Na all 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)) -> (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) = Na -> hBOOL(hAPP(nat,bool,P_1,J_1)))))) & (zero_zero(nat) = K -> hBOOL(hAPP(nat,bool,P_1,Na))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Na),K))))) # label(fact_1552_split__mod) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4021 (all X_b all X_c all 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)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4022 (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_4717_real__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4023 (all Na 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)),Na)))))) # label(fact_3895_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4024 (all X_a (ordere236663937imp_le(X_a) -> (all A_3 all C all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_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_3),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_2),C))))))) # label(fact_331_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4025 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),Na))))) # label(fact_3410_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4026 (all X_a (linordered_idom(X_a) -> (all Xa all Na (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),Xa),Na))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)))))) # label(fact_2487_zero__le__power__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4027 (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_566_leI) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4028 (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_2772_complex__divide__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4029 (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_2451_tan__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4030 (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_558_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4031 (all X_a all X_b lex_prod(X_a,X_b) = ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b))) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4032 (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),hAPP(X_a,X_a,abs_abs(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)))))) # label(fact_981_dvd__abs__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4033 (all Xa all Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)))) # label(fact_857_zdvd__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4034 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Xa),Na)),zOdd))))) # label(fact_1224_power__preserves__odd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4035 (all X_a all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) <-> 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_2))))) # label(fact_2849_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4036 (all X_b all X_a all X_c all F all Xa 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),Xa)) = hAPP(X_c,X_a,F,hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Xa))) # label(fact_4092_snd__apsnd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4037 (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_3308_ceiling__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4038 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),hAPP(int,int,bit0,K))))) # label(fact_678_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4039 (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),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)))) = 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_2035_power2__minus) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4040 (all X_a (real_normed_algebra(X_a) -> (all Y all S_3 all X all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_3)) -> (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_3),S_3)))))))) # label(fact_2005_norm__mult__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4041 (all K all Na 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)),Na)) = 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),Na),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_4204_sumr__offset2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4042 (all X_a (metric_space(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_1_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4043 (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_4869_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4044 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))))) # label(fact_4780_scaleR_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4045 (all X_a all F all A_2 all Na (hAPP(nat,nat,suc,Na) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) -> (exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_1))))))) # label(fact_4328_setsum__SucD) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4046 (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_2282_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4047 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Xa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,Xa)))))) # label(fact_1728_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4048 (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]. 7.70/7.68 4049 (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_1509_int__power__div__base) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4050 (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_3432_log__powr__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4051 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)) = ti(X_a,B))))) # label(fact_1091_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4052 (all Ra 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),Ra)),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)))))),Ra),sequentially))) # label(fact_4523_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4053 (all X_a (archim1727834104eiling(X_a) -> (all Va all Xa (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),Va)),one_one(X_a))),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),Va)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))))))) # label(fact_2919_number__of__less__floor) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4054 (all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,int,fact_fact(int),X) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)))) & (-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_3203_fact__int__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4055 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all G all Xa 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),Xa),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)),Xa),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,Xa))),Ma))))))) # label(fact_3884_DERIV__fun__exp) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4056 (all X_a (real_n2089651433ebra_1(X_a) -> (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Xa)),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),Xa)),zero_zero(X_a)),sequentially)))))) # label(fact_4460_LIMSEQ__power__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4057 (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),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_4831_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4058 (all X_a all Xa hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),Xa)) = ti(X_a,Xa)) # label(fact_4810_some__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4059 (all X_a (semiring_1(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),zero_zero(X_a))))) # label(fact_2145_iszero__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4060 (all Na hAPP(nat,fun(nat,bool),ord_atMost(nat),Na) = 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),Na)))) # label(fact_4959_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4061 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),hAPP(real,real,sin,X)))) # label(fact_2286_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4062 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N)) # label(fact_4828_min__0L) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4063 (all X_a (topological_space(X_a) -> (all A_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),combi(X_a)),A_3),hAPP(X_a,filter(X_a),at(X_a),A_3)))))) # label(fact_4581_LIM__ident) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4064 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_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_3)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),B_2)),zero_zero(X_a))))))) # label(fact_1834_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4065 (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_446_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4066 (all Q_2 all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),hAPP(nat,nat,suc,Q_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),Q_2)),Ma)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),Na) = Q_2))) # label(fact_1495_split__div__lemma) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4067 (all X_a all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) <-> (exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))))) # label(fact_4812_some__eq__ex) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4068 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) | Ya = Xa <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)))) # label(fact_960_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4069 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),min)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) # label(fact_1501_zmod__minus1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4070 (all X_a all C all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> (hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,P_1,C))))) # label(fact_4803_exE__some) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4071 (all A_3 all B_2 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),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_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),B_2)),Ma)))))) # label(fact_3495_zcong__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4072 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),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))))) # label(fact_4434_gcd__int__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4073 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_1517_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4074 (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_3220_fact__gt__zero__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4075 (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_2131_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4076 (all N all D_3 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))))) # label(fact_2874_coprime__exp) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4077 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,Xa)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),zero_zero(real))))) # label(fact_2139_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4078 (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_1060_Euler_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4079 (all A_3 all B_2 (one_one(complex) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) <-> one_one(real) = A_3 & B_2 = zero_zero(real))) # label(fact_2761_Complex__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4080 (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,bit0,L))))) # label(fact_221_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4081 (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_974_abs__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4082 (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_2709_real__root__less__mono__lemma) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4083 -(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_656__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4084 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa) = one_one(real) <-> Xa = one_one(real)))) # label(fact_2690_real__root__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4085 (all X_a (sgn_div_norm(X_a) -> ti(fun(X_a,real),norm_norm(X_a)) = norm_norm(X_a))) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4086 (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_503_order__trans) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4087 (all X_a (real_normed_field(X_a) -> (all Y_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_2)) -> 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_2)),Y_2)))))))) # label(fact_4038_summable__diff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4088 (all M hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M))) # label(fact_1450_int__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4089 (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_4499_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4090 (all X all Y Y = hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2997_Im) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4091 (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_101_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4092 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),Xa)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),zero_zero(real))))) # label(fact_1784_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4093 (all N all D_3 all A_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),A_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)) = one_one(nat))) # label(fact_3302_coprime__exp__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4094 (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),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_4413_gcd__mult__cancel__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4095 (all X_a (sgn_div_norm(X_a) -> ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)) = scaleR_scaleR(X_a))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4096 (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_1105_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4097 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Ya),Xa)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),Ya),Xa)) = Xa)) # label(fact_4549_Sup__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4098 (all X_a (archim1727834104eiling(X_a) -> (all R_3 hAPP(X_a,int,archimedean_ceiling(X_a),R_3) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R_3)))))) # label(fact_3380_floor__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4099 (all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (exists X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),X_1),M)) & (all Y_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),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),Y_1),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_1),M)) -> ti(int,X_1) = ti(int,Y_1))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))))) # label(fact_929_zcong__zless__unique) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4100 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))) = zero_zero(real))) # label(fact_2770_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4101 (all A_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),A_3),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_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,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)))),A_3))),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)))),A_3))),sequentially))))) # label(fact_4451_summable__Leibniz_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4102 (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_2382_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4103 (all X_a all X_b (real_n1866405975lgebra(X_b) -> (all F all A_3 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),A_3),A_2)) -> (ti(X_b,A_3) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),A_3)),A_2))))))) # label(fact_4476_tendsto__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4104 (all X_1 hAPP(real,real,cos,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)))) # label(fact_3999_lemma__cos__ext) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4105 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_3)) -> 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_3))))))) # label(fact_4925_isCont__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4106 (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),plus_plus(nat),M),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))))) # label(fact_173_of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4107 (all K all F (hAPP(nat,nat,F,zero_zero(nat)) = 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_4614_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4108 (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_2537_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4109 (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_2612_inverse__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4110 (exists K_2 ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) # label(fact_3012_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4111 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) = hAPP(real,real,cos,X)) # label(fact_2300_cos__sin__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4112 (all X_a (real_normed_algebra(X_a) -> (all Xa_2 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),Y))))) # label(fact_1244_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4113 (all X_a all F all A_2 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_2) = 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_2))) # label(fact_4272_real__of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4114 (all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),zero_zero(real))) -> (exists N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),R_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))))))) # label(fact_3448_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4115 (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_469_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4116 (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_2548_fact__ge__one__nat) # label(axiom) # label(non_clause). [assumption]. 7.70/7.68 4117 (all D all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (Xa != zero_zero(real) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat)))))) = D)) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) -> 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),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))))) = D)) -> ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> D = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,Na)),Xa),D)))))))) # label(fact_2670_DERIV__real__root__generic) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4118 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N))))) # label(fact_1656_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4119 (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_968_dvd__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4120 (all Xa all Na 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,Xa)),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))),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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))))),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),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),Xa)),Na))))) # label(fact_4189_Maclaurin__sin__bound) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4121 (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_560_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4122 (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,M),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)))) # label(fact_3485_zgcd__non__0) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4123 (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_2075_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4124 (all X_a (linorder(X_a) -> (all Ya all Xa (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)) <-> ti(X_a,Xa) = ti(X_a,Ya)))))) # label(fact_532_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4125 (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,A_1) = ti(X_a,B))))))) # label(fact_1424_power__inject__base) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4126 (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_46_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4127 (all X_b all X_c all X_a (real_normed_vector(X_c) & real_normed_vector(X_b) & topological_space(X_a) -> (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),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> ((all X_1 (ti(X_a,X_1) != ti(X_a,A_3) -> 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_1)),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_1)),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_3)))))))) # label(fact_4679_LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4128 (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_13_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4129 (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_1561_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4130 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),min)))) # label(fact_675_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4131 (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_lessThan(X_a),K))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),I),K)))))) # label(fact_4341_lessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4132 (all Ma all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),B_2)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_3),Ma))))) # label(fact_3232_Bnor__mem__zle__swap) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4133 (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_3557_divides__fact) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4134 (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_4847_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4135 (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_9_semiring__one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4136 (all X_a (dist_norm(X_a) -> ti(fun(X_a,real),norm_norm(X_a)) = norm_norm(X_a))) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4137 (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_3221_fact__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4138 (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_3 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_3))) -> 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_3)))))))) # label(fact_4583_LIM__compose) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4139 (all X_2 ((all R_1 exists N_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_1),hAPP(nat,real,X_2,N_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)),X_2)),zero_zero(real)),sequentially)))) # label(fact_4685_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4140 (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_3081_prime__dvd__power) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4141 (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_4844_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4142 (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_3394_ceiling__le__real) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4143 (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_627_mult__less__mono1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4144 (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_2976_mult__idem) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4145 (all A_2 all B_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_2)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_1))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_2),B_1)))) # label(fact_3675_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4146 (all X_a (field_char_0(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),B_2)),field_char_0_Rats(X_a)))))))) # label(fact_3708_Rats__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4147 (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_614_le__cube) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4148 (all X_a all X_b all F all A_2 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_2))) # label(fact_1335_transfer__morphism__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4149 (all A_3 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_3),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_3)) -> 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_3),P_4)))))))) # label(fact_1689_SetS__card) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4150 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_3)),field_char_0_Rats(X_a))))))) # label(fact_3717_Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4151 (all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),one_one(nat))))))) # label(fact_2514_even__num__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4152 (all X_a (linord219039673up_add(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) <-> 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_3),A_3))))))) # label(fact_232_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4153 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (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)),hAPP(X_a,filter(X_a),at(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),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4634_LIM__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4154 (all A_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),A_3),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,A_3,zero_zero(nat)))) -> (all N_1 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)))),A_3))),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)))),A_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),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),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),power_power(real),hAPP(int,real,number_number_of(real),min)))),A_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),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_4547_summable__Leibniz_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4155 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all M_1 all F all L_2 all A_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_2),hAPP(X_a,filter(X_a),at(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),G),M_1),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4591_LIM__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4156 (all X all Y all Xa_2 all Ya_1 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_2),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_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,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_2),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_1),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_2177_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4157 (all X all Y all N (zero_zero(nat) != N -> (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_856_divides__exp2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4158 (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_1860_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4159 (all Va all Na (hAPP(int,nat,number_number_of(nat),Va) = hAPP(nat,nat,suc,Na) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va))) = Na) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va)))))) # label(fact_3914_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4160 (all X_b all X_a all X_c all F all G all A_2 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_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_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_2))) # label(fact_3873_image__image) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4161 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_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_2) = 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_2)))))) # label(fact_4293_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4162 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,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),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_2916_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4163 (all Xa all P_4 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Xa),zero_zero(int)),P_4)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),Xa) != zero_zero(int))) # label(fact_1416_StandardRes__prop3) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4164 (all A_1 all B all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_1434_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4165 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Ya)))) # label(fact_2140_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4166 (all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Na)) -> 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)),Na))))) = ti(int,Na))) # label(fact_3906_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4167 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),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_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))))) # label(fact_380_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4168 (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)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = zero_zero(int)))) # label(fact_794_Legendre__def) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4169 (all M all N all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),Z_1)) # label(fact_22_zadd__int__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4170 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = one_one(X_a) -> ti(X_a,B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2596_inverse__unique) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4171 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))))) # label(fact_1730_ln__mult) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4172 (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_934_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4173 (all X_a (group_add(X_a) -> (all Xa all Ya (ti(X_a,Ya) = hAPP(X_a,X_a,uminus_uminus(X_a),Xa) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Xa),Ya))))) # label(fact_1956_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4174 (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_2610_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4175 (all Na 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),Na)),Ma)) <-> one_one(int) = hAPP(int,int,abs_abs(int),Na)))) # label(fact_1044_zdvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4176 (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_2426_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4177 (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_1075_div__by__1) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4178 (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_1911_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4179 (all X_a (comm_monoid_add(X_a) -> (all F all K all Na 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)),Na)) = 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),Na),K)))))) # label(fact_4198_sumr__group) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4180 (all X_a (linordered_idom(X_a) -> (all A_3 (hAPP(X_a,X_a,sgn_sgn(X_a),A_3) = 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_3)))))) # label(fact_2304_sgn__1__pos) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4181 (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(int),pls),hAPP(int,int,bit1,K))))) # label(fact_276_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4182 (all X_a (real_algebra_1(X_a) & number_ring(X_a) -> (all W hAPP(real,X_a,of_real(X_a),hAPP(int,real,number_number_of(real),W)) = hAPP(int,X_a,number_number_of(X_a),W)))) # label(fact_2796_of__real__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 7.70/7.69 4183 (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_1129_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4184 (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_2868_int__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4185 (all X_a all Xa 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,Xa)) -> hBOOL(hAPP(X_a,bool,Q_1,Xa))))) # label(fact_4363_predicate1D) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4186 (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_907_zdvd__bounds) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4187 (all Na (zero_zero(nat) = Na <-> hAPP(nat,real,real_1(nat),Na) = zero_zero(real))) # label(fact_2381_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4188 (all X_b all X_a (real_normed_algebra(X_b) & power(X_b) & topological_space(X_a) -> (all Na 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),hAPP(X_a,filter(X_a),at(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),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)),Na)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),L),Na)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4585_LIM__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4189 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,Na))) <-> Ma = Na | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_1333_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4190 (all X_a (ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_776_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4191 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> zero_zero(nat) = 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)) # label(fact_887_divides__cases) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4192 (all X_a (comm_monoid_add(X_a) -> (all K all F (hAPP(nat,X_a,F,zero_zero(nat)) = zero_zero(X_a) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),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_4221_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4193 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> sums(X_a) = ti(fun(fun(nat,X_a),fun(X_a,bool)),sums(X_a)))) # label(tsy_c_Series_Osums_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4194 (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),times_times(X_a),B),A_1)),B) = zero_zero(X_a)))) # label(fact_1352_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4195 (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_3706_iszero__rat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4196 (all X_b all X_a (real_n1866405975lgebra(X_b) & topological_space(X_a) -> (all F all L_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),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> (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_3)))))))) # label(fact_4613_LIM__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4197 (all W hAPP(int,nat,number_number_of(nat),W) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),W))) # label(fact_1005_nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4198 (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_1983_abs__power__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4199 (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_3377_powr__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4200 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> ti(fun(fun(nat,X_a),bool),summable(X_a)) = summable(X_a))) # label(tsy_c_Series_Osummable_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4201 (all X hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,X)) = X) # label(fact_3562_int__of__inverse) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4202 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4203 (all D_3 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),hAPP(int,int,abs_abs(int),D_3)))) # label(fact_1226_zdvd__self__abs1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4204 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M)) # label(fact_1318_zpower__zmod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4205 (all X_a (number_semiring(X_a) -> (all V_2 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_2)) -> 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_2)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))))))) # label(fact_422_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4206 (all Ma all Na (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),Na))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ma),hAPP(int,int,number_number_of(int),Na))))) # label(fact_3415_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4207 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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_2))))) # label(fact_4235_setsum_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4208 (all X_a (real_normed_field(X_a) -> (all F all Xa all L (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),Xa),L)) <-> (exists G_1 (ti(X_a,L) = hAPP(X_a,X_a,G_1,Xa) & hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),G_1),Xa)) & (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,Xa)) = 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),Xa))))))))) # label(fact_4903_CARAT__DERIV) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4209 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D)) -> (all X_1 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_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D))),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_1),Ta))))))))) # label(fact_718_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4210 (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_3737_rat__sgn__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4211 (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_3142_mod__neg__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4212 (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_2938_accp__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4213 (all N hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_3032_complex__Re__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4214 (all X_a (idom(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)) | ti(X_a,C) = zero_zero(X_a) <-> 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),A_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_2))))))) # label(fact_747_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4215 (all X all D_3 (zero_zero(int) != ti(int,D_3) -> 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_3))),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_3))),hAPP(int,real,real_1(int),D_3))) = 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_3)))) # label(fact_3436_real__of__int__div__aux) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4216 (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),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_4729_scaleR__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4217 (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_2875_coprime__exp__imp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4218 (all Xa all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Xa))))) # label(fact_3685_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4219 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_1 Y = hAPP(real,real,exp(real),X_1)))) # label(fact_2114_exp__total) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4220 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all C 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)),hAPP(X_a,filter(X_a),at(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),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)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4600_LIM__mult__left__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4221 (all B all Q_5 all R_4 all Q_3 all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_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),B),Q_3)),R_3))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))) # label(fact_585_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4222 (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_2445_cos__2npi) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4223 (all A_3 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_3),P_4)))))) # label(fact_2725_Union__SetS__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4224 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa),D)) -> (zero_zero(X_a) != hAPP(X_a,X_a,F,Xa) -> 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)),Xa),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,Xa))),D)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,Xa))))))))))) # label(fact_3888_DERIV__inverse_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4225 (all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,Ya))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Ya)))) # label(fact_2149_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4226 (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)) -> Z_1 = W))) # label(fact_596_real__le__antisym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4227 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))))) # label(fact_768_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4228 (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_254_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4229 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_1073_div__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4230 (all X_2 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_2)) <-> (all R_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_2,N_1))),R_1)))))))) # label(fact_4889_vanishes__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4231 (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_1583_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4232 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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,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))))))) # label(fact_2613_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4233 (all X_b all X_a image(X_b,X_a) = ti(fun(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool))),image(X_b,X_a))) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4234 (all N N = hAPP(nat,nat,size_size(nat),N)) # label(fact_2948_nat__size) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4235 (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_2636_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4236 (all X_a (real_normed_vector(X_a) -> (all Y all S_3 all X all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_3)) -> (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_3),S_3)))))))) # label(fact_2008_norm__add__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4237 (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_3265_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4238 (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(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),W))))) # label(fact_1632_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4239 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,F2,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))) # label(fact_4138_nat__case__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4240 (all K all L hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),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)))))) # label(fact_3490_zgcd__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4241 (all X_a all A_2 all B_1 (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_2),B_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(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_2)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_1))))) # label(fact_1797_Union__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4242 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) # label(fact_1485_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4243 (all L all U 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)))) # label(fact_4559_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4244 (all V_2 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_2)) = zero_zero(nat)) & (-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_2)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))))) # label(fact_649_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4245 (all R_3 all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),R_3) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),R_3))) # label(fact_1757_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4246 (all X_a all A_2 all B_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)),A_2),B_1)) -> (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_1),A_2)))))) # label(fact_2721_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4247 (all X_a (archim1727834104eiling(X_a) -> (all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Xa)))))) # label(fact_2906_zero__le__floor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4248 (all Ya all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)) -> (exists X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Ya))))))) # label(fact_3702_Rats__dense__in__nn__real) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4249 (all X_a (real_normed_field(X_a) -> (all Ya all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_2)) -> 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_2)),Ya))))))) # label(fact_4036_divide_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4250 (all X_b (uminus(X_b) -> ti(fun(X_b,X_b),uminus_uminus(X_b)) = uminus_uminus(X_b))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4251 (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_994_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4252 (all B all Bq all Br all A_1 all C_1 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_1),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_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Bq),Br))) -> (ti(int,C_1) != 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_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),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_1))),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_1)))))))) # label(fact_1628_zadd1__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4253 (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_1472_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4254 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y))))) # label(fact_1985_dvd__neg__div) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4255 (all X_a (ring_1(X_a) -> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4256 (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_4402_dvd__gcd__D1__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4257 (all A_3 all B_2 all C all D_1 all Xa (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_3),B_2)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_1),hAPP(int,nat,nat_1,Xa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,Xa))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_3),B_2) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_2),C) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C),A_3) = one_one(int) -> (exists K_1 exists L_3 exists M_2 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),hAPP(int,nat,nat_1,Xa)) = ti(int,C) & ti(int,B_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),hAPP(int,nat,nat_1,Xa)) & hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,Xa)) = ti(int,A_3)))))))))) # label(fact_3506_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4258 (all A_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),A_1) = A_1) # label(fact_3252_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4259 (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_836_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4260 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4261 (all X_a (linordered_idom(X_a) -> (all Wa 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),Wa)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z)))))) # label(fact_3605_of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4262 (all Ta all B_1 all D_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1))))) -> (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_1),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_1),D)),Ta)))))))) # label(fact_4674_bset_I9_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4263 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) <-> Ma != Na)) # label(fact_124_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4264 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))) # label(fact_1650_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4265 (all X_a (number_ring(X_a) & linordered_idom(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)))) # label(fact_1015_abs__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4266 (all X_a all X_b all A_2 all B_1 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_2),B_1)),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_1)))) # label(fact_4949_fin__bijRr) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4267 (all Xa 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,Xa) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)))) # label(fact_1230_zOddI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4268 (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]. 7.75/7.69 4269 (all X_a (linorder(X_a) -> (all B all A_1 all C_1 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_1)) = 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_1))))) # label(fact_4835_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.69 4270 (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_3101_prime__dvd__square) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4271 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_3036_complex__Re__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4272 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4273 (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_767_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4274 (all X_a (topological_space(X_a) -> (all F all K all A_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),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_3),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_3),sequentially)))))) # label(fact_4504_LIMSEQ__offset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4275 (all X_a (real_normed_field(X_a) -> (all E_3 all F all Xa all D (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),Xa),D)) -> (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),Xa),E_3)) -> ti(X_a,D) = ti(X_a,E_3)))))) # label(fact_2648_DERIV__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4276 (all X_a (ring_div(X_a) -> (all A_1 all B all C_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),minus_minus(X_a),A_1),B)),C_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),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C_1)),B)),C_1)))) # label(fact_1300_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4277 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1)))) # label(fact_87_add__numeral__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4278 (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_546_semiring__mult__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4279 (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_3580_upto_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4280 (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_2253_sin__diff2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4281 (all X_a (real_normed_algebra(X_a) -> (all Xa all A_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(X_a,fun(X_a,X_a),times_times(X_a),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),A_3)),hAPP(X_a,filter(X_a),at(X_a),A_3)))))) # label(fact_4587_mult__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4282 (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_4974_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4283 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)))))) # label(fact_1972_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4284 (all X_a all C all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_2))) = 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)),X_2))) # label(fact_4289_setsum__const) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4285 (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_3148_surjective__pairing) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4286 (all Sb all Ta all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2)) -> 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_3),Sb)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_2),Ta))),pair_leq)))) # label(fact_3514_pair__leqI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4287 (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_561_leD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4288 (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_2301_sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4289 (all A_3 all D_1 all Na 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_3)),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),Na))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Na),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),one_one(nat))),D_1))))) # label(fact_4349_arith__series__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4290 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),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_3)),zero_zero(X_a))))))) # label(fact_2593_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4291 (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_4423_gcd__le1__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4292 (all R_3 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_3),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_3))))) # label(fact_3425_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4293 (all X_a (linordered_idom(X_a) -> (all A_3 (zero_zero(X_a) != ti(X_a,A_3) <-> 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_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_98_zero__less__power2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4294 (all Xa all A_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),Xa)),A_3)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),hAPP(int,real,real_1(int),A_3))))) # label(fact_3386_floor__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4295 (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_2292_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4296 (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_1745_aux4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4297 (all N hAPP(nat,nat,fact_fact(nat),N) != zero_zero(nat)) # label(fact_2538_fact__nonzero__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4298 (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_2774_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4299 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2964_cnj_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4300 (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),B),A_1)) # label(fact_3250_gcd__commute__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4301 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa (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),Xa)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),hAPP(int,int,bit1,pls))))))) # label(fact_240_le__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4302 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma)),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),Na)))) # label(fact_4147_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4303 (all X_a (real_normed_field(X_a) -> (all Ya all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> 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_2)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),Ya))))))) # label(fact_4113_divide_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4304 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all Na 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),Na)) = 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),Na),K)))))) # label(fact_4207_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4305 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C_1)))))))) # label(fact_227_add__increasing2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4306 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1107_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4307 (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_285_succ__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4308 (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_2306_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4309 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),Q_3)))) # label(fact_607_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4310 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_814_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4311 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),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_2354_arccos__lbound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4312 (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_64_odd__less__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4313 (all A_3 all B_2 all Na (zero_zero(nat) != Na -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_3),B_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_3),Na)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_2),Na)))))) # label(fact_1234_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4314 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4409_gcd__neg1__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4315 (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_3305_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4316 -(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)),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_705__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]. 7.75/7.70 4317 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all A_3 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_3))),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_3))))))) # label(fact_4606_LIM__offset__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4318 (all X_a all X_b (real_normed_vector(X_b) -> (all X_2 ((exists N_2 all N_1 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_2,N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))))) <-> (exists K_2 ((all N_1 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_2,N_1))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))))) # label(fact_2418_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4319 (all A_1 all 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)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2071_zmod__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4320 (all K all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Na)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),Na))))) # label(fact_3256_gcd__greatest__iff__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4321 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,Y)))) # label(fact_2362_sin__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4322 (all X_b all X_c all X_a all F1 all A_3 all B_2 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_3),B_2)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_3),B_2)) # label(fact_4022_Product__Type_Oprod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4323 (all X_a (metric_space(X_a) -> (all X_2 all L_2 all A_3 ((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_3),sequentially)) & (all N_1 hAPP(nat,real,S_2,N_1) != A_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),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_2),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_2),L_2),hAPP(real,filter(real),at(real),A_3))))))) # label(fact_4686_LIMSEQ__SEQ__conv2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4324 (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),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,Xa)))) # label(fact_1741_zEvenE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4325 (all X_a (topological_space(X_a) -> (all G 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),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),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)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4640_Re_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4326 (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_3009_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4327 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 all A_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_2),A_3),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),Ra)),X_2)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),A_3)),sequentially)))))) # label(fact_4754_scaleR__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4328 (all Code_numeral all Code_numeral_5 (Code_numeral_5 = Code_numeral <-> hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_5) = hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral))) # label(fact_2961_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4329 (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_493_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4330 (all X_a all A_2 all B_1 (ti(fun(X_a,bool),B_1) = ti(fun(X_a,bool),A_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_1),A_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_2),B_1)))) # label(fact_2209_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4331 (all X_a all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_2741_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4332 (all Ma (Ma = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat))))) # label(fact_828_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4333 (all X_a (real_normed_field(X_a) -> (all F all Xa all D (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),Xa),D)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),F),Xa)))))) # label(fact_4926_DERIV__isCont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4334 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Xa)) -> (Xa = one_one(real) <-> zero_zero(real) = hAPP(real,real,ln,Xa)))) # label(fact_1722_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4335 (all X_a all X_b (ord(X_b) -> (all Xa all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa))))))) # label(fact_510_le__funD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4336 (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))) -> (ti(X_a,A_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a)))))))) # label(fact_2587_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4337 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2230_arcsin__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4338 (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_3206_fact__mono__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4339 (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_1361_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4340 (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))))) # label(fact_2158_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4341 (all A_1 zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),one_one(real))) # label(fact_1995_log__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4342 (all X_a all X_b all X_c all Y -(all A_4 all B_4 all C_4 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4)))) # label(fact_3179_prod__cases3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4343 (all R_3 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(complex,real,im,X))) # label(fact_4725_complex__Im__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4344 (all X_a (ord(X_a) -> ord_max(X_a) = ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a)))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4345 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_1182_inv__not__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4346 (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_416_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4347 (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_51_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4348 (all Xa all Ya all P_1 ((-hBOOL(P_1) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),Xa),Ya)) = hAPP(int,nat,nat_1,Ya)) & (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),Xa),Ya)) = hAPP(int,nat,nat_1,Xa)))) # label(fact_964_nat__if__cong) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4349 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)) | Na = Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)))) # label(fact_401_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4350 (all X_a all X_b (comm_semiring_1(X_b) -> (all D_1 all F all A_2 ((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_2)) -> 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_2))))))) # label(fact_4798_dvd__setsum) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4351 (all X_a (real_n2089651433ebra_1(X_a) & number_ring(X_a) -> (all W hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),W)) = hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2019_norm__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4352 (all X_a (comm_semiring_1(X_a) -> (all C_1 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_1))))))) # label(fact_727_dvd__mult2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4353 (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_3601_complex__cnj__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4354 (all X_a (linord219039673up_add(X_a) -> (all A_3 (ti(X_a,A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),A_3) <-> ti(X_a,A_3) = zero_zero(X_a))))) # label(fact_1933_neg__equal__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4355 (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_1540_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4356 (all Na hAPP(nat,nat,suc,Na) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na)))) # label(fact_3868_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4357 (all X_b all X_a all F all A_2 all B_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)),A_2),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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_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),B_1))))) # label(fact_3664_image__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4358 (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_3345_ln__powr__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4359 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,im,Z_1)))),ii) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_2995_complex__diff__cnj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4360 (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_1526_mod__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4361 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_1338_add__Suc__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4362 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1505_power__odd__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4363 (all X_a all F all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_1))))) -> 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_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_2))) # label(fact_4887_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4364 (all X_a (preorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)))))) # label(fact_568_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4365 (all A_3 hAPP(int,int,zfact,A_3) = 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_3))) # label(fact_3957_d22set__prod__zfact) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4366 (all Xa all Na (-hBOOL(hAPP(nat,bool,even_odd_even(nat),Na)) -> (zero_zero(real) != Xa -> 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,Na)),Xa),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),Na)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Xa)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2720_DERIV__odd__real__root) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4367 (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_1681_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4368 (all X_a (comm_monoid_add(X_a) -> (all F all Na 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,Na))) = 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),Na))),hAPP(nat,X_a,F,Na))))) # label(fact_4348_setsum__lessThan__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4369 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> 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_2))))) # label(fact_4073_Re_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4370 (all Ma all Na all Qr (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)),Na)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)) = Ma & (Na != zero_zero(nat) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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),Na),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),Na)))) & (zero_zero(nat) = Na -> 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),Na),Qr)))) # label(fact_3152_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4371 (all X_a (archim1727834104eiling(X_a) -> (all Xa all Va (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),Xa)),hAPP(int,int,number_number_of(int),Va))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),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),Va)),one_one(X_a)))))))) # label(fact_2920_floor__le__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4372 (all X_a (ordered_ab_group_add(X_a) -> (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(X_a,X_a,uminus_uminus(X_a),A_3))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))))))) # label(fact_1951_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4373 (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_3607_le__of__int__ceiling) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4374 (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_3561_of__int__int__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4375 (all R_3 all S_3 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_3),hAPP(real,real,uminus_uminus(real),S_3)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_3),S_3)) # label(fact_1992_real__diff__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4376 (all X_a (ring_1(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_3),B_2)),ring_1_Ints(X_a)))))))) # label(fact_3824_Ints__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4377 (all Na 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),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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),Na),K))))))) # label(fact_815_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4378 (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_1999_power__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4379 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),A_1)))) # label(fact_540_power3__eq__cube) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4380 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,cos,hAPP(real,real,arcsin,X))))) # label(fact_2250_cos__arcsin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4381 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((exists X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) & hAPP(X_a,X_b,F,X_1) = 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_2) = zero_zero(X_b)))))) # label(fact_3976_setprod__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4382 (all Na all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),Na)),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),Na)),Ma)))) # label(fact_3413_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4383 (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_258_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4384 (all X hAPP(real,real,cos,X) = hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2255_cos__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4385 (all Xa 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),Xa)),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_4061_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4386 (all X_a (number(X_a) & linorder(X_a) -> (all Va all Wa (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),Va)),hAPP(int,X_a,number_number_of(X_a),Wa))) <-> -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),Wa)),hAPP(int,X_a,number_number_of(X_a),Va))))))) # label(fact_250_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4387 (all M all N (M = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_355_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4388 (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)),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_792_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4389 (all N all P_5 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)))))) # label(fact_922_zprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4390 (all F all Xa all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),Xa),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_2 ((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_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Xa)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),H_1))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2))))))) # label(fact_2666_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4391 (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,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),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)))))) # label(fact_789_zdiff__power2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4392 (all X_a ti(fun(fun(X_a,bool),X_a),hilbert_Eps(X_a)) = hilbert_Eps(X_a)) # label(tsy_c_Hilbert__Choice_OEps_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4393 (all X_a (ab_group_add(X_a) -> (all A_1 all C_1 all B all D_3 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_1),D_3)) = 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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_3))))) # label(fact_741_add__diff__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4394 (all Xa all A_3 (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_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),A_3),Xa),sequentially)) -> (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(nat,real,A_3,N_1)))) & (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,N_1)),hAPP(nat,real,A_3,M_2))))) | (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,M_2)),hAPP(nat,real,A_3,N_1))))) & (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,N_1)),Xa)))))) # label(fact_4515_monoseq__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4395 (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_2871_coprime__sos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4396 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_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_2) = 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_2)))))) # label(fact_3972_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4397 (all Xa hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sin),Xa),hAPP(real,real,cos,Xa)))) # label(fact_2650_DERIV__sin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4398 (all X_a (real_field(X_a) -> (all A_1 all B all C_1 all D_3 all H_2 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_1),D_3))),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_3)),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_1)),H_2)),D_3))))) # label(fact_1780_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4399 (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_417_add__leD2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4400 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F all Sb (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sb)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = ti(X_a,Sb))))) # label(fact_4116_sums__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4401 (all X_a (real_normed_field(X_a) -> (all E_3 all F all Xa all D (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),Xa),D)) -> (ti(X_a,D) = ti(X_a,E_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),Xa),E_3))))))) # label(fact_2646_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4402 (all X_a (real_normed_algebra(X_a) -> (all Xa_2 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_2),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_1910_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4403 (all A_1 all B all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_1)) -> 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_1)) = 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_1))) # label(fact_1100_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4404 (all X_a (topological_space(X_a) -> (all G 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),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),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)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4641_Im_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4405 (all X_a (order(X_a) -> (all Xa all Ya (ti(X_a,Ya) = ti(X_a,Xa) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)))))) # label(fact_512_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4406 (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_4050_summable__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4407 (all Ma all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)))) # label(fact_153_zless__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4408 (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_1492_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4409 (all Wa (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),Wa))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,Wa)))))) # label(fact_1604_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4410 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Xa),Ya)),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),Xa),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Ya))) # label(fact_1736_even__prod__div__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4411 (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_334_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4412 (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_1098_int__div__less__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4413 (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_428_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4414 (all X_b (number(X_b) & division_ring(X_b) -> (all W hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),one_one(X_b)),hAPP(int,X_b,number_number_of(X_b),W)) = hAPP(X_b,X_b,inverse_inverse(X_b),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_2622_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4415 (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_2257_sgn__sgn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4416 (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_3558_mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4417 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Na)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Ma)))) # label(fact_1447_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4418 (all Ma all Na (hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(nat,int,semiring_1_of_nat(int),Na) <-> Ma = Na)) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4419 (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_95_Bit1__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4420 (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_3267_dvd__gcd__D1__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4421 (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_1302_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4422 (all X_b all X_a (ord(X_a) & comm_monoid_add(X_b) -> (all F all G all B_2 all D_1 all A_3 all C (ti(X_a,C) = ti(X_a,A_3) -> (ti(X_a,D_1) = ti(X_a,B_2) -> ((all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),D_1)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,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),G),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),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_3),B_2)))))))) # label(fact_4329_setsum__ivl__cong) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4423 (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_4405_gcd__commute__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4424 (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)),X))))) # label(fact_2513_Parity_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4425 (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))) # label(fact_1022_nat__0__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4426 (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))) -> (zero_zero(nat) != N -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B))))) # label(fact_1235_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4427 (all A_3 all P_4 all X_1 (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_3),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_1)))) # label(fact_2731_SetS__elems__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4428 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)))) # label(fact_1966_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4429 (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_2345_arcsin__sin) # label(axiom) # label(non_clause). [assumption]. 7.75/7.70 4430 (all X_a (linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),D_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),D_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3)))))) # label(fact_4230_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4431 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),F_1)) -> hAPP(X_a,nat,F,X_1) = 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) = zero_zero(nat)))) # label(fact_4281_setsum__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4432 (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_3527_dist__triangle__half__l) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4433 (all X_a (comm_semiring_1(X_a) -> (all A_3 all D_1 all Na 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_3)),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),Na))) = 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),Na)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),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(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),one_one(nat)))),D_1))))))) # label(fact_4351_arith__series__general) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4434 (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_2117_arctan__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4435 (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))) & (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_1468_div__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4436 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_2 all F all A_3 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),A_3),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),B_2),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),A_3),B_2)),A_2))))))) # label(fact_4500_tendsto__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4437 (all R_3 exists N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),R_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))))) # label(fact_3449_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4438 (all X_a all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> ((exists X_1 (hAPP(X_a,nat,F,X_1) = one_one(nat) & (all Xa_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa_1),A_2)) -> (ti(X_a,X_1) != ti(X_a,Xa_1) -> zero_zero(nat) = hAPP(X_a,nat,F,Xa_1)))) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)))) <-> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_2) = one_one(nat)))) # label(fact_4284_setsum__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4439 (all Xa 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)),Xa))))) # label(fact_3896_bdd__nat__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4440 (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]. 7.75/7.71 4441 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))))) # label(fact_385_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4442 (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_2592_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4443 (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_2161_arctan__half) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4444 (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]. 7.75/7.71 4445 (all X_b all X_a (real_normed_algebra(X_b) & metric_space(X_a) -> (all G 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)),hAPP(X_a,filter(X_a),at(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),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(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),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_3)))))))) # label(fact_4598_LIM__mult__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4446 (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_1050_power2__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4447 (all Y all X (hAPP(real,real,exp(real),Y) = X -> Y = hAPP(real,real,ln,X))) # label(fact_1761_ln__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4448 (all X_a (real_normed_field(X_a) -> (all C all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_3)) -> 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)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),C))))))) # label(fact_4112_sums__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4449 (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_2076_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4450 (all X_b all X_a (real_normed_vector(X_b) & metric_space(X_a) -> (all L all F all G 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_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_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),L),hAPP(X_a,filter(X_a),at(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),hAPP(X_a,filter(X_a),at(X_a),A_3)))))))) # label(fact_4625_LIM__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4451 (all X_a nat_rec(X_a) = ti(fun(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a))),nat_rec(X_a))) # label(tsy_c_Nat_Onat_Onat__rec_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4452 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C 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)),hAPP(X_a,filter(X_a),at(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),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)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4602_LIM__mult__right__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4453 (all X_a (real_vector(X_a) -> (all A_1 all B all X (zero_zero(X_a) != ti(X_a,X) -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) -> B = A_1))))) # label(fact_4733_scaleR__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4454 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2803_of__real_Odiff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4455 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),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),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_438_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4456 (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_2386_real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4457 (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_2011_norm__power__ineq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4458 (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_3882_power__number__of__even__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4459 (all M all N all R_4 all R_3 all S_4 all S_3 all T_6 all T_5 all K_4 ((exists Sn exists Tn hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_4),R_3),S_4),S_3),T_6),T_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_3)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_4),R_3) = ti(int,K_4)))) # label(fact_3502_xzgcd__correct__aux2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4460 (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_204_zle__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4461 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4462 (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_45_zadd__assoc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4463 (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_183_less__add__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4464 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all G all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> ((all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(int,X_a,G,X_1) = hAPP(int,X_a,F,X_1))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),G),B_1) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_2))))))) # label(fact_4324_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4465 (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(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_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)))) # label(fact_4369_predicate2I) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4466 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))))) # label(fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4467 (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_1597_Parity_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4468 (all A_3 hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),cnj),A_3))) # label(fact_4932_cnj_OisCont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4469 (all N hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N)) # label(fact_3303_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4470 (all X_a all C all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))))) # label(fact_2238_Compl__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4471 (all X_a all A_3 all F all Va 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_3),F),hAPP(int,nat,number_number_of(nat),Va)) = 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,Va)))),A_3),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,Va)))),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_3),F),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,Va))))))) # label(fact_4184_nat__rec__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4472 (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_1025_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4473 (all A_3 all B_2 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_3),B_2) <-> -(exists P_6 (hBOOL(hAPP(int,bool,zprime,P_6)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),B_2)))))) # label(fact_3492_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4474 (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),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_1),zero_zero(real)))) # label(fact_3936_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4475 (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) != ti(int,A_1))))) # label(fact_1179_inv__distinct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4476 (all X_a (metric_space(X_a) -> (all X_2 all A_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_2),A_3),sequentially)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)))))) # label(fact_4459_LIMSEQ__imp__Cauchy) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4477 (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_1964_diff__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4478 (all A_3 all A_2 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_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> 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_2),Ma),A_3)),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_3),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),Ma),A_3)),Ma)))))) # label(fact_3647_RRset2norRR__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4479 (all X_a (linorder(X_a) -> (all Xa all Ya all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),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),Xa),Ya)),Z)))))) # label(fact_4823_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4480 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),Z_1),hAPP(complex,complex,cnj,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)))) # label(fact_3042_complex__add__cnj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4481 (all X_a (ord(X_a) -> max(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4482 (all Na 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)),Na)))))) # label(fact_3852_bdd__int__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4483 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_2 all C all A_3 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_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),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_3))),B_2)),C)),S) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C),hAPP(fun(X_a,bool),nat,finite_card(X_a),S))) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_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),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_3))),B_2)),C)),S) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,B_2,A_3)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C),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))))))))) # label(fact_3963_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4484 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_6)),B)))) # label(fact_1248_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4485 (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_363_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4486 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3587_of__int__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4487 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2068_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4488 (all X_b all X_a (order(X_b) & order(X_a) -> (all C all F all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C),hAPP(X_a,X_b,F,B_2))) -> ((all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_3))))))))) # label(fact_2862_xt5) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4489 (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),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_4836_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4490 (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_360_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4491 (all Wa all Z ((exists N_1 ti(int,Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Wa),Z)))) # label(fact_269_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4492 (all K all L (hAPP(int,int,bit1,L) = hAPP(int,int,bit1,K) <-> ti(int,L) = ti(int,K))) # label(fact_42_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4493 (all X_2 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_2)) -> 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_2))))) # label(fact_4074_Im_Osummable) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4494 (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_1358_mod__div__trivial) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4495 (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]. 7.75/7.71 4496 (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_390_mult__1__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4497 (all X_2 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_2)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2))))) # label(fact_2940_ResSet__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4498 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = M -> hAPP(nat,nat,suc,zero_zero(nat)) = N))) # label(fact_1441_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4499 (all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),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_3),B_2),Ma)))) # label(fact_2064_zcong__zminus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4500 (all P_1 all Na all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Na),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Na),K))) <-> (all I_2 all J_1 (ti(int,Na) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))))) # label(fact_1500_split__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4501 (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),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)) = 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))))) # label(fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4502 (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_4251_setsum__image__gen) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4503 (all X_a (linord1117847801e_zero(X_a) -> (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,inverse_inverse(X_a),A_3)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))))))) # label(fact_2584_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4504 (all Real1_1 all Real2_1 hAPP(complex,nat,complex_size,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2769_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4505 (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_1166_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4506 (all A_1 all B all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3780_normalize__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4507 (all X_a (real_normed_vector(X_a) -> bseq(X_a) = ti(fun(fun(nat,X_a),bool),bseq(X_a)))) # label(tsy_c_SEQ_OBseq_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4508 (all Y_2 all B_2 all X_2 all A_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),X_2),A_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),Y_2),B_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,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_2)),Y_2)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2)),sequentially))))) # label(fact_4538_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4509 (all X_a (archim1727834104eiling(X_a) -> (all Z all Xa (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))),Xa)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))))))) # label(fact_3633_less__floor__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4510 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B)))) # label(fact_740_diff__add__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4511 (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_3048_expi__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4512 -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))) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min)),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_697__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]. 7.75/7.71 4513 (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_3105_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4514 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_3)),hAPP(X_a,X_a,inverse_inverse(X_a),B_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),times_times(X_a),A_3),B_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),A_3))) & (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_3),B_2)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2))))))) # label(fact_2627_inverse__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4515 (all X all K_4 hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4)) # label(fact_2130_real__sqrt__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4516 (all X_a all A_3 all Ra all B_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),Ra),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),Ra,A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),Ra),A_3))))) # label(fact_2943_accp__downward) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4517 (all A_1 all B all C_1 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_1) = 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_1))),C_1)) # label(fact_1309_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4518 (all Q_3 all R_3 all B all C_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_3),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_1))),R_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C_1)))))) # label(fact_1553_mod__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4519 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,J_2),I_1)) # label(fact_3465_zgcd__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4520 (all X_a (real_normed_vector(X_a) -> (all Ra all X_2 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_2),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ra)) -> (exists No all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_1)) -> 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_2,N_1)),L_2))),Ra))))))))) # label(fact_4543_LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4521 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_1 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_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_2107_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4522 (all N all M all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),R_3)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = one_one(int) -> 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_3)))))) # label(fact_4376_divides__mult__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4523 (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_2153_real__sqrt__abs2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4524 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_1830_divide__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4525 (all Xa 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),Xa))) = hAPP(real,real,sin,Xa)) # label(fact_3996_sin__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4526 (all X_a (field(X_a) -> (all A_1 all N 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(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_1764_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4527 (all X_a all A_2 all B_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,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_2),B_1)),A_2))) # label(fact_2213_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4528 (all Xa all Ya (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Xa),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(rat,real,ratreal,Xa)),hAPP(rat,real,ratreal,Ya))))) # label(fact_3788_real__less__eq__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4529 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_2))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)))))) # label(fact_3892_Bseq__minus__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4530 (all Ya all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,Na),Ya)))))) # label(fact_2704_real__root__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4531 (all X_a (metric_space(X_a) -> (all Xa all Ya (zero_zero(real) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Xa),Ya) <-> ti(X_a,Xa) = ti(X_a,Ya))))) # label(fact_3542_dist__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4532 (all X_b all X_a (linordered_field(X_a) -> (all F all A_2 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_2)) = 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_2)))) # label(fact_3975_abs__setprod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4533 (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_3455_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4534 (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_94_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4535 (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]. 7.75/7.71 4536 (all T_1 order(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4537 (all X (zero_zero(real) = hAPP(real,real,sin,X) -> hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X)) = one_one(real))) # label(fact_2268_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4538 (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_3393_ceiling__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4539 t = one_one(int) -> (exists X_1 exists Y_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)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_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),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_594__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4540 (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_1512_odd__power__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4541 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Ya (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),Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Ya)))))) # label(fact_236_le__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4542 (all R_3 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),hAPP(complex,real,re,X))) # label(fact_4726_complex__Re__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4543 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_1317_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4544 (all X_a (linord20386208strict(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_483_mult__strict__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4545 (all X_a (linordered_idom(X_a) -> (all B all D_3 all A_1 all C_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)),C_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),B)),D_3)) -> 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_1),D_3)))))))) # label(fact_992_abs__mult__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4546 (all M all N (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)) = one_one(int) -> one_one(int) = hAPP(int,int,abs_abs(int),M))) # label(fact_999_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4547 (all Ta all A_2 all D_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_2)) -> ti(int,X_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa_1))))) -> (-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_1),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_1),D)),Ta)))))))) # label(fact_4672_aset_I10_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4548 (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_3602_complex__Re__of__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4549 (all N (N != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N) = hAPP(nat,nat,suc,hAPP(nat,nat,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))))) # label(fact_1514_Suc__mult__two__diff__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4550 (all X_a (linord581940658strict(X_a) -> (all C_1 all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))))))) # label(fact_455_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4551 (all Z (ti(int,Z) = zero_zero(int) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int))))) # label(fact_1018_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4552 (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_1556_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4553 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all Ra all F all L_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),L_2),hAPP(X_a,filter(X_a),at(X_a),A_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ra)) -> (exists S_1 ((all X_1 (ti(X_a,X_1) != ti(X_a,A_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),minus_minus(X_a),X_1),A_3))),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_1)),L_2))),Ra)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1))))))))) # label(fact_4670_LIM__D) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4554 (all A_3 all A_2 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_2),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_3),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_2),Ma),A_3)),Ma)))))) # label(fact_3649_RRset2norRR__correct1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4555 (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_2400_le__natfloor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4556 (all X_a (comm_monoid_add(X_a) -> (all F all Na 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),Na),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)),Na))),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_4199_sumr__offset3) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4557 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_1)))) -> 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_4100_suminf__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4558 (all T_1 preorder(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4559 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> 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)))))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),one_one(int))))) # label(fact_1516_inv__is__inv__aux) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4560 (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]. 7.75/7.71 4561 (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_3463_zgcd__greatest) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4562 (all Xa all Ya (hAPP(real,real,uminus_uminus(real),Xa) = Ya <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa),Ya))) # label(fact_1989_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4563 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_277_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4564 (all Na 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),Na),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)),Na))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4302_series__pos__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4565 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))))) # label(fact_849_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4566 (all X_a (ordered_ab_group_add(X_a) -> ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)) = ord_gr676655987ssThan(X_a))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4567 (all Xa all A_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_3)),one_one(real)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),Xa)),A_3)))) # label(fact_3439_floor__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4568 (all X_a (semiring_div(X_a) -> (all A_3 all B_2 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_2),A_3) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_3),B_2)))))) # label(fact_1357_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4569 (all X_a (real_algebra_1(X_a) -> (all X all N hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),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)))) # label(fact_2800_of__real__power) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4570 (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_1978_abs__leI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4571 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),B) -> ti(X_a,B) = ti(X_a,A_1))))) # label(fact_2568_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4572 (all X all Y all Z_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))) # label(fact_625_zpower__zpower) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4573 (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)) = zero_zero(int)) & (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)))) # label(fact_1024_int__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4574 (all X_a (banach(X_a) & real_normed_field(X_a) -> ti(fun(X_a,X_a),exp(X_a)) = exp(X_a))) # label(tsy_c_Transcendental_Oexp_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4575 (all M one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),one_one(int))) # label(fact_3458_zgcd__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4576 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all L all F all G all A_3 all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> ((all X_1 (ti(X_a,A_3) != ti(X_a,X_1) -> (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_1),A_3))),R_2)) -> hAPP(X_a,X_b,G,X_1) = hAPP(X_a,X_b,F,X_1)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(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),hAPP(X_a,filter(X_a),at(X_a),A_3))))))))) # label(fact_4671_LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4577 (all X_a (group_add(X_a) -> (all A_3 all B_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_3),B_2) = zero_zero(X_a) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_2) = ti(X_a,A_3))))) # label(fact_1958_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4578 (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_2343_cos__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4579 (all X_c all X_a all X_b all F all A_3 all B_2 all A_2 (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_3),B_2)),A_2)) -> 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_3),B_2)),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_2))))) # label(fact_4008_pair__imageI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4580 (all K_4 all L_4 ((ti(int,L_4) != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,abs_abs(int),L_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)),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)))) # label(fact_1654_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4581 (all X_a (monoid_mult(X_a) & comm_semiring_0(X_a) -> (all Xa all Ya all Na hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),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),Xa))),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),Ya)),hAPP(nat,fun(nat,nat),minus_minus(nat),Na)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,Na)))) = 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),Xa))),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),Ya)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,Na))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,Na)))))) # label(fact_4202_lemma__realpow__diff__sumr) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4582 (all N all D_3 (zero_zero(int) != ti(int,D_3) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),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_3)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),D_3))))) # label(fact_3420_real__of__int__div) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4583 (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_821_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4584 (all A_3 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_3),hAPP(real,int,archim2085082626_floor(real),Xa))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_3)),Xa)))) # label(fact_3389_le__floor__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4585 (all Ma all Na (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),Na) <-> zero_zero(nat) = Na & zero_zero(nat) = Ma)) # label(fact_3281_gcd__zero__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4586 (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_2980_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4587 (all A_3 all B_2 (hAPP(int,int,abs_abs(int),B_2) = hAPP(int,int,abs_abs(int),A_3) <-> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_3),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1053_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4588 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3151_mod__nat__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.71 4589 (all B_2 all A_3 all D_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_3),B_2) = ti(int,D_1) <-> (all E (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),A_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),B_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),D_1)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),B_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),A_3)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_1)))) # label(fact_4422_gcd__unique__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4590 (all A_1 all B (ti(int,B) != zero_zero(int) -> (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),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),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int))))) # label(fact_2099_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4591 (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_861_dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4592 (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)))))) & Y = hAPP(real,real,tan,hAPP(real,real,arctan,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_2452_arctan) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4593 (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_3060_bezw__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4594 (all Xa hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arctan),Xa))) # label(fact_4931_isCont__arctan) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4595 (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_818_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4596 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))) # label(fact_1082_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4597 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),min)))) # label(fact_684_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4598 (all Xa 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)),Xa))) = hAPP(nat,nat,suc,Xa)) # label(fact_3869_card__bdd__nat__set__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4599 (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_2545_fact__less__mono__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4600 (all X_a (linord1117847801e_zero(X_a) -> (all A_3 all B_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_3),B_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),zero_zero(X_a))))))) # label(fact_1833_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4601 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all 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),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_2) = 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_2))))) # label(fact_4246_abs__setsum__abs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4602 (all F all K all A_3 all B_2 (B_2 != A_3 -> ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),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_2)),hAPP(real,real,F,A_3))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3))))) # label(fact_2668_DERIV__const__ratio__const2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4603 (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_81_Bit0__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4604 (all Na all A_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),A_3),zero_zero(real)),sequentially)) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_3,N_1)))) -> ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_3,hAPP(nat,nat,suc,N_1))),hAPP(nat,real,A_3,N_1)))) -> 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)))),A_3))),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)))),A_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),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)))),Na)),one_one(nat)))))))))) # label(fact_4528_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4605 (all U_1 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),I_1),U_1)),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_1)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U_1)),M)),N))) # label(fact_868_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4606 (all Na all Ma (hAPP(nat,real,real_1(nat),Na) = hAPP(nat,real,real_1(nat),Ma) <-> Na = Ma)) # label(fact_2371_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4607 (all I_1 all N hAPP(nat,nat,hAPP(int,fun(nat,nat),nat_aux,I_1),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,I_1)),N)) # label(fact_1069_nat__aux__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4608 (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_3315_coprime__dvd__mult__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4609 (all X_a (order(X_a) -> (all Xa all Ya 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),Xa),Ya)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,Xa)),hAPP(nat,X_a,F,Ya)))))))) # label(fact_4818_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4610 (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & (all Y_1 (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),Y_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hAPP(real,real,cos,Y_1) = zero_zero(real) -> Y_1 = X_1)) & hAPP(real,real,cos,X_1) = zero_zero(real) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_2349_cos__is__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4611 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_4)) -> (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_4)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_113_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4612 (all X_a (semiring_1(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),one_one(X_a))))) # label(fact_2152_not__iszero__1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4613 (all A_3 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_3)),hAPP(complex,filter(complex),at(complex),A_3)))) # label(fact_4571_Re_Ocont) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4614 (all X_a (linorder(X_a) -> (all Z all Xa all Ya (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),Xa),Ya))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Ya)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Xa)))))) # label(fact_4984_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4615 (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_2055_negative__zless) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4616 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min)),Xa)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arccos),Xa),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),Xa),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))))) # label(fact_2642_DERIV__arccos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4617 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_1)))))) # label(fact_2852_pinf_I8_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4618 (all F all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_3),B_2)) -> ((all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),X_1)) -> (exists Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),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_1),Y_1)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,B_2)),hAPP(real,real,F,A_3)))))) # label(fact_2864_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4619 (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_414_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4620 (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,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),plus_plus(real),X),Y))) # label(fact_2271_cos__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4621 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Xa)),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),Xa)),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_3947_monoseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4622 (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_347_order__refl) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4623 (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_3192_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4624 (all A_3 all P_4 hAPP(fun(int,bool),fun(fun(int,bool),bool),hAPP(fun(int,fun(int,bool)),fun(fun(int,bool),fun(fun(int,bool),bool)),image(int,fun(int,bool)),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_3),P_4)),hAPP(int,fun(int,bool),sRStar,P_4)) = hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_3),P_4)) # label(fact_3677_SetS__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4625 (all X_a (ordere142940540dd_abs(X_a) -> (all A_3 (zero_zero(X_a) = ti(X_a,A_3) <-> hAPP(X_a,X_a,abs_abs(X_a),A_3) = zero_zero(X_a))))) # label(fact_969_abs__eq__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4626 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X))) # label(fact_2958_cnj_Ominus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4627 (all X_a (topological_space(X_a) -> (all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_3)) -> 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_3)))))) # label(fact_4923_isCont__rabs) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4628 (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_3462_zgcd__power__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4629 (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_3144_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4630 (all X_a (linorder(X_a) -> (all Xa all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ya),Xa)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)))))) # label(fact_572_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4631 (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_3630_floor__unique) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4632 (all Xa all Ya 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Xa),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ya),Z))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))))) # label(fact_634_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4633 (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_1571_mod__induct__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4634 (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_3528_dist__triangle__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4635 (all R_3 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_3),X)),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),R_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2819_complex__of__real__add__Complex) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4636 (all Xa all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Xa)),hAPP(int,real,real_1(int),Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Xa),Ya)))) # label(fact_3357_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4637 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),zero_zero(int))) -> (exists N_1 ti(int,X) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_1)))))) # label(fact_2105_negD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4638 (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_1266_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4639 (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_3372_powr__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4640 (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_3226_fact__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4641 (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_2549_of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4642 (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_2455_cos__pi__eq__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4643 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_256_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4644 (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_3008_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4645 (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_2431_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4646 (all X_b all X_a all B_1 all F all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_1),hAPP(fun(X_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_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_1))))) # label(fact_3656_finite__surj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4647 (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_3381_powr__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4648 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_1398_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4649 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),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_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,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_3),B_2)),field_char_0_Rats(X_a)))))))) # label(fact_3715_Rats__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4650 (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),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,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)))))))) # label(fact_2367_cos__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4651 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all A_1 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4727_inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4652 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_4850_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4653 (all X_a (archim1727834104eiling(X_a) -> (all R_3 hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R_3))) = hAPP(X_a,int,archim2085082626_floor(X_a),R_3)))) # label(fact_3382_ceiling__floor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4654 (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_3628_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4655 (all X_b all X_a (ab_group_add(X_a) -> (all F all 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),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_2) = 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_2))))) # label(fact_4238_setsum__negf) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4656 (all K all L ((exists N_1 L = 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_eq(nat),K),L)))) # label(fact_1209_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4657 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_2),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_3),B_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_3),zero_zero(int)))))) # label(fact_1106_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4658 (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_1724_ln__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4659 (all C_1 all A_1 all B all Q_3 all R_3 (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_3))) -> (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_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,A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C_1)),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_1)),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_1))),R_3)))))))) # label(fact_3120_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4660 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (exists N_1 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_1)))),X))))) # label(fact_2641_reals__Archimedean) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4661 (all X_a all X_b all X_c product_prod_case(X_a,X_b,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))) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4662 (all X_a (ring(X_a) -> (all A_3 all E_2 all C all B_2 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_2),A_3)),E_2)),D_1) = ti(X_a,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),B_2),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_3),E_2)),C))))) # label(fact_754_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4663 (all Xa all Ya (hAPP(real,real,exp(real),Ya) = hAPP(real,real,exp(real),Xa) <-> Xa = Ya)) # label(fact_1749_exp__inj__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4664 (all U (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U)) -> 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))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U))) # label(fact_4350_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4665 (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_4980_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4666 (all Z (hAPP(int,int,abs_abs(int),Z) = one_one(int) <-> ti(int,Z) = hAPP(int,int,number_number_of(int),min) | ti(int,Z) = one_one(int))) # label(fact_1007_abs__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4667 (all X_a (division_ring(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),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,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))) # label(fact_2595_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4668 (all P_1 all Na all A_3 all B_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_3),B_2)) -> 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_3),B_2),Na))),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_3),B_2),Na))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_2),A_3)),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)))),Na)))) # label(fact_3162_Bolzano__bisect__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4669 (all X_a (real_normed_vector(X_a) -> (all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) <-> (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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_1)) -> 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_2,M_2)),hAPP(nat,X_a,X_2,N_1)))),E)))))))))))) # label(fact_3340_Cauchy__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4670 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_1)) -> (B_1 = A_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_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_2))))) # label(fact_3687_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4671 (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]. 7.75/7.72 4672 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2227_arctan__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4673 (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_882_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4674 (all X_a (linorder(X_a) -> (all C all D_1 all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_3),B_2) <-> ti(X_a,D_1) = ti(X_a,B_2) & ti(X_a,C) = ti(X_a,A_3))))))) # label(fact_4224_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4675 (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_2609_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4676 (all X_a all C all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C),A_2)))) # label(fact_2236_ComplD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4677 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,zero_zero(real)),A_1) = zero_zero(complex)) # label(fact_3193_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4678 (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_541_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4679 (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_272_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4680 (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_3245_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4681 (all N (one_one(nat) != N -> (exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),N)) & hBOOL(hAPP(nat,bool,prime,P_6)))))) # label(fact_3113_prime__factor) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4682 (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_3776_Fract__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4683 (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_4750_sgn__div__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4684 (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),B_4),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_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_1680_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4685 (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]. 7.75/7.72 4686 (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_3610_of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4687 (all Ma all K all Na (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K) <-> Na = Ma)) # label(fact_129_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4688 (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]. 7.75/7.72 4689 (all K_4 all 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)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_93_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4690 (all A_3 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Xa)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,Xa)),A_3)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Xa),hAPP(nat,real,real_1(nat),A_3)))))) # label(fact_2411_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4691 (all Xa all A_2 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_2)) -> hBOOL(hAPP(int,bool,nat_is_nat,Xa))))) # label(fact_4868_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4692 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all P_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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)),P_1)),F)),zero_zero(X_b))),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),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_2))),P_1))))))) # label(fact_4216_setsum__restrict__set_H_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4693 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3468_zgcd__zminus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4694 (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_612_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4695 (all X_b (ord(X_b) & number(X_b) -> (all U_1 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_1)),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_1)),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_1)),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_1)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U_1)))))) # label(fact_4856_min__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4696 (all X_a (linordered_field(X_a) -> (all B_2 all A_3 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C)),A_3)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),C)))))))) # label(fact_1870_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4697 (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)),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),A_1),B)))) # label(fact_1905_minus__mult__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4698 (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_1410_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4699 (all Xa 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)),Xa))) = Xa) # label(fact_3893_card__bdd__nat__set__l) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4700 (all Na all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,Na)),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),Na),Ma)))) # label(fact_3184_less__eq__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4701 (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_706_dvd__0__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4702 (all C_1 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_1),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),C_1),M))))) # label(fact_871_zcong__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4703 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 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),A_3),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),A_3)),A_2)))))) # label(fact_4477_tendsto__minus) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4704 (all X_a (real_n1866405975lgebra(X_a) -> (all A_3 (ti(X_a,A_3) != zero_zero(X_a) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),inverse_inverse(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_3)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4594_LIM__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4705 (all A_3 all B_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_3),B_2),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_3),B_2))))) # label(fact_911_zcong__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4706 (all X_a all C_2 all A_2 all B_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)),A_2),B_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)),B_1),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_2),C_2))))) # label(fact_2200_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4707 (all Va (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),Va))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)))) # label(fact_164_less__0__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4708 (all X_a (linord219039673up_add(X_a) -> (all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_3)) <-> 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_3)),A_3)))))) # label(fact_1948_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4709 (all X_a all A_2 all F all Na (ti(fun(X_a,bool),A_2) = 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)),Na))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_3899_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4710 (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_4854_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4711 (all X_2 all A_3 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_2),A_3)) -> 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_2)),hAPP(complex,complex,cnj,A_3))))) # label(fact_4136_cnj_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4712 (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)),X)))) # label(fact_4690_scaleR__minus1__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4713 (all Ya all Xa 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),Xa),hAPP(int,fun(int,bool),sRStar,P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1566_SRStar__mult__prop1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4714 (all Na (Na != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_148_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4715 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_225_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4716 (all X_a (field_inverse_zero(X_a) -> (all B_2 all C all A_3 ((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_3),C) = ti(X_a,B_2)) & (ti(X_a,C) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_3)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_2),C) = ti(X_a,A_3))))) # label(fact_1847_divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4717 (all Ma all K all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Na)) -> ((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),Na)) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),Na) = ti(int,K)))) # label(fact_3500_xzgcd__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4718 (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_504_order__antisym) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4719 (all X_c all X_b all X_a (topological_space(X_b) & topological_space(X_c) & metric_space(X_a) -> (all G all L all F all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),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),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_3)))) -> ((exists D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_2)) & (all X_1 (ti(X_a,X_1) != ti(X_a,A_3) & 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_1),A_3)),D_2)) -> hAPP(X_a,X_b,F,A_3) != hAPP(X_a,X_b,F,X_1))))) -> 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_3))))))))) # label(fact_4944_metric__isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4720 (all L_4 hAPP(int,int,bit1,L_4) != pls) # label(fact_67_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4721 (all X_a (real_normed_algebra(X_a) -> (all Xa all X_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_2),A_3)) -> 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),Xa)),X_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),A_3))))))) # label(fact_4109_mult__right_Osums) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4722 (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_4122_sums__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4723 (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_4258_sums__group) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4724 (all X_a (ord(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1))))))) # label(fact_520_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4725 (all C_1 all D_3 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_1),D_3),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_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D_3)),M))))) # label(fact_899_zcong__zadd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4726 (all X hAPP(complex,real,re,X) = hAPP(complex,real,re,hAPP(complex,complex,cnj,X))) # label(fact_3020_complex__Re__cnj) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4727 (all F all Xa all F_2 all Na all Ma ((all R_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),R_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),Na))) -> 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_1)),Xa),hAPP(real,real,hAPP(nat,fun(real,real),F_2,R_1),Xa))))) -> 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),Na))),Xa),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),Xa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),Na)))))) # label(fact_4316_DERIV__sumr) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4728 (all Ma all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),Na)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na))))) # label(fact_471_zle__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4729 (all X_a all X_b (comm_monoid_mult(X_b) & dvd(X_b) -> (all F all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_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)),A_2),B_1)) -> 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_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),B_1)))))))) # label(fact_3985_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4730 (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_1269_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4731 (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_1969_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4732 (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_784_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4733 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X)) = hAPP(int,nat,nat_1,hAPP(int,int,fact_fact(int),X)))) # label(fact_3224_transfer__nat__int__factorial) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4734 (all A_3 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_3),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_3)) -> (all X_1 (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_3),P_4))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),X_1)))))))) # label(fact_1683_SetS__elems__card) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4735 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all R_3 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_3),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_3),X))))) # label(fact_4714_of__real_OscaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4736 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1940_minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4737 (all X_a (real_normed_vector(X_a) -> (all R_3 exists K_2 all X_1 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_3),X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_1)),K_2)))))) # label(fact_4786_scaleR__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4738 (all A_1 all B (hAPP(rat,product_prod(int,int),quotient_of,B) = hAPP(rat,product_prod(int,int),quotient_of,A_1) -> A_1 = B)) # label(fact_3739_quotient__of__inject) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4739 (all Ya all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ya),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),Xa),Ya)),zEven))))) # label(fact_1715_odd__minus__odd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4740 (all A_1 all B all C_1 all D_3 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_1),D_3)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D_3))) # label(fact_3778_mult__rat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4741 (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_2634_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4742 (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_3373_powr__less__mono2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4743 (all Xa hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_lessThan(real),Xa)) = Xa) # label(fact_4354_Sup__lessThan) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4744 (all W all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z2))) # label(fact_745_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4745 (all N all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)))) # label(fact_1635_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4746 (all X_a (linorder(X_a) -> (all Xa all Ya (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),Xa)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Ya))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Xa),Ya)))))) # label(fact_4346_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4747 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,zero_zero(nat)),D_1)) <-> one_one(nat) = D_1)) # label(fact_2893_coprime__0_H) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4748 (all X_a (linord219039673up_add(X_a) -> (all A_3 (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_3),A_3)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),zero_zero(X_a))))))) # label(fact_198_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4749 (all B all D_3 all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_3),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)))))) # label(fact_2880_coprime__mul) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4750 (all R_3 all A_1 all B hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_3),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_3),B))) # label(fact_4724_complex__scaleR) # label(axiom) # label(non_clause). [assumption]. 7.75/7.72 4751 (all X_a all X_b (real_normed_vector(X_b) -> (all X_2 ((exists N_2 all N_1 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_2,N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))))) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_1 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_2,N_1))),K_2))))))))) # label(fact_2417_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4752 (all B_5 all A_6 all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) != zero_zero(int) -> (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) -> (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)) = ti(int,B) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_6),B_5))))) # label(fact_4418_gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4753 (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_1828_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4754 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> zero_zero(nat) = B | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_1),B)))) # label(fact_839_divides__ge) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4755 (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_3543_dist__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4756 (all Na ((exists M_2 hAPP(nat,nat,suc,M_2) = Na) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)))) # label(fact_1376_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4757 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,number_number_of(int),min)) = hAPP(int,int,uminus_uminus(int),A_1)) # label(fact_2091_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4758 (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_3160_prod__eqI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4759 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,Na)),Xa))))) # label(fact_4940_isCont__root__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4760 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4761 (all X_a (semiring_div(X_a) -> (all A_1 all B all C_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),times_times(X_a),A_1),B)),C_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),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_1))),C_1)))) # label(fact_1283_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4762 (all F all B_2 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B_2),Xa)) -> ((all X_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),B_2),Xa))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_1))))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Xa)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,Xa))))))) # label(fact_4945_LIM__less__bound) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4763 (all X_1 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) -> 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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X_1),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_1))) = hAPP(nat,real,cos_coeff,X_1)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) -> hAPP(nat,real,cos_coeff,X_1) = zero_zero(real)))) # label(fact_2535_cos__coeff__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4764 (all Q_3 all B all R_3 all C_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_3),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_1))),R_3)),zero_zero(int))))))) # label(fact_1477_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4765 (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_2112_mult_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4766 (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_787_power2__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4767 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,uminus_uminus(X_a),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)),Z_1)))) # label(fact_2013_mult__minus1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4768 (all X_a (metric_space(X_a) -> (all E_2 all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_2)) -> (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_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_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),hAPP(nat,X_a,X_2,M_2)),hAPP(nat,X_a,X_2,N_1))),E_2))))))))))) # label(fact_3547_metric__CauchyD) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4769 (all Na all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)))) <-> Na = zero_zero(nat) & zero_zero(nat) = Ma)) # label(fact_2084_int__zle__neg) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4770 (all A_1 all B all Q_3 all R_3 (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_3))) -> (zero_zero(int) != ti(int,B) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = ti(int,Q_3)))) # label(fact_1618_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4771 (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_1811_real__average__minus__first) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4772 (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_2284_sin__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4773 (all X all Y all R_3 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_3)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),R_3)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),R_3))) # label(fact_2817_Complex__mult__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4774 (all Q_3 all R_3 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_3)) = 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_3))) # label(fact_3097_negateSnd__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4775 (all Q_5 all R_4 all A_1 all B all Q_3 all R_3 (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_3))) -> (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_4))) -> (zero_zero(int) != ti(int,B) -> ti(int,R_3) = ti(int,R_4))))) # label(fact_1612_unique__remainder) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4776 (all X_a (plus(X_a) & linorder(X_a) & dvd(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_0_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4777 (all X_a (real_normed_algebra(X_a) -> (all Ya all X_2 all A_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_2),A_3),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_2)),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_3),Ya)),sequentially)))))) # label(fact_4483_mult__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4778 (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_279_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4779 (all Ma all Na all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))))) # label(fact_662_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4780 (all Y (Y != zero_zero(real) -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2773_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4781 (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_1201_int__less__induct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4782 (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_2752_Suc__lessE) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4783 (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_3418_lemma__floor2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4784 (all X_a (real_normed_field(X_a) -> (all C 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) = 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)))))) # label(fact_4012_suminf__divide) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4785 (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_3117_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4786 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all Ma all F all G all A_3 all B_2 (ti(X_a,B_2) = ti(X_a,A_3) -> ((all X_1 (ti(X_a,B_2) != ti(X_a,X_1) -> hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1))) -> (ti(X_b,Ma) = ti(X_b,L) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),B_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_3)))))))))) # label(fact_4787_LIM__cong) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4787 (all R_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_3),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_3))),one_one(real))))) # label(fact_3422_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4788 (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_889_zcong__id) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4789 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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(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_2) = 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_2)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_2)))))) # label(fact_4245_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4790 (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_1826_divide__zero__left) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4791 (all M all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) = one_one(int) -> one_one(int) = ti(int,M) | ti(int,M) = hAPP(int,int,number_number_of(int),min))) # label(fact_690_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4792 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_132_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4793 (all Na all Xa exists T_4 (hAPP(real,real,cos,Xa) = 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))),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),Xa))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na))),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),Na))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa),Na))) & 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),Xa))))) # label(fact_4269_Maclaurin__cos__expansion) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4794 (all X_a all X_b all Xa all Ya 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),Xa),Ya) = 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),Xa)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Ya))))) # label(fact_4805_Eps__split__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4795 (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_4848_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4796 (all N (zero_zero(nat) != N -> hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))) # label(fact_1507_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4797 (all X_b all X_a (real_normed_field(X_a) -> (all G all A_2 all Ya 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_2)),Ya) = 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)),Ya)),A_2)))) # label(fact_4208_divide_Osetsum) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4798 (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_4018_prod__case__beta) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4799 (all X_a (zero(X_a) -> (all Diff all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)) -> 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)),Na))),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,Na),zero_zero(X_a))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),Na))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),Na)))) = hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,zero_zero(nat)),zero_zero(X_a)))))) # label(fact_4263_Maclaurin__bi__le__lemma) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4800 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3567_minus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4801 (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_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),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,N_1)))),X))))))) # label(fact_2662_ex__inverse__of__nat__Suc__less) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4802 (all X_a (field(X_a) -> (all Z all Na 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),Na),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),Na),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),Na),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)),Na)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),Na))),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),Na)),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),Na),hAPP(nat,nat,suc,zero_zero(nat)))))))))) # label(fact_4265_lemma__termdiff2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4803 (all X_a all B_1 all A_2 ((all X_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_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)),A_2),B_1)))) # label(fact_2249_subsetI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4804 (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)),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_1644_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4805 (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(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(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))))))) # label(fact_2027_abs__number__of) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4806 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_3),B_2)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_3),zero_zero(int)))))) # label(fact_1078_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4807 (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_735_diff__self) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4808 (all Ta all B_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_1)) -> (all X_1 ((all Xa_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa_1) != ti(int,X_1))))) -> (ti(int,Ta) != ti(int,X_1) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),D) != ti(int,Ta))))))) # label(fact_4667_bset_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4809 (all X_a (ord(X_a) -> ord_min(X_a) = ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4810 (all Y all U_1 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_1))) -> 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_1),hAPP(real,real,inverse_inverse(real),X1_1)))))))) # label(fact_2623_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4811 (all X_a (field(X_a) -> (all N all M all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_1798_power__diff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4812 (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) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))) # label(fact_2081_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4813 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Ya))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)))))) # label(fact_50_less__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4814 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_513_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4815 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_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),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_2) = 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_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_2)))))) # label(fact_3981_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4816 (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_4852_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4817 (all M all K_4 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) -> (exists S_1 exists T_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N)) = ti(int,K_4))))) # label(fact_3507_zgcd__ex__linear) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4818 (exists K_2 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_1)),K_2)))) # label(fact_2993_cnj_Obounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4819 (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_2402_natceiling__le) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4820 (all Sb all Ta all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_3),B_2)) -> 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_3),Sb)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_2),Ta))),pair_less)))) # label(fact_3511_pair__lessI1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4821 (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))) # label(fact_1480_tsub__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4822 (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))) = 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)))) & (-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)))))) # label(fact_3927_power__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4823 (all X_a all A_2 all B_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)),A_2),B_1)) -> 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_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_1))))) # label(fact_2842_PowI) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4824 (all I all M_1 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3902_card__less__Suc2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4825 (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_2173_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4826 (all X all Y all 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)) = 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))) # label(fact_126_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4827 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))) = hAPP(X_a,int,archimedean_ceiling(X_a),X)))) # label(fact_3320_ceiling__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4828 (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_1865_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4829 (all X_a (real_normed_vector(X_a) -> (all X ((ti(X_a,X) = zero_zero(X_a) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = zero_zero(real)) & (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)))))) # label(fact_2319_norm__sgn) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4830 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat)) # label(fact_833_diff__add__0) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4831 (all Z all Wa (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Z),Wa)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Z),Wa)) & Wa != Z)) # label(fact_3735_less__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4832 (all D_1 all A_3 all B_2 (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_3),B_2)) = one_one(int) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),B_2) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),A_3) = one_one(int))) # label(fact_4412_coprime__mul__eq__int) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4833 (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]. 7.75/7.73 4834 (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_3540_dist__norm) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4835 (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_160_power__one__right) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4836 (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_1189_aux______4) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4837 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))) # label(fact_3359_real__of__int__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4838 (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_2050_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4839 (all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))))) # label(fact_2142_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4840 (all X_b all X_c all X_a all F all G ((all X_1 all Y_1 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_1),Y_1)) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_1),Y_1)) -> 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_4356_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4841 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))) # label(fact_1971_norm__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4842 (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_2561_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4843 (all N all 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))) = 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))) # label(fact_3059_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4844 (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_3240_gcd__dvd__prod__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4845 (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_1407_divides__rexp) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4846 (all X_a (division_ring(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1))))) # label(fact_2576_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4847 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),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),F),A_2) = zero_zero(X_b))))) # label(fact_4234_setsum__infinite) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4848 (all Z_4 all Z_1 all W_2 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_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_2),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)))))) # label(fact_263_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4849 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4850 (all P_1 all I (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,I))) <-> (all N_1 (hAPP(nat,int,semiring_1_of_nat(int),N_1) = ti(int,I) -> hBOOL(hAPP(nat,bool,P_1,N_1)))) & (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)))))) # label(fact_1036_split__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4851 (all Xa all Ya all F ((all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),zero_zero(real)))) -> hAPP(real,real,F,Xa) = hAPP(real,real,F,Ya))) # label(fact_2723_DERIV__isconst__all) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4852 (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),plus_plus(nat),Y),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))) # label(fact_472_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4853 (all X_a (dense_linorder(X_a) -> (all A_3 all B_2 all C 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_3),B_2)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_3))))))) # label(fact_4554_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4854 (all X_a (real_normed_vector(X_a) -> (all K all X_2 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_2)) -> 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_2),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_3864_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4855 (all Xa all Ya (-hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Ya)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Xa)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),Ya)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Xa),Ya))))) # label(fact_2470_even__sum__nat) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4856 (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_3067_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4857 (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_1040_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4858 (all W all 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))) = 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)))) # label(fact_966_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4859 (all X_a all Xa all Ya all F (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,Xa)),hAPP(X_a,nat,F,Ya))) <-> 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),Xa),Ya)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))))) # label(fact_3344_in__measure) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4860 (all X_a (topological_space(X_a) -> (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,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_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),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_3))))))) # label(fact_4619_LIM__rabs__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4861 (all X_a (archim1727834104eiling(X_a) -> (all Z all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),Xa))) <-> 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)),Xa)))))) # label(fact_3618_le__floor__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4862 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_1347_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4863 (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_3253_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4864 (all Q_3 ((Q_3 != zero_zero(rat) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = one_one(rat)) & (-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))) & (Q_3 = zero_zero(rat) -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = zero_zero(rat)))) # label(fact_3724_sgn__rat__def) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4865 (all Sb all Ta all A_3 all B_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Sb),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_3),Sb)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_2),Ta))),pair_leq))))) # label(fact_3513_pair__leqI2) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4866 (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_3686_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4867 (all D_1 all K all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (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))) <-> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2) = D_1))))) # label(fact_3093_divides__primepow) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4868 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X)))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))),one_one(X_a))),X)))))) # label(fact_3632_ceiling__correct) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4869 (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_624_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4870 (all X_a (preorder(X_a) -> (all X all Y (Y = X -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_511_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4871 (all Xa all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Xa),Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)) | zero_zero(nat) = Na)) # label(fact_146_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption]. 7.75/7.73 4872 (all X_a (division_ring(X_a) -> (all A_1 all B all C_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)),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),inverse_divide(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C_1))))) # label(fact_1829_add__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4873 (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_2040_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4874 (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_4046_summable__rabs) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4875 (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_12_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4876 (all X_a all Q_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> ((all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4892_someI2__ex) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4877 (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_1599_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4878 (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_967_int__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4879 (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_1895_lemma__termdiff3) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4880 (all X_a all X_b all X_c all X_d all X_e all Xa all P_1 ((all A_4 all B_4 all C_4 all D_2 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_2),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,Xa)))) # label(fact_3174_prod__induct5) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4881 (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_4253_lemma__termdiff1) # label(axiom) # label(non_clause). [assumption]. 7.79/7.73 4882 (all A_1 all B (zero_zero(int) != ti(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)),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_1623_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4883 (all X_a all X_c (comm_monoid_add(X_c) -> ti(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),big_co1399186613setsum(X_a,X_c)) = big_co1399186613setsum(X_a,X_c))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4884 (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)),X) = hAPP(int,X_a,number_number_of(X_a),min))))) # label(fact_2498_Parity_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4885 (all Na all Xa (Xa != 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),Xa),Na)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Xa),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),Xa)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Na)))) # label(fact_4233_sumr__geometric) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4886 (all X_a (linord20386208strict(X_a) -> (all C_1 all D_3 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_3)))))))))) # label(fact_482_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4887 (all X_a (topological_space(X_a) -> (all K all F all A_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),F),A_3),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_3),sequentially)))))) # label(fact_4507_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4888 (all Xa all Ya (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ya),Xa)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Xa),Ya)) <-> Ya = Xa)) # label(fact_963_divides__antisym) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4889 (all X_a (group_add(X_a) -> (all A_3 all B_2 (hAPP(X_a,X_a,uminus_uminus(X_a),A_3) = ti(X_a,B_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_2) = ti(X_a,A_3))))) # label(fact_1923_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4890 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_3)) -> 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_3),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1808_half__gt__zero) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4891 (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)),J_2)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),K_4)),M)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),K_4) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),J_2)))) # label(fact_790_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4892 (all X_a all X_b (metric_space(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),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),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_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_2))))))) # label(fact_4485_tendsto__dist) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4893 (all X_a (group_add(X_a) -> (all A_3 all B_2 (hAPP(X_a,X_a,uminus_uminus(X_a),A_3) = hAPP(X_a,X_a,uminus_uminus(X_a),B_2) <-> ti(X_a,A_3) = ti(X_a,B_2))))) # label(fact_1924_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4894 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),pls)) = zero_zero(X_a)))) # label(fact_1781_divide__Numeral0) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4895 (all X_a (linordered_field(X_a) -> (all C_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),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(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_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C_1),B))))))))) # label(fact_1876_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4896 (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_1487_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4897 (all X all Y all Xa_2 all Ya_1 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_2),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_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2181_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4898 (all F all G ((all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_1))),hAPP(nat,real,G,N_1)))) -> (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_4097_summable__le2) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4899 (all Na 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)),Na)))))) # label(fact_3853_bdd__int__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4900 (all X_a all X_b (topological_space(X_b) -> (all F all L all A_2 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_2),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_2))))))) # label(fact_4516_tendsto__mono) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4901 (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_617_mult__le__mono) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4902 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_3 all A_1 all B all R_3 (ti(X_a,R_3) != zero_zero(X_a) -> (ti(X_a,B) = ti(X_a,A_1) & ti(X_a,D_3) != ti(X_a,C_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),D_3)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_3),C_1))))))) # label(fact_458_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4903 (all A_3 all B_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_2)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_3),B_2)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_3),zero_zero(int)))))) # label(fact_3813_Fract__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4904 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z_1)))) # label(fact_90_add__number__of__left) # label(axiom) # label(non_clause). [assumption]. 7.79/7.74 4905 (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_3452_Euler__Fermat) # label(axiom) # label(non_clause). [assumption]. 11.20/11.21 4906 (all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),B)) # label(fact_1072_zdiv__zero) # label(axiom) # label(non_clause). [assumption]. 11.20/11.21 4907 (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_1217_Euler_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 11.20/11.21 4908 (all X_a (linord581940658strict(X_a) -> (all Xa all Ya (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),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya)) <-> ti(X_a,Ya) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Xa))))) # label(fact_457_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 11.20/11.21 4909 -(zero_zero(int) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 11.20/11.21 11.20/11.21 ============================== end of process non-clausal formulas === 11.20/11.21 11.20/11.21 ============================== PROCESS INITIAL CLAUSES =============== 11.20/11.21 11.20/11.21 ============================== PREDICATE ELIMINATION ================= 11.20/11.21 4910 -real_algebra(A) | 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)) = 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) # label(fact_4721_mult__scaleR__left) # label(axiom). [clausify(2172)]. 11.20/11.21 4911 real_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__algebra) # label(axiom). [assumption]. 11.20/11.21 4912 real_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__algebra) # label(axiom). [assumption]. 11.20/11.21 Derived: 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)) = 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). [resolve(4910,a,4911,a)]. 11.20/11.21 Derived: 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)) = 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). [resolve(4910,a,4912,a)]. 11.20/11.21 4913 -real_algebra(A) | 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)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4719_mult__scaleR__right) # label(axiom). [clausify(3120)]. 11.20/11.21 Derived: 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)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)). [resolve(4913,a,4911,a)]. 11.20/11.21 Derived: 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)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C)). [resolve(4913,a,4912,a)]. 11.20/11.21 4914 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption]. 11.20/11.21 4915 -linorder(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_4977_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(5)]. 11.20/11.22 4916 -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_eq(A),B),C)) # label(fact_564_linorder__antisym__conv1) # label(axiom). [clausify(78)]. 11.20/11.22 4917 -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_eq(A),B),C)) # label(fact_564_linorder__antisym__conv1) # label(axiom). [clausify(78)]. 11.20/11.22 4918 -linorder(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)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(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),D)) # label(fact_4978_min__max_Osup__inf__distrib2) # label(axiom). [clausify(85)]. 11.20/11.22 4919 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_534_not__less__iff__gr__or__eq) # label(axiom). [clausify(99)]. 11.20/11.22 4920 -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_534_not__less__iff__gr__or__eq) # label(axiom). [clausify(99)]. 11.20/11.22 4921 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_534_not__less__iff__gr__or__eq) # label(axiom). [clausify(99)]. 11.20/11.22 4922 -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_4834_min__max_Oinf__left__idem) # label(axiom). [clausify(113)]. 11.20/11.22 4923 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f22(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2853_minf_I6_J) # label(axiom). [clausify(121)]. 11.20/11.22 Derived: 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(4914,a,4915,a)]. 11.20/11.22 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(4914,a,4916,a)]. 11.20/11.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(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),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),C)). [resolve(4914,a,4918,a)]. 11.20/11.22 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(4914,a,4920,a)]. 11.20/11.22 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(4914,a,4922,a)]. 11.20/11.22 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f22(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(4914,a,4923,a)]. 11.20/11.22 4924 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_535_linorder__neq__iff) # label(axiom). [clausify(193)]. 11.20/11.22 4925 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_535_linorder__neq__iff) # label(axiom). [clausify(193)]. 11.20/11.22 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B). [resolve(4925,a,4914,a)]. 11.20/11.22 4926 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_535_linorder__neq__iff) # label(axiom). [clausify(193)]. 11.35/11.32 4927 -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_4825_min__max_Oless__infI2) # label(axiom). [clausify(261)]. 11.35/11.32 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(4927,a,4914,a)]. 11.35/11.32 4928 -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_4845_min__max_Ole__iff__inf) # label(axiom). [clausify(270)]. 11.35/11.32 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(4928,a,4914,a)]. 11.35/11.32 4929 -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_4845_min__max_Ole__iff__inf) # label(axiom). [clausify(270)]. 11.35/11.32 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(4929,a,4914,a)]. 11.35/11.32 4930 -linorder(A) | -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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_4824_min__less__iff__conj) # label(axiom). [clausify(417)]. 11.35/11.32 Derived: -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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(4930,a,4914,a)]. 11.35/11.32 4931 -linorder(A) | -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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4824_min__less__iff__conj) # label(axiom). [clausify(417)]. 11.35/11.32 Derived: -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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4931,a,4914,a)]. 11.35/11.32 4932 -linorder(A) | 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))) | -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),C)) # label(fact_4824_min__less__iff__conj) # label(axiom). [clausify(417)]. 11.35/11.32 Derived: 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))) | -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),B)). [resolve(4932,a,4914,a)]. 11.35/11.32 4933 -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_4833_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(487)]. 11.35/11.32 4934 -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_571_linorder__not__le) # label(axiom). [clausify(690)]. 11.35/11.32 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(4934,a,4914,a)]. 11.35/11.32 4935 -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_571_linorder__not__le) # label(axiom). [clausify(690)]. 11.35/11.32 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(4935,a,4914,a)]. 11.35/11.32 4936 linorder(rat) # label(arity_Rat_Orat___Orderings_Olinorder) # label(axiom). [assumption]. 11.35/11.32 Derived: 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(4936,a,4915,a)]. 11.35/11.36 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(4936,a,4916,a)]. 11.35/11.36 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(4936,a,4917,a)]. 11.35/11.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(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),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),C)). [resolve(4936,a,4918,a)]. 11.35/11.36 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,B) = ti(rat,A). [resolve(4936,a,4919,a)]. 11.35/11.36 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(4936,a,4920,a)]. 11.35/11.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) != ti(rat,A). [resolve(4936,a,4921,a)]. 11.35/11.36 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(4936,a,4922,a)]. 11.35/11.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f22(rat,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(4936,a,4923,a)]. 11.35/11.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,A) != ti(rat,B). [resolve(4936,a,4925,a)]. 11.35/11.36 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(4936,a,4927,a)]. 11.35/11.36 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(4936,a,4928,a)]. 11.35/11.36 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(4936,a,4929,a)]. 11.35/11.36 Derived: -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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(4936,a,4930,a)]. 11.35/11.36 Derived: -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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(4936,a,4931,a)]. 11.35/11.36 Derived: 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))) | -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),B)). [resolve(4936,a,4932,a)]. 11.35/11.36 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),B),A)). [resolve(4936,a,4934,a)]. 11.35/11.36 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),B),A)). [resolve(4936,a,4935,a)]. 11.35/11.36 4937 -linorder(A) | -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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4347_lessThan__strict__subset__iff) # label(axiom). [clausify(1020)]. 11.35/11.36 Derived: -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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4937,a,4914,a)]. 11.35/11.36 Derived: -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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(4937,a,4936,a)]. 11.43/11.42 4938 -linorder(A) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4347_lessThan__strict__subset__iff) # label(axiom). [clausify(1020)]. 11.43/11.42 Derived: 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))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4938,a,4914,a)]. 11.43/11.42 Derived: 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))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(4938,a,4936,a)]. 11.43/11.42 4939 -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_533_linorder__less__linear) # label(axiom). [clausify(1091)]. 11.43/11.42 4940 -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_4855_min__le__iff__disj) # label(axiom). [clausify(1175)]. 11.43/11.42 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(4940,a,4914,a)]. 11.43/11.42 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(4940,a,4936,a)]. 11.43/11.42 4941 -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_4855_min__le__iff__disj) # label(axiom). [clausify(1175)]. 11.43/11.42 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)). [resolve(4941,a,4914,a)]. 11.43/11.42 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)). [resolve(4941,a,4936,a)]. 11.43/11.42 4942 -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_4855_min__le__iff__disj) # label(axiom). [clausify(1175)]. 11.43/11.42 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(4942,a,4914,a)]. 11.43/11.42 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(4942,a,4936,a)]. 11.43/11.42 4943 -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_4985_min__max_Oless__supI2) # label(axiom). [clausify(1209)]. 11.43/11.42 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(4943,a,4914,a)]. 11.51/11.49 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(4943,a,4936,a)]. 11.51/11.49 4944 -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_4220_ivl__diff) # label(axiom). [clausify(1272)]. 11.51/11.49 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(4944,a,4914,a)]. 11.51/11.49 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(4944,a,4936,a)]. 11.51/11.49 4945 -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_4851_min__max_Ole__infI) # label(axiom). [clausify(1307)]. 11.51/11.49 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),C)) | 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))). [resolve(4945,a,4914,a)]. 11.51/11.49 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),C)) | 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))). [resolve(4945,a,4936,a)]. 11.51/11.49 4946 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption]. 11.51/11.49 Derived: 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(4946,a,4915,a)]. 11.51/11.49 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4946,a,4916,a)]. 11.51/11.49 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4946,a,4917,a)]. 11.51/11.49 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(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),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),C)). [resolve(4946,a,4918,a)]. 11.51/11.49 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,B) = ti(nat,A). [resolve(4946,a,4919,a)]. 11.51/11.49 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(4946,a,4920,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(4946,a,4921,a)]. 11.51/11.52 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(4946,a,4922,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f22(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(4946,a,4923,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B). [resolve(4946,a,4925,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)). [resolve(4946,a,4927,a)]. 11.51/11.52 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(4946,a,4928,a)]. 11.51/11.52 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(4946,a,4929,a)]. 11.51/11.52 Derived: -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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(4946,a,4930,a)]. 11.51/11.52 Derived: -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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4946,a,4931,a)]. 11.51/11.52 Derived: 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))) | -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),B)). [resolve(4946,a,4932,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(4946,a,4934,a)]. 11.51/11.52 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(4946,a,4935,a)]. 11.51/11.52 Derived: -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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4946,a,4937,a)]. 11.51/11.52 Derived: 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))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(4946,a,4938,a)]. 11.51/11.52 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(4946,a,4940,a)]. 11.51/11.52 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)). [resolve(4946,a,4941,a)]. 11.51/11.52 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(4946,a,4942,a)]. 11.51/11.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(4946,a,4943,a)]. 11.51/11.52 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(4946,a,4944,a)]. 11.64/11.61 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),C)) | 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))). [resolve(4946,a,4945,a)]. 11.64/11.61 4947 -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_570_linorder__le__less__linear) # label(axiom). [clausify(1481)]. 11.64/11.61 4948 -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),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,D) # label(fact_4223_atLeastLessThan__inj_I1_J) # label(axiom). [clausify(1508)]. 11.64/11.61 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),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) = ti(int,C). [resolve(4948,a,4914,a)]. 11.64/11.61 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),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,A) = ti(rat,C). [resolve(4948,a,4936,a)]. 11.64/11.61 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),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) = ti(nat,C). [resolve(4948,a,4946,a)]. 11.64/11.61 4949 -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_4975_min__max_Oinf__sup__absorb) # label(axiom). [clausify(1596)]. 11.64/11.61 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(4949,a,4914,a)]. 11.64/11.61 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(4949,a,4936,a)]. 11.64/11.61 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(4949,a,4946,a)]. 11.64/11.61 4950 -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_565_not__leE) # label(axiom). [clausify(1632)]. 11.64/11.61 4951 -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_4853_min__max_Oinf__mono) # label(axiom). [clausify(1684)]. 11.64/11.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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(4951,a,4914,a)]. 11.64/11.61 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),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(4951,a,4936,a)]. 11.90/11.82 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(4951,a,4946,a)]. 11.90/11.82 4952 -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_4986_min__max_Oless__supI1) # label(axiom). [clausify(1706)]. 11.90/11.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(4952,a,4914,a)]. 11.90/11.82 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),B),C))). [resolve(4952,a,4936,a)]. 11.90/11.82 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(4952,a,4946,a)]. 11.90/11.82 4953 -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_515_linorder__cases) # label(axiom). [clausify(1866)]. 11.90/11.82 4954 -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_4859_dual__max) # label(axiom). [clausify(2110)]. 11.90/11.82 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(4954,a,4914,a)]. 11.90/11.82 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(4954,a,4936,a)]. 11.90/11.82 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(4954,a,4946,a)]. 11.90/11.82 4955 -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_4837_min__max_Oinf_Oassoc) # label(axiom). [clausify(2158)]. 11.90/11.82 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(4955,a,4914,a)]. 11.90/11.82 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(4955,a,4936,a)]. 11.90/11.82 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(4955,a,4946,a)]. 11.90/11.82 4956 -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_559_linorder__antisym__conv2) # label(axiom). [clausify(2207)]. 11.90/11.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4956,a,4914,a)]. 11.90/11.82 4957 -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_559_linorder__antisym__conv2) # label(axiom). [clausify(2207)]. 11.90/11.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4957,a,4914,a)]. 11.96/11.92 4958 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4830_min__max_Oinf_Oidem) # label(axiom). [clausify(2376)]. 11.96/11.92 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A). [resolve(4958,a,4914,a)]. 11.96/11.92 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),A). [resolve(4958,a,4936,a)]. 11.96/11.92 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A). [resolve(4958,a,4946,a)]. 11.96/11.92 4959 linorder(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Orderings_Olinorder) # label(axiom). [assumption]. 11.96/11.92 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_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(4959,a,4915,a)]. 11.96/11.92 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) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(4959,a,4916,a)]. 11.96/11.92 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) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(4959,a,4917,a)]. 11.96/11.92 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_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),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),C)). [resolve(4959,a,4918,a)]. 11.96/11.92 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,B) = ti(quickcheck_code_int,A). [resolve(4959,a,4919,a)]. 11.96/11.92 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(4959,a,4920,a)]. 11.96/11.92 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(4959,a,4921,a)]. 11.96/11.92 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(4959,a,4922,a)]. 11.96/11.93 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f22(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(4959,a,4923,a)]. 11.96/11.93 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(4959,a,4925,a)]. 11.96/11.93 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(4959,a,4927,a)]. 11.96/11.93 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(4959,a,4928,a)]. 11.96/11.93 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(4959,a,4929,a)]. 11.96/11.93 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),ord_min(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(4959,a,4930,a)]. 11.96/11.93 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),ord_min(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),B)). [resolve(4959,a,4931,a)]. 11.96/11.93 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),ord_min(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)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)). [resolve(4959,a,4932,a)]. 11.96/11.93 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),B),A)). [resolve(4959,a,4934,a)]. 11.96/11.93 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),B),A)). [resolve(4959,a,4935,a)]. 11.96/11.93 Derived: -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))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)). [resolve(4959,a,4937,a)]. 11.96/11.94 Derived: 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))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)). [resolve(4959,a,4938,a)]. 11.96/11.94 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(4959,a,4940,a)]. 11.96/11.94 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)). [resolve(4959,a,4941,a)]. 11.96/11.94 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(4959,a,4942,a)]. 11.96/11.94 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(4959,a,4943,a)]. 11.96/11.94 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(4959,a,4944,a)]. 11.96/11.94 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),C)) | 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))). [resolve(4959,a,4945,a)]. 12.06/11.99 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),C),D)) | -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,C). [resolve(4959,a,4948,a)]. 12.06/11.99 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(4959,a,4949,a)]. 12.06/11.99 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(4959,a,4951,a)]. 12.06/11.99 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(4959,a,4952,a)]. 12.06/11.99 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(4959,a,4954,a)]. 12.06/11.99 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(4959,a,4955,a)]. 12.06/11.99 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(4959,a,4958,a)]. 12.06/11.99 4960 -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_4846_min__max_Ole__inf__iff) # label(axiom). [clausify(2522)]. 12.11/12.05 4961 -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_min(A),C),D))) # label(fact_4846_min__max_Ole__inf__iff) # label(axiom). [clausify(2522)]. 12.11/12.05 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_min(int),B),C))). [resolve(4961,a,4914,a)]. 12.11/12.05 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_min(rat),B),C))). [resolve(4961,a,4936,a)]. 12.11/12.05 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_min(nat),B),C))). [resolve(4961,a,4946,a)]. 12.11/12.05 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_min(quickcheck_code_int),B),C))). [resolve(4961,a,4959,a)]. 12.11/12.05 4962 -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_min(A),D),C))) # label(fact_4846_min__max_Ole__inf__iff) # label(axiom). [clausify(2522)]. 12.11/12.05 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_min(int),C),B))). [resolve(4962,a,4914,a)]. 12.11/12.05 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_min(rat),C),B))). [resolve(4962,a,4936,a)]. 12.11/12.05 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_min(nat),C),B))). [resolve(4962,a,4946,a)]. 12.11/12.05 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_min(quickcheck_code_int),C),B))). [resolve(4962,a,4959,a)]. 12.11/12.05 4963 -linorder(A) | hAPP(A,fun(A,bool),ord_lessThan(A),B) != hAPP(A,fun(A,bool),ord_lessThan(A),C) | ti(A,B) = ti(A,C) # label(fact_4343_lessThan__eq__iff) # label(axiom). [clausify(2609)]. 12.11/12.05 Derived: hAPP(int,fun(int,bool),ord_lessThan(int),A) != hAPP(int,fun(int,bool),ord_lessThan(int),B) | ti(int,A) = ti(int,B). [resolve(4963,a,4914,a)]. 12.11/12.05 Derived: hAPP(rat,fun(rat,bool),ord_lessThan(rat),A) != hAPP(rat,fun(rat,bool),ord_lessThan(rat),B) | ti(rat,A) = ti(rat,B). [resolve(4963,a,4936,a)]. 12.11/12.05 Derived: hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) != hAPP(nat,fun(nat,bool),ord_lessThan(nat),B) | ti(nat,A) = ti(nat,B). [resolve(4963,a,4946,a)]. 12.11/12.05 Derived: 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) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B). [resolve(4963,a,4959,a)]. 12.11/12.05 4964 -linorder(A) | hAPP(A,fun(A,bool),ord_lessThan(A),B) = hAPP(A,fun(A,bool),ord_lessThan(A),C) | ti(A,B) != ti(A,C) # label(fact_4343_lessThan__eq__iff) # label(axiom). [clausify(2609)]. 12.11/12.05 Derived: hAPP(int,fun(int,bool),ord_lessThan(int),A) = hAPP(int,fun(int,bool),ord_lessThan(int),B) | ti(int,A) != ti(int,B). [resolve(4964,a,4914,a)]. 12.11/12.08 Derived: hAPP(rat,fun(rat,bool),ord_lessThan(rat),A) = hAPP(rat,fun(rat,bool),ord_lessThan(rat),B) | ti(rat,A) != ti(rat,B). [resolve(4964,a,4936,a)]. 12.11/12.08 Derived: hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),B) | ti(nat,A) != ti(nat,B). [resolve(4964,a,4946,a)]. 12.11/12.08 Derived: 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) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B). [resolve(4964,a,4959,a)]. 12.11/12.08 4965 -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),B),D)),C)) # label(fact_4983_max__less__iff__conj) # label(axiom). [clausify(2642)]. 12.11/12.08 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),A),C)),B)). [resolve(4965,a,4914,a)]. 12.11/12.08 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),A),C)),B)). [resolve(4965,a,4936,a)]. 12.11/12.08 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),A),C)),B)). [resolve(4965,a,4946,a)]. 12.11/12.08 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),A),C)),B)). [resolve(4965,a,4959,a)]. 12.11/12.08 4966 -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_4983_max__less__iff__conj) # label(axiom). [clausify(2642)]. 12.11/12.08 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(4966,a,4914,a)]. 12.11/12.08 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(4966,a,4936,a)]. 12.11/12.08 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(4966,a,4946,a)]. 12.11/12.08 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(4966,a,4959,a)]. 12.11/12.08 4967 -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_4983_max__less__iff__conj) # label(axiom). [clausify(2642)]. 12.11/12.08 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(4967,a,4914,a)]. 12.18/12.14 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(4967,a,4936,a)]. 12.18/12.14 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(4967,a,4946,a)]. 12.18/12.14 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(4967,a,4959,a)]. 12.18/12.14 4968 linorder(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Orderings_Olinorder) # label(axiom). [assumption]. 12.18/12.14 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_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(4968,a,4915,a)]. 12.18/12.14 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) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(4968,a,4916,a)]. 12.18/12.14 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) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(4968,a,4917,a)]. 12.18/12.14 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_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),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),C)). [resolve(4968,a,4918,a)]. 12.18/12.14 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),B),A)) | ti(code_code_numeral,B) = ti(code_code_numeral,A). [resolve(4968,a,4919,a)]. 12.18/12.14 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),B),A)). [resolve(4968,a,4920,a)]. 12.18/12.14 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(4968,a,4921,a)]. 12.18/12.14 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),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(4968,a,4922,a)]. 12.18/12.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f22(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(4968,a,4923,a)]. 12.18/12.15 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(4968,a,4925,a)]. 12.18/12.15 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),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(4968,a,4927,a)]. 12.18/12.15 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(4968,a,4928,a)]. 12.18/12.15 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(4968,a,4929,a)]. 12.18/12.15 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),ord_min(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(4968,a,4930,a)]. 12.18/12.15 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),ord_min(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),B)). [resolve(4968,a,4931,a)]. 12.18/12.15 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),ord_min(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)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)). [resolve(4968,a,4932,a)]. 12.18/12.15 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_eq(code_code_numeral),B),A)). [resolve(4968,a,4934,a)]. 12.18/12.15 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_eq(code_code_numeral),B),A)). [resolve(4968,a,4935,a)]. 12.18/12.15 Derived: -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))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)). [resolve(4968,a,4937,a)]. 12.18/12.16 Derived: 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))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)). [resolve(4968,a,4938,a)]. 12.18/12.16 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(4968,a,4940,a)]. 12.18/12.16 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)). [resolve(4968,a,4941,a)]. 12.18/12.16 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(4968,a,4942,a)]. 12.18/12.16 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(4968,a,4943,a)]. 12.18/12.16 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | 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(4968,a,4944,a)]. 12.18/12.16 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),A),C)) | 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))). [resolve(4968,a,4945,a)]. 12.18/12.16 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),C),D)) | -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,C). [resolve(4968,a,4948,a)]. 12.18/12.17 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(4968,a,4949,a)]. 12.18/12.17 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -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(4968,a,4951,a)]. 12.18/12.17 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(4968,a,4952,a)]. 12.18/12.17 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(4968,a,4954,a)]. 12.18/12.17 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_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(4968,a,4955,a)]. 12.18/12.17 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(4968,a,4958,a)]. 12.18/12.17 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -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))). [resolve(4968,a,4961,a)]. 12.18/12.17 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -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),C),B))). [resolve(4968,a,4962,a)]. 12.18/12.17 Derived: 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) | ti(code_code_numeral,A) = ti(code_code_numeral,B). [resolve(4968,a,4963,a)]. 12.25/12.19 Derived: 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) | ti(code_code_numeral,A) != ti(code_code_numeral,B). [resolve(4968,a,4964,a)]. 12.25/12.19 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),A),C)),B)). [resolve(4968,a,4965,a)]. 12.25/12.19 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(4968,a,4966,a)]. 12.25/12.19 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(4968,a,4967,a)]. 12.25/12.19 4969 -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_4826_min__max_Oless__infI1) # label(axiom). [clausify(2774)]. 12.25/12.19 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),A),C)),B)). [resolve(4969,a,4914,a)]. 12.25/12.19 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),A),C)),B)). [resolve(4969,a,4936,a)]. 12.25/12.19 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),A),C)),B)). [resolve(4969,a,4946,a)]. 12.25/12.19 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),A),C)),B)). [resolve(4969,a,4959,a)]. 12.25/12.19 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_min(code_code_numeral),A),C)),B)). [resolve(4969,a,4968,a)]. 12.25/12.19 4970 -linorder(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_4976_min__max_Osup__inf__distrib1) # label(axiom). [clausify(2787)]. 12.25/12.19 Derived: 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(4970,a,4914,a)]. 12.50/12.47 Derived: 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(4970,a,4936,a)]. 12.50/12.47 Derived: 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(4970,a,4946,a)]. 12.50/12.47 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),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(4970,a,4959,a)]. 12.50/12.47 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_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(4970,a,4968,a)]. 12.50/12.47 4971 -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_4849_min__max_Oinf__absorb1) # label(axiom). [clausify(2899)]. 12.50/12.47 4972 -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),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,E) # label(fact_4222_atLeastLessThan__inj_I2_J) # label(axiom). [clausify(3084)]. 12.50/12.47 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),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,D). [resolve(4972,a,4914,a)]. 12.50/12.47 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),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) = ti(rat,D). [resolve(4972,a,4936,a)]. 12.50/12.47 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),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,D). [resolve(4972,a,4946,a)]. 12.50/12.47 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),C),D)) | -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,D). [resolve(4972,a,4959,a)]. 12.69/12.67 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),C),D)) | -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,D). [resolve(4972,a,4968,a)]. 12.69/12.67 4973 -linorder(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),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_4979_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(3258)]. 12.69/12.67 Derived: 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),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(4973,a,4914,a)]. 12.69/12.67 Derived: 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),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(4973,a,4936,a)]. 12.69/12.67 Derived: 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),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B). [resolve(4973,a,4946,a)]. 12.69/12.67 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_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),C),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(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(4973,a,4959,a)]. 12.69/12.67 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_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),C),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(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(4973,a,4968,a)]. 12.69/12.67 4974 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f606(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2851_minf_I8_J) # label(axiom). [clausify(3365)]. 12.86/12.85 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f606(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(4974,a,4914,a)]. 12.86/12.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f606(rat,B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(4974,a,4936,a)]. 12.86/12.85 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f606(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(4974,a,4946,a)]. 12.86/12.85 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f606(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(4974,a,4959,a)]. 12.86/12.85 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f606(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(4974,a,4968,a)]. 12.86/12.85 4975 -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_4965_atMost__eq__iff) # label(axiom). [clausify(3438)]. 12.86/12.85 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(4975,a,4914,a)]. 12.86/12.85 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(4975,a,4936,a)]. 12.86/12.85 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(4975,a,4946,a)]. 12.86/12.85 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(4975,a,4959,a)]. 12.86/12.85 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(4975,a,4968,a)]. 12.86/12.85 4976 -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_4965_atMost__eq__iff) # label(axiom). [clausify(3438)]. 12.86/12.85 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(4976,a,4914,a)]. 12.86/12.85 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(4976,a,4936,a)]. 12.86/12.85 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(4976,a,4946,a)]. 12.86/12.85 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(4976,a,4959,a)]. 12.86/12.85 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(4976,a,4968,a)]. 12.86/12.85 4977 -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_4843_min__max_Oinf__le1) # label(axiom). [clausify(3442)]. 12.86/12.85 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(4977,a,4914,a)]. 12.86/12.85 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(4977,a,4936,a)]. 13.01/13.02 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(4977,a,4946,a)]. 13.01/13.02 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(4977,a,4959,a)]. 13.01/13.02 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(4977,a,4968,a)]. 13.01/13.02 4978 -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_499_linorder__le__cases) # label(axiom). [clausify(3647)]. 13.01/13.02 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(4978,a,4914,a)]. 13.01/13.02 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(4978,a,4936,a)]. 13.01/13.02 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(4978,a,4946,a)]. 13.01/13.02 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(4978,a,4959,a)]. 13.01/13.02 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(4978,a,4968,a)]. 13.01/13.02 4979 -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_4981_min__max_Odistrib__inf__le) # label(axiom). [clausify(3653)]. 13.01/13.02 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(4979,a,4914,a)]. 13.01/13.02 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(4979,a,4936,a)]. 13.01/13.02 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(4979,a,4946,a)]. 13.01/13.02 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(4979,a,4959,a)]. 13.25/13.20 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(4979,a,4968,a)]. 13.25/13.20 4980 -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_4832_min__max_Oinf__commute) # label(axiom). [clausify(3692)]. 13.25/13.20 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(4980,a,4914,a)]. 13.25/13.20 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(4980,a,4936,a)]. 13.25/13.20 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(4980,a,4946,a)]. 13.25/13.20 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(4980,a,4959,a)]. 13.25/13.20 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(4980,a,4968,a)]. 13.25/13.20 4981 -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_4838_min__max_Oinf__assoc) # label(axiom). [clausify(3802)]. 13.25/13.20 4982 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4842_Min_Oidem) # label(axiom). [clausify(3806)]. 13.25/13.20 4983 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f695(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2857_pinf_I6_J) # label(axiom). [clausify(3867)]. 13.25/13.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f695(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(4983,a,4914,a)]. 13.25/13.20 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f695(rat,A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(4983,a,4936,a)]. 13.25/13.20 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f695(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(4983,a,4946,a)]. 13.25/13.20 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f695(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(4983,a,4959,a)]. 13.25/13.20 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f695(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(4983,a,4968,a)]. 13.55/13.54 4984 -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_531_linorder__neqE) # label(axiom). [clausify(3947)]. 13.55/13.54 Derived: ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(4984,a,4914,a)]. 13.55/13.54 4985 -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_566_leI) # label(axiom). [clausify(4027)]. 13.55/13.54 4986 -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_4831_min__max_Oinf_Ocommute) # label(axiom). [clausify(4057)]. 13.55/13.54 4987 -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_532_linorder__antisym__conv3) # label(axiom). [clausify(4124)]. 13.55/13.54 4988 -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_532_linorder__antisym__conv3) # label(axiom). [clausify(4124)]. 13.55/13.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | ti(int,A) != ti(int,B). [resolve(4988,a,4914,a)]. 13.55/13.54 4989 -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_4847_min__max_Ole__infI1) # label(axiom). [clausify(4134)]. 13.55/13.54 4990 -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_4844_min__max_Oinf__le2) # label(axiom). [clausify(4141)]. 13.55/13.54 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(4990,a,4914,a)]. 13.55/13.54 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(4990,a,4936,a)]. 13.55/13.54 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(4990,a,4946,a)]. 13.55/13.54 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(4990,a,4959,a)]. 13.55/13.54 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(4990,a,4968,a)]. 13.55/13.54 4991 -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_4835_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(4269)]. 13.55/13.54 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(4991,a,4914,a)]. 13.55/13.54 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(4991,a,4936,a)]. 13.55/13.54 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(4991,a,4946,a)]. 13.72/13.69 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(4991,a,4959,a)]. 13.72/13.69 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(4991,a,4968,a)]. 13.72/13.69 4992 -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_4974_min__max_Osup__inf__absorb) # label(axiom). [clausify(4282)]. 13.72/13.69 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(4992,a,4914,a)]. 13.72/13.69 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(4992,a,4936,a)]. 13.72/13.69 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(4992,a,4946,a)]. 13.72/13.69 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),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(4992,a,4959,a)]. 13.72/13.69 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(4992,a,4968,a)]. 13.72/13.69 4993 -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_561_leD) # label(axiom). [clausify(4287)]. 13.72/13.69 4994 -number(A) | -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_250_le__number__of__eq__not__less) # label(axiom). [clausify(4386)]. 13.72/13.69 4995 -number(A) | -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_250_le__number__of__eq__not__less) # label(axiom). [clausify(4386)]. 13.72/13.69 4996 -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_4230_atLeastLessThan__subset__iff) # label(axiom). [clausify(4430)]. 13.72/13.69 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(4996,a,4914,a)]. 13.72/13.69 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(4996,a,4936,a)]. 13.72/13.69 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(4996,a,4946,a)]. 13.72/13.69 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(4996,a,4959,a)]. 13.72/13.69 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(4996,a,4968,a)]. 13.72/13.69 4997 -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_4230_atLeastLessThan__subset__iff) # label(axiom). [clausify(4430)]. 13.72/13.69 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(4997,a,4914,a)]. 13.72/13.69 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(4997,a,4936,a)]. 13.78/13.73 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(4997,a,4946,a)]. 13.78/13.73 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(4997,a,4959,a)]. 13.78/13.73 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(4997,a,4968,a)]. 13.78/13.73 4998 -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_4823_min__less__iff__disj) # label(axiom). [clausify(4479)]. 13.78/13.73 4999 -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_4823_min__less__iff__disj) # label(axiom). [clausify(4479)]. 13.78/13.73 5000 -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_min(A),B),D)),C)) # label(fact_4823_min__less__iff__disj) # label(axiom). [clausify(4479)]. 13.78/13.73 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_min(int),A),C)),B)). [resolve(5000,a,4914,a)]. 13.78/13.73 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_min(rat),A),C)),B)). [resolve(5000,a,4936,a)]. 13.78/13.73 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_min(nat),A),C)),B)). [resolve(5000,a,4946,a)]. 13.78/13.73 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_min(quickcheck_code_int),A),C)),B)). [resolve(5000,a,4959,a)]. 13.83/13.80 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_min(code_code_numeral),A),C)),B)). [resolve(5000,a,4968,a)]. 13.83/13.80 5001 -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_4836_min__max_Oinf__left__commute) # label(axiom). [clausify(4489)]. 13.83/13.80 5002 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom). [assumption]. 13.83/13.80 Derived: 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(5002,a,4915,a)]. 13.83/13.80 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5002,a,4916,a)]. 13.83/13.80 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5002,a,4917,a)]. 13.83/13.80 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(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),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),C)). [resolve(5002,a,4918,a)]. 13.83/13.80 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | ti(real,B) = ti(real,A). [resolve(5002,a,4919,a)]. 13.83/13.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5002,a,4920,a)]. 13.83/13.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A). [resolve(5002,a,4921,a)]. 13.83/13.80 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(5002,a,4922,a)]. 13.83/13.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f22(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5002,a,4923,a)]. 13.83/13.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) != ti(real,B). [resolve(5002,a,4925,a)]. 13.83/13.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),C),A)),B)). [resolve(5002,a,4927,a)]. 13.83/13.80 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(5002,a,4928,a)]. 13.83/13.80 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(5002,a,4929,a)]. 13.83/13.80 Derived: -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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5002,a,4930,a)]. 13.83/13.81 Derived: -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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5002,a,4931,a)]. 13.83/13.81 Derived: 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))) | -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),B)). [resolve(5002,a,4932,a)]. 13.83/13.81 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),B),A)). [resolve(5002,a,4934,a)]. 13.83/13.81 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),B),A)). [resolve(5002,a,4935,a)]. 13.83/13.81 Derived: -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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5002,a,4937,a)]. 13.83/13.81 Derived: 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))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5002,a,4938,a)]. 13.83/13.81 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(5002,a,4940,a)]. 13.83/13.81 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)). [resolve(5002,a,4941,a)]. 13.83/13.81 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(5002,a,4942,a)]. 13.83/13.81 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),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5002,a,4943,a)]. 13.83/13.81 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(5002,a,4944,a)]. 13.83/13.81 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_eq(real),A),C)) | 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))). [resolve(5002,a,4945,a)]. 13.83/13.81 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),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) = ti(real,C). [resolve(5002,a,4948,a)]. 13.83/13.81 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(5002,a,4949,a)]. 13.83/13.81 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_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(5002,a,4951,a)]. 13.83/13.81 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),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))). [resolve(5002,a,4952,a)]. 13.83/13.81 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(5002,a,4954,a)]. 13.83/13.81 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(5002,a,4955,a)]. 13.83/13.81 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),A). [resolve(5002,a,4958,a)]. 13.83/13.81 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_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))). [resolve(5002,a,4961,a)]. 13.83/13.81 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_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),C),B))). [resolve(5002,a,4962,a)]. 13.83/13.81 Derived: hAPP(real,fun(real,bool),ord_lessThan(real),A) != hAPP(real,fun(real,bool),ord_lessThan(real),B) | ti(real,A) = ti(real,B). [resolve(5002,a,4963,a)]. 13.83/13.81 Derived: hAPP(real,fun(real,bool),ord_lessThan(real),A) = hAPP(real,fun(real,bool),ord_lessThan(real),B) | ti(real,A) != ti(real,B). [resolve(5002,a,4964,a)]. 13.83/13.81 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),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(5002,a,4965,a)]. 13.83/13.81 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),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B)). [resolve(5002,a,4966,a)]. 13.83/13.81 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),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),A)),B)). [resolve(5002,a,4967,a)]. 13.83/13.81 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),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B)). [resolve(5002,a,4969,a)]. 13.83/13.81 Derived: 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(5002,a,4970,a)]. 13.83/13.81 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),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) = ti(real,D). [resolve(5002,a,4972,a)]. 13.83/13.81 Derived: 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),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(5002,a,4973,a)]. 13.93/13.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f606(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5002,a,4974,a)]. 13.93/13.87 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(5002,a,4975,a)]. 13.93/13.87 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(5002,a,4976,a)]. 13.93/13.87 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(5002,a,4977,a)]. 13.93/13.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5002,a,4978,a)]. 13.93/13.87 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(5002,a,4979,a)]. 13.93/13.87 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(5002,a,4980,a)]. 13.93/13.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f695(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5002,a,4983,a)]. 13.93/13.87 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(5002,a,4990,a)]. 13.93/13.87 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(5002,a,4991,a)]. 13.93/13.87 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(5002,a,4992,a)]. 13.93/13.87 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(5002,a,4996,a)]. 13.93/13.87 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(5002,a,4997,a)]. 13.93/13.87 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_min(real),A),C)),B)). [resolve(5002,a,5000,a)]. 13.93/13.87 5003 -linorder(A) | -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))) | 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),C)) # label(fact_4984_less__max__iff__disj) # label(axiom). [clausify(4614)]. 13.93/13.87 Derived: -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))) | 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),B)). [resolve(5003,a,4914,a)]. 13.93/13.87 Derived: -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))) | 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),B)). [resolve(5003,a,4936,a)]. 13.93/13.88 Derived: -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))) | 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),B)). [resolve(5003,a,4946,a)]. 13.93/13.88 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),ord_max(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)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)). [resolve(5003,a,4959,a)]. 13.93/13.88 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),ord_max(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)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)). [resolve(5003,a,4968,a)]. 13.93/13.88 Derived: -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))) | 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),B)). [resolve(5003,a,5002,a)]. 13.93/13.88 5004 -linorder(A) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_4984_less__max__iff__disj) # label(axiom). [clausify(4614)]. 13.93/13.88 5005 -linorder(A) | 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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_4984_less__max__iff__disj) # label(axiom). [clausify(4614)]. 13.93/13.88 5006 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f793(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2852_pinf_I8_J) # label(axiom). [clausify(4617)]. 13.93/13.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f793(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5006,a,4914,a)]. 13.93/13.88 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f793(rat,A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5006,a,4936,a)]. 13.93/13.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f793(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5006,a,4946,a)]. 13.93/13.88 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f793(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(5006,a,4959,a)]. 13.93/13.88 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f793(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(5006,a,4968,a)]. 13.93/13.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f793(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5006,a,5002,a)]. 13.93/13.88 5007 -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_572_linorder__not__less) # label(axiom). [clausify(4630)]. 13.97/13.91 5008 -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_572_linorder__not__less) # label(axiom). [clausify(4630)]. 13.97/13.91 5009 -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_4850_min__max_Oinf__absorb2) # label(axiom). [clausify(4652)]. 13.97/13.91 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(5009,a,4914,a)]. 13.97/13.91 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(5009,a,4936,a)]. 13.97/13.91 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(5009,a,4946,a)]. 13.97/13.91 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(5009,a,4959,a)]. 13.97/13.91 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | 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(5009,a,4968,a)]. 13.97/13.91 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(5009,a,5002,a)]. 13.97/13.91 5010 -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_4980_min__max_Odistrib__sup__le) # label(axiom). [clausify(4665)]. 13.97/13.91 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(5010,a,4914,a)]. 13.97/13.91 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(5010,a,4936,a)]. 13.97/13.91 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(5010,a,4946,a)]. 13.97/13.91 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(5010,a,4959,a)]. 13.97/13.93 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(5010,a,4968,a)]. 13.97/13.93 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(5010,a,5002,a)]. 13.97/13.93 5011 -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)) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) | ti(A,E) = ti(A,C) # label(fact_4224_atLeastLessThan__eq__iff) # label(axiom). [clausify(4674)]. 13.97/13.93 5012 -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)) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) != hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) | ti(A,D) = ti(A,B) # label(fact_4224_atLeastLessThan__eq__iff) # label(axiom). [clausify(4674)]. 13.97/13.93 5013 -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)) | hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),D),E) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C) | ti(A,E) != ti(A,C) | ti(A,D) != ti(A,B) # label(fact_4224_atLeastLessThan__eq__iff) # label(axiom). [clausify(4674)]. 13.97/13.93 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)) | hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),C),D) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),A),B) | ti(int,D) != ti(int,B) | ti(int,C) != ti(int,A). [resolve(5013,a,4914,a)]. 13.97/13.93 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)) | hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),C),D) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B) | ti(rat,D) != ti(rat,B) | ti(rat,C) != ti(rat,A). [resolve(5013,a,4936,a)]. 13.97/13.93 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)) | hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B) | ti(nat,D) != ti(nat,B) | ti(nat,C) != ti(nat,A). [resolve(5013,a,4946,a)]. 13.97/13.93 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)) | 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) = 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) | ti(quickcheck_code_int,D) != ti(quickcheck_code_int,B) | ti(quickcheck_code_int,C) != ti(quickcheck_code_int,A). [resolve(5013,a,4959,a)]. 14.02/13.99 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)) | 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) = 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) | ti(code_code_numeral,D) != ti(code_code_numeral,B) | ti(code_code_numeral,C) != ti(code_code_numeral,A). [resolve(5013,a,4968,a)]. 14.02/13.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),C),D) = hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),A),B) | ti(real,D) != ti(real,B) | ti(real,C) != ti(real,A). [resolve(5013,a,5002,a)]. 14.02/13.99 5014 -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_4854_min__max_Ole__infE) # label(axiom). [clausify(4710)]. 14.02/13.99 5015 -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_4854_min__max_Ole__infE) # label(axiom). [clausify(4710)]. 14.02/13.99 5016 -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),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4346_lessThan__subset__iff) # label(axiom). [clausify(4746)]. 14.02/13.99 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),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5016,a,4914,a)]. 14.02/13.99 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),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5016,a,4936,a)]. 14.02/13.99 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),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5016,a,4946,a)]. 14.02/13.99 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),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(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(5016,a,4959,a)]. 14.02/13.99 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),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(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(5016,a,4968,a)]. 14.08/14.02 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),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5016,a,5002,a)]. 14.08/14.02 5017 -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),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4346_lessThan__subset__iff) # label(axiom). [clausify(4746)]. 14.08/14.02 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),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5017,a,4914,a)]. 14.08/14.02 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),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5017,a,4936,a)]. 14.08/14.02 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),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5017,a,4946,a)]. 14.08/14.02 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),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(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(5017,a,4959,a)]. 14.08/14.02 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),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(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(5017,a,4968,a)]. 14.08/14.02 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),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5017,a,5002,a)]. 14.08/14.02 5018 -plus(A) | -linorder(A) | -dvd(A) | ti(fun(A,fun(A,A)),plus_plus(A)) = plus_plus(A) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(4776)]. 14.08/14.02 Derived: -plus(int) | -dvd(int) | ti(fun(int,fun(int,int)),plus_plus(int)) = plus_plus(int). [resolve(5018,b,4914,a)]. 14.08/14.02 Derived: -plus(rat) | -dvd(rat) | ti(fun(rat,fun(rat,rat)),plus_plus(rat)) = plus_plus(rat). [resolve(5018,b,4936,a)]. 14.08/14.02 Derived: -plus(nat) | -dvd(nat) | ti(fun(nat,fun(nat,nat)),plus_plus(nat)) = plus_plus(nat). [resolve(5018,b,4946,a)]. 14.08/14.02 Derived: -plus(quickcheck_code_int) | -dvd(quickcheck_code_int) | ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)) = plus_plus(quickcheck_code_int). [resolve(5018,b,4959,a)]. 14.08/14.02 Derived: -plus(code_code_numeral) | -dvd(code_code_numeral) | ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)) = plus_plus(code_code_numeral). [resolve(5018,b,4968,a)]. 14.94/14.89 Derived: -plus(real) | -dvd(real) | ti(fun(real,fun(real,real)),plus_plus(real)) = plus_plus(real). [resolve(5018,b,5002,a)]. 14.94/14.89 5019 -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_4848_min__max_Ole__infI2) # label(axiom). [clausify(4795)]. 14.94/14.89 5020 -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_513_linorder__linear) # label(axiom). [clausify(4814)]. 14.94/14.89 5021 -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_4852_min__max_Oinf__greatest) # label(axiom). [clausify(4816)]. 14.94/14.89 5022 ordered_ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 14.94/14.89 5023 -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_1902_le__minus__iff) # label(axiom). [clausify(6)]. 14.94/14.89 5024 -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_1902_le__minus__iff) # label(axiom). [clausify(6)]. 14.94/14.89 5025 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_737_diff__eq__diff__less__eq) # label(axiom). [clausify(238)]. 14.94/14.89 5026 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_737_diff__eq__diff__less__eq) # label(axiom). [clausify(238)]. 14.94/14.89 5027 -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),f35(B,A,D,E,C)),C)) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | zero_zero(A) = hAPP(B,A,E,D) # label(fact_4327_setsum__nonneg__0) # label(axiom). [clausify(267)]. 14.94/14.89 5028 -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,f35(B,A,E,D,C)))) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | zero_zero(A) = hAPP(B,A,D,E) # label(fact_4327_setsum__nonneg__0) # label(axiom). [clausify(267)]. 14.94/14.89 5029 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_1932_neg__less__iff__less) # label(axiom). [clausify(536)]. 14.94/14.89 5030 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_1932_neg__less__iff__less) # label(axiom). [clausify(536)]. 14.94/14.89 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(5022,a,5023,a)]. 14.94/14.89 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),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5022,a,5025,a)]. 15.00/14.95 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),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5022,a,5026,a)]. 15.00/14.95 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),f35(A,rat,C,D,B)),B)) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(rat) = hAPP(A,rat,D,C). [resolve(5022,a,5027,a)]. 15.00/14.95 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,f35(A,rat,D,C,B)))) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(rat) = hAPP(A,rat,C,D). [resolve(5022,a,5028,a)]. 15.00/14.95 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,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5022,a,5029,a)]. 15.00/14.95 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,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5022,a,5030,a)]. 15.00/14.95 5031 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_1953_neg__0__less__iff__less) # label(axiom). [clausify(741)]. 15.00/14.95 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5031,a,5022,a)]. 15.00/14.95 5032 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_1953_neg__0__less__iff__less) # label(axiom). [clausify(741)]. 15.00/14.95 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(5032,a,5022,a)]. 15.00/14.95 5033 -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_4551_image__uminus__atLeastAtMost) # label(axiom). [clausify(801)]. 15.00/14.95 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(5033,a,5022,a)]. 15.00/14.95 5034 -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_1899_le__imp__neg__le) # label(axiom). [clausify(924)]. 15.00/14.95 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(5034,a,5022,a)]. 15.14/15.11 5035 -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_1954_neg__less__0__iff__less) # label(axiom). [clausify(1026)]. 15.14/15.11 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(5035,a,5022,a)]. 15.14/15.11 5036 -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_1954_neg__less__0__iff__less) # label(axiom). [clausify(1026)]. 15.14/15.11 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(5036,a,5022,a)]. 15.14/15.11 5037 -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_752_less__iff__diff__less__0) # label(axiom). [clausify(1150)]. 15.14/15.11 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(5037,a,5022,a)]. 15.14/15.11 5038 -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_752_less__iff__diff__less__0) # label(axiom). [clausify(1150)]. 15.14/15.11 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(5038,a,5022,a)]. 15.14/15.11 5039 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_1949_neg__le__0__iff__le) # label(axiom). [clausify(1256)]. 15.14/15.11 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),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))). [resolve(5039,a,5022,a)]. 15.14/15.11 5040 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_1949_neg__le__0__iff__le) # label(axiom). [clausify(1256)]. 15.14/15.11 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),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))). [resolve(5040,a,5022,a)]. 15.14/15.11 5041 -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),f240(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_4326_setsum__nonneg__leq__bound) # label(axiom). [clausify(1452)]. 15.14/15.11 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),f240(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(5041,a,5022,a)]. 15.14/15.11 5042 -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,f240(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_4326_setsum__nonneg__leq__bound) # label(axiom). [clausify(1452)]. 15.46/15.39 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,f240(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(5042,a,5022,a)]. 15.46/15.39 5043 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_738_diff__eq__diff__less) # label(axiom). [clausify(1463)]. 15.46/15.39 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)). [resolve(5043,a,5022,a)]. 15.46/15.39 5044 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_738_diff__eq__diff__less) # label(axiom). [clausify(1463)]. 15.46/15.39 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)). [resolve(5044,a,5022,a)]. 15.46/15.39 5045 -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_3948_monoseq__minus) # label(axiom). [clausify(1918)]. 15.46/15.39 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(5045,a,5022,a)]. 15.46/15.39 5046 -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_3696_image__uminus__greaterThanLessThan) # label(axiom). [clausify(2012)]. 15.46/15.39 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(5046,a,5022,a)]. 15.46/15.39 5047 -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_1931_minus__less__iff) # label(axiom). [clausify(2072)]. 15.46/15.39 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(5047,a,5022,a)]. 15.46/15.39 5048 -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_1931_minus__less__iff) # label(axiom). [clausify(2072)]. 15.52/15.47 5049 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 15.52/15.47 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(5049,a,5023,a)]. 15.52/15.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5049,a,5025,a)]. 15.52/15.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5049,a,5026,a)]. 15.52/15.47 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),f35(A,int,C,D,B)),B)) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(int) = hAPP(A,int,D,C). [resolve(5049,a,5027,a)]. 15.52/15.47 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,f35(A,int,D,C,B)))) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(int) = hAPP(A,int,C,D). [resolve(5049,a,5028,a)]. 15.52/15.47 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,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5049,a,5029,a)]. 15.52/15.47 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,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5049,a,5030,a)]. 15.52/15.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5049,a,5031,a)]. 15.52/15.47 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5049,a,5032,a)]. 15.52/15.47 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(5049,a,5033,a)]. 15.52/15.47 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),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(5049,a,5034,a)]. 15.52/15.47 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(5049,a,5035,a)]. 15.52/15.47 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(5049,a,5036,a)]. 15.52/15.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))). [resolve(5049,a,5039,a)]. 16.06/16.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),zero_zero(int))). [resolve(5049,a,5040,a)]. 16.06/16.00 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),f240(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(5049,a,5041,a)]. 16.06/16.00 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,f240(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(5049,a,5042,a)]. 16.06/16.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(5049,a,5043,a)]. 16.06/16.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(5049,a,5044,a)]. 16.06/16.00 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(5049,a,5045,a)]. 16.06/16.00 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(5049,a,5046,a)]. 16.06/16.00 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(5049,a,5047,a)]. 16.06/16.00 5050 -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_4840_min__diff__distrib__left) # label(axiom). [clausify(2928)]. 16.06/16.00 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(5050,a,5022,a)]. 16.06/16.00 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(5050,a,5049,a)]. 16.06/16.00 5051 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_751_le__iff__diff__le__0) # label(axiom). [clausify(2939)]. 16.06/16.00 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5051,a,5022,a)]. 16.36/16.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5051,a,5049,a)]. 16.36/16.30 5052 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_751_le__iff__diff__le__0) # label(axiom). [clausify(2939)]. 16.36/16.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(5052,a,5022,a)]. 16.36/16.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(5052,a,5049,a)]. 16.36/16.30 5053 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 16.36/16.30 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(5053,a,5023,a)]. 16.36/16.30 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),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5053,a,5025,a)]. 16.36/16.30 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),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5053,a,5026,a)]. 16.36/16.30 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),f35(A,real,C,D,B)),B)) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(real) = hAPP(A,real,D,C). [resolve(5053,a,5027,a)]. 16.36/16.30 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,f35(A,real,D,C,B)))) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | zero_zero(real) = hAPP(A,real,C,D). [resolve(5053,a,5028,a)]. 16.36/16.30 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,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5053,a,5029,a)]. 16.36/16.30 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,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5053,a,5030,a)]. 16.36/16.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5053,a,5031,a)]. 16.36/16.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,uminus_uminus(real),A))). [resolve(5053,a,5032,a)]. 16.36/16.30 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(5053,a,5033,a)]. 16.36/16.31 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(5053,a,5034,a)]. 16.36/16.31 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(5053,a,5035,a)]. 16.36/16.31 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(5053,a,5036,a)]. 16.36/16.31 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(5053,a,5037,a)]. 16.36/16.31 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(5053,a,5038,a)]. 16.36/16.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))). [resolve(5053,a,5039,a)]. 16.36/16.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),zero_zero(real))). [resolve(5053,a,5040,a)]. 16.36/16.31 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),f240(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(5053,a,5041,a)]. 16.36/16.31 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,f240(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(5053,a,5042,a)]. 16.36/16.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)). [resolve(5053,a,5043,a)]. 16.36/16.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)). [resolve(5053,a,5044,a)]. 16.36/16.31 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(5053,a,5045,a)]. 16.36/16.31 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(5053,a,5046,a)]. 17.03/16.96 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(5053,a,5047,a)]. 17.03/16.96 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(5053,a,5050,a)]. 17.03/16.96 5054 -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_1901_minus__le__iff) # label(axiom). [clausify(3527)]. 17.03/16.96 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(5054,a,5022,a)]. 17.03/16.96 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(5054,a,5049,a)]. 17.03/16.96 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(5054,a,5053,a)]. 17.03/16.96 5055 -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_1901_minus__le__iff) # label(axiom). [clausify(3527)]. 17.03/16.96 5056 -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_1900_neg__le__iff__le) # label(axiom). [clausify(3666)]. 17.03/16.96 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(5056,a,5022,a)]. 17.03/16.96 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(5056,a,5049,a)]. 17.03/16.96 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(5056,a,5053,a)]. 17.03/16.96 5057 -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_1900_neg__le__iff__le) # label(axiom). [clausify(3666)]. 17.03/16.96 5058 -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_1930_less__minus__iff) # label(axiom). [clausify(3917)]. 17.03/16.96 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(5058,a,5022,a)]. 17.03/16.96 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(5058,a,5049,a)]. 17.03/16.96 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(5058,a,5053,a)]. 18.73/18.67 5059 -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_1930_less__minus__iff) # label(axiom). [clausify(3917)]. 18.73/18.67 5060 -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_1951_neg__0__le__iff__le) # label(axiom). [clausify(4372)]. 18.73/18.67 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(5060,a,5022,a)]. 18.73/18.67 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(5060,a,5049,a)]. 18.73/18.67 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(5060,a,5053,a)]. 18.73/18.67 5061 -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_1951_neg__0__le__iff__le) # label(axiom). [clausify(4372)]. 18.73/18.67 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(5061,a,5022,a)]. 18.73/18.67 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(5061,a,5049,a)]. 18.73/18.67 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(5061,a,5053,a)]. 18.73/18.67 5062 -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(4566)]. 18.73/18.67 Derived: ord_gr676655987ssThan(rat) = ti(fun(rat,fun(rat,fun(rat,bool))),ord_gr676655987ssThan(rat)). [resolve(5062,a,5022,a)]. 18.73/18.67 Derived: ord_gr676655987ssThan(int) = ti(fun(int,fun(int,fun(int,bool))),ord_gr676655987ssThan(int)). [resolve(5062,a,5049,a)]. 18.73/18.67 Derived: ord_gr676655987ssThan(real) = ti(fun(real,fun(real,fun(real,bool))),ord_gr676655987ssThan(real)). [resolve(5062,a,5053,a)]. 18.73/18.67 5063 group_add(real) # label(arity_RealDef_Oreal___Groups_Ogroup__add) # label(axiom). [assumption]. 18.73/18.67 5064 -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_739_add__diff__cancel) # label(axiom). [clausify(7)]. 18.73/18.67 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(5063,a,5064,a)]. 18.73/18.67 5065 -group_add(A) | zero_zero(A) = hAPP(A,A,uminus_uminus(A),zero_zero(A)) # label(fact_1937_minus__zero) # label(axiom). [clausify(405)]. 18.73/18.67 Derived: zero_zero(real) = hAPP(real,real,uminus_uminus(real),zero_zero(real)). [resolve(5065,a,5063,a)]. 18.73/18.67 5066 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_1921_minus__minus) # label(axiom). [clausify(617)]. 18.73/18.67 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(5066,a,5063,a)]. 18.73/18.67 5067 -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_1967_Groups_Odiff__def) # label(axiom). [clausify(1265)]. 19.26/19.25 5068 -group_add(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,uminus_uminus(A),B) # label(fact_1936_neg__0__equal__iff__equal) # label(axiom). [clausify(1468)]. 19.26/19.25 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,uminus_uminus(real),A). [resolve(5068,a,5063,a)]. 19.26/19.25 5069 -group_add(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,uminus_uminus(A),B) # label(fact_1936_neg__0__equal__iff__equal) # label(axiom). [clausify(1468)]. 19.26/19.25 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,uminus_uminus(real),A). [resolve(5069,a,5063,a)]. 19.26/19.25 5070 -group_add(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_1961_minus__unique) # label(axiom). [clausify(1545)]. 19.26/19.25 Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A). [resolve(5070,a,5063,a)]. 19.26/19.25 5071 -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_1970_diff__minus__eq__add) # label(axiom). [clausify(1862)]. 19.26/19.25 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(5071,a,5063,a)]. 19.26/19.25 5072 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) # label(fact_736_diff__0__right) # label(axiom). [clausify(2038)]. 19.26/19.25 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),zero_zero(real)). [resolve(5072,a,5063,a)]. 19.26/19.25 5073 group_add(complex) # label(arity_Complex_Ocomplex___Groups_Ogroup__add) # label(axiom). [assumption]. 19.26/19.25 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(5073,a,5064,a)]. 19.26/19.25 Derived: zero_zero(complex) = hAPP(complex,complex,uminus_uminus(complex),zero_zero(complex)). [resolve(5073,a,5065,a)]. 19.26/19.25 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(5073,a,5066,a)]. 19.26/19.25 Derived: zero_zero(complex) != ti(complex,A) | zero_zero(complex) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5073,a,5068,a)]. 19.26/19.25 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) != hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5073,a,5069,a)]. 19.26/19.25 Derived: zero_zero(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5073,a,5070,a)]. 19.26/19.25 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(5073,a,5071,a)]. 19.26/19.25 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),zero_zero(complex)). [resolve(5073,a,5072,a)]. 19.26/19.25 5074 -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_1913_minus__add__cancel) # label(axiom). [clausify(2767)]. 19.26/19.25 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(5074,a,5063,a)]. 19.26/19.25 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(5074,a,5073,a)]. 19.26/19.25 5075 -group_add(A) | 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)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_1915_minus__add) # label(axiom). [clausify(2798)]. 19.81/19.73 Derived: 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)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)). [resolve(5075,a,5063,a)]. 19.81/19.73 Derived: 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)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)). [resolve(5075,a,5073,a)]. 19.81/19.73 5076 -group_add(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) | ti(A,C) = ti(A,B) # label(fact_733_right__minus__eq) # label(axiom). [clausify(2879)]. 19.81/19.73 Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) | ti(real,B) = ti(real,A). [resolve(5076,a,5063,a)]. 19.81/19.73 Derived: zero_zero(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) | ti(complex,B) = ti(complex,A). [resolve(5076,a,5073,a)]. 19.81/19.73 5077 -group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) | ti(A,C) != ti(A,B) # label(fact_733_right__minus__eq) # label(axiom). [clausify(2879)]. 19.81/19.73 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) | ti(real,B) != ti(real,A). [resolve(5077,a,5063,a)]. 19.81/19.73 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) | ti(complex,B) != ti(complex,A). [resolve(5077,a,5073,a)]. 19.81/19.73 5078 -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_1922_equation__minus__iff) # label(axiom). [clausify(2920)]. 19.81/19.73 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A). [resolve(5078,a,5063,a)]. 19.81/19.73 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5078,a,5073,a)]. 19.81/19.73 5079 -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_1922_equation__minus__iff) # label(axiom). [clausify(2920)]. 19.81/19.73 5080 group_add(rat) # label(arity_Rat_Orat___Groups_Ogroup__add) # label(axiom). [assumption]. 19.81/19.73 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(5080,a,5064,a)]. 19.81/19.73 Derived: zero_zero(rat) = hAPP(rat,rat,uminus_uminus(rat),zero_zero(rat)). [resolve(5080,a,5065,a)]. 19.81/19.73 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5080,a,5066,a)]. 19.81/19.73 Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5080,a,5068,a)]. 19.81/19.73 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) != hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5080,a,5069,a)]. 19.81/19.73 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5080,a,5070,a)]. 19.81/19.73 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(5080,a,5071,a)]. 19.81/19.73 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),zero_zero(rat)). [resolve(5080,a,5072,a)]. 19.81/19.73 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(5080,a,5074,a)]. 19.81/19.73 Derived: 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)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)). [resolve(5080,a,5075,a)]. 19.81/19.73 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) | ti(rat,B) = ti(rat,A). [resolve(5080,a,5076,a)]. 20.63/20.61 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) | ti(rat,B) != ti(rat,A). [resolve(5080,a,5077,a)]. 20.63/20.61 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5080,a,5078,a)]. 20.63/20.61 5081 -group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),B)) # label(fact_1957_right__minus) # label(axiom). [clausify(3501)]. 20.63/20.61 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),A)). [resolve(5081,a,5063,a)]. 20.63/20.61 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(5081,a,5073,a)]. 20.63/20.61 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5081,a,5080,a)]. 20.63/20.61 5082 -group_add(A) | zero_zero(A) != hAPP(A,A,uminus_uminus(A),B) | zero_zero(A) = ti(A,B) # label(fact_1934_neg__equal__0__iff__equal) # label(axiom). [clausify(3543)]. 20.63/20.61 5083 -group_add(A) | zero_zero(A) = hAPP(A,A,uminus_uminus(A),B) | zero_zero(A) != ti(A,B) # label(fact_1934_neg__equal__0__iff__equal) # label(axiom). [clausify(3543)]. 20.63/20.61 5084 -group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) # label(fact_1959_left__minus) # label(axiom). [clausify(3831)]. 20.63/20.61 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),A). [resolve(5084,a,5063,a)]. 20.63/20.61 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),A). [resolve(5084,a,5073,a)]. 20.63/20.61 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A). [resolve(5084,a,5080,a)]. 20.63/20.61 5085 -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_1914_add__minus__cancel) # label(axiom). [clausify(3851)]. 20.63/20.61 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(5085,a,5063,a)]. 20.63/20.61 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(5085,a,5073,a)]. 20.63/20.61 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(5085,a,5080,a)]. 20.63/20.61 5086 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_1956_add__eq__0__iff) # label(axiom). [clausify(4173)]. 20.63/20.61 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(5086,a,5063,a)]. 20.63/20.61 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(5086,a,5073,a)]. 20.63/20.61 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(5086,a,5080,a)]. 20.63/20.61 5087 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_1956_add__eq__0__iff) # label(axiom). [clausify(4173)]. 20.63/20.61 5088 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption]. 20.63/20.61 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(5088,a,5064,a)]. 20.63/20.61 Derived: zero_zero(int) = hAPP(int,int,uminus_uminus(int),zero_zero(int)). [resolve(5088,a,5065,a)]. 20.86/20.80 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(5088,a,5066,a)]. 20.86/20.80 Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,uminus_uminus(int),A). [resolve(5088,a,5068,a)]. 20.86/20.80 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,uminus_uminus(int),A). [resolve(5088,a,5069,a)]. 20.86/20.80 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(5088,a,5070,a)]. 20.86/20.80 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(5088,a,5071,a)]. 20.86/20.80 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)). [resolve(5088,a,5072,a)]. 20.86/20.80 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(5088,a,5074,a)]. 20.86/20.80 Derived: 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)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)). [resolve(5088,a,5075,a)]. 20.86/20.80 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) | ti(int,B) = ti(int,A). [resolve(5088,a,5076,a)]. 20.86/20.80 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) | ti(int,B) != ti(int,A). [resolve(5088,a,5077,a)]. 20.86/20.80 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(5088,a,5078,a)]. 20.86/20.80 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),A)). [resolve(5088,a,5081,a)]. 20.86/20.80 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),A). [resolve(5088,a,5084,a)]. 20.86/20.80 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(5088,a,5085,a)]. 20.86/20.80 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(5088,a,5086,a)]. 20.86/20.80 5089 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),zero_zero(A)),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_1964_diff__0) # label(axiom). [clausify(4477)]. 20.86/20.80 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),zero_zero(real)),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5089,a,5063,a)]. 20.86/20.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),zero_zero(complex)),A) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5089,a,5073,a)]. 20.86/20.80 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),zero_zero(rat)),A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5089,a,5080,a)]. 20.86/20.80 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),A) = hAPP(int,int,uminus_uminus(int),A). [resolve(5089,a,5088,a)]. 20.86/20.80 5090 -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_740_diff__add__cancel) # label(axiom). [clausify(4510)]. 20.86/20.80 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(5090,a,5063,a)]. 20.86/20.80 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(5090,a,5073,a)]. 20.86/20.80 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(5090,a,5080,a)]. 20.86/20.80 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(5090,a,5088,a)]. 20.86/20.80 5091 -group_add(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) # label(fact_1958_eq__neg__iff__add__eq__0) # label(axiom). [clausify(4577)]. 21.15/21.08 Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) | ti(real,A) = hAPP(real,real,uminus_uminus(real),B). [resolve(5091,a,5063,a)]. 21.15/21.08 Derived: zero_zero(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) | ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),B). [resolve(5091,a,5073,a)]. 21.15/21.08 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) | ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),B). [resolve(5091,a,5080,a)]. 21.15/21.08 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) | ti(int,A) = hAPP(int,int,uminus_uminus(int),B). [resolve(5091,a,5088,a)]. 21.15/21.08 5092 -group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) # label(fact_1958_eq__neg__iff__add__eq__0) # label(axiom). [clausify(4577)]. 21.15/21.08 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) | ti(real,A) != hAPP(real,real,uminus_uminus(real),B). [resolve(5092,a,5063,a)]. 21.15/21.08 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) | ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B). [resolve(5092,a,5073,a)]. 21.15/21.08 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) | ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B). [resolve(5092,a,5080,a)]. 21.15/21.08 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) | ti(int,A) != hAPP(int,int,uminus_uminus(int),B). [resolve(5092,a,5088,a)]. 21.15/21.08 5093 -group_add(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) # label(fact_735_diff__self) # label(axiom). [clausify(4807)]. 21.15/21.08 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),A). [resolve(5093,a,5063,a)]. 21.15/21.08 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),A). [resolve(5093,a,5073,a)]. 21.15/21.08 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),A). [resolve(5093,a,5080,a)]. 21.15/21.08 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A). [resolve(5093,a,5088,a)]. 21.15/21.08 5094 -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_1923_minus__equation__iff) # label(axiom). [clausify(4889)]. 21.15/21.08 5095 -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_1923_minus__equation__iff) # label(axiom). [clausify(4889)]. 21.15/21.08 5096 -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_1924_neg__equal__iff__equal) # label(axiom). [clausify(4893)]. 21.15/21.08 Derived: hAPP(real,real,uminus_uminus(real),A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,A) = ti(real,B). [resolve(5096,a,5063,a)]. 21.15/21.08 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) = ti(complex,B). [resolve(5096,a,5073,a)]. 21.15/21.08 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) = ti(rat,B). [resolve(5096,a,5080,a)]. 21.15/21.08 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(5096,a,5088,a)]. 21.15/21.08 5097 -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_1924_neg__equal__iff__equal) # label(axiom). [clausify(4893)]. 21.15/21.08 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,uminus_uminus(real),B) | ti(real,A) != ti(real,B). [resolve(5097,a,5063,a)]. 21.15/21.08 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) != ti(complex,B). [resolve(5097,a,5073,a)]. 21.15/21.08 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) != ti(rat,B). [resolve(5097,a,5080,a)]. 21.15/21.08 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(5097,a,5088,a)]. 22.66/22.57 5098 banach(complex) # label(arity_Complex_Ocomplex___SEQ_Obanach) # label(axiom). [assumption]. 22.66/22.57 5099 -banach(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f3(A,C,D,B))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D)) # label(fact_4082_ratio__test__lemma2) # label(axiom). [clausify(13)]. 22.66/22.57 5100 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,B,hAPP(nat,nat,suc,f3(A,B,C,D))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(A,real,norm_norm(A),hAPP(nat,A,B,f3(A,B,C,D)))))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) # label(fact_4082_ratio__test__lemma2) # label(axiom). [clausify(13)]. 22.66/22.57 5101 -banach(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f21(A,C,D,B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) # label(fact_4019_summable__comparison__test) # label(axiom). [clausify(109)]. 22.66/22.57 5102 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,B,f21(A,B,C,D)))),hAPP(nat,real,C,f21(A,B,C,D)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4019_summable__comparison__test) # label(axiom). [clausify(109)]. 22.66/22.57 5103 -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_4646_Cauchy__product) # label(axiom). [clausify(377)]. 22.66/22.57 5104 -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_4929_isCont__exp) # label(axiom). [clausify(531)]. 22.66/22.57 5105 -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_4775_lemma__exp__ext) # label(axiom). [clausify(654)]. 22.66/22.57 5106 -banach(A) | -real_normed_field(A) | hAPP(real,A,of_real(A),hAPP(real,real,exp(real),B)) = hAPP(A,A,exp(A),hAPP(real,A,of_real(A),B)) # label(fact_2810_exp__of__real) # label(axiom). [clausify(786)]. 22.66/22.57 5107 -banach(A) | -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(A,A,exp(A),B))) # label(fact_4777_exp__converges) # label(axiom). [clausify(951)]. 22.66/22.57 5108 -banach(A) | -real_n2089651433ebra_1(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)),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))))) # label(fact_4774_summable__norm__exp) # label(axiom). [clausify(992)]. 22.66/22.57 5109 -real_n2089651433ebra_1(A) | -banach(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_4053_complete__algebra__summable__geometric) # label(axiom). [clausify(1061)]. 22.66/22.57 5110 -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_4776_exp__def) # label(axiom). [clausify(1475)]. 22.66/22.57 5111 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(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_4151_termdiffs) # label(axiom). [clausify(1592)]. 22.66/22.58 5112 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_1748_exp__diff) # label(axiom). [clausify(1785)]. 22.66/22.58 5113 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),one_one(real))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),f338(A,D,C,B))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),D)) # label(fact_4081_ratio__test) # label(axiom). [clausify(1983)]. 22.66/22.58 5114 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),one_one(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,C,hAPP(nat,nat,suc,f338(A,C,D,B))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(A,real,norm_norm(A),hAPP(nat,A,C,f338(A,C,D,B)))))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) # label(fact_4081_ratio__test) # label(axiom). [clausify(1983)]. 22.66/22.58 5115 -banach(A) | -real_n2089651433ebra_1(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,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)))) # label(fact_4773_summable__exp__generic) # label(axiom). [clausify(1998)]. 22.66/22.58 5116 -real_normed_field(A) | -banach(A) | zero_zero(A) != hAPP(A,A,exp(A),B) # label(fact_1763_exp__not__eq__zero) # label(axiom). [clausify(2028)]. 22.66/22.58 5117 -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_4051_powser__inside) # label(axiom). [clausify(2484)]. 22.66/22.58 5118 -banach(A) | -real_normed_field(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_2606_exp__minus) # label(axiom). [clausify(2557)]. 22.66/22.58 5119 -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_1774_mult__exp__exp) # label(axiom). [clausify(2800)]. 22.66/22.58 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f3(complex,B,C,A))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5098,a,5099,a)]. 22.66/22.58 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,A,hAPP(nat,nat,suc,f3(complex,A,B,C))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,A,f3(complex,A,B,C)))))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5098,a,5100,a)]. 22.66/22.58 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f21(complex,B,C,A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)). [resolve(5098,a,5101,a)]. 22.66/22.58 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,A,f21(complex,A,B,C)))),hAPP(nat,real,B,f21(complex,A,B,C)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5098,a,5102,a)]. 22.66/22.58 Derived: -real_normed_algebra(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(5098,a,5103,b)]. 22.66/22.58 Derived: -real_normed_field(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),exp(complex)),A)). [resolve(5098,a,5104,b)]. 22.66/22.58 Derived: -real_normed_field(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(5098,a,5105,b)]. 22.66/22.59 Derived: -real_normed_field(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),A)) = hAPP(complex,complex,exp(complex),hAPP(real,complex,of_real(complex),A)). [resolve(5098,a,5106,a)]. 22.66/22.59 Derived: -real_normed_field(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(5098,a,5107,a)]. 22.66/22.59 Derived: -real_n2089651433ebra_1(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)),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))))). [resolve(5098,a,5108,a)]. 22.66/22.59 Derived: -real_n2089651433ebra_1(complex) | -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(5098,a,5109,b)]. 22.66/22.59 Derived: -real_normed_field(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(5098,a,5111,b)]. 22.68/22.59 Derived: -real_normed_field(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(5098,a,5112,b)]. 22.68/22.59 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f338(complex,C,B,A))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),C)). [resolve(5098,a,5113,a)]. 22.68/22.59 Derived: -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_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,B,hAPP(nat,nat,suc,f338(complex,B,C,A))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,B,f338(complex,B,C,A)))))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)). [resolve(5098,a,5114,a)]. 22.68/22.59 Derived: -real_n2089651433ebra_1(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,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)))). [resolve(5098,a,5115,a)]. 22.68/22.59 Derived: -real_normed_field(complex) | zero_zero(complex) != hAPP(complex,complex,exp(complex),A). [resolve(5098,a,5116,b)]. 22.68/22.59 Derived: -real_normed_field(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(5098,a,5117,a)]. 22.87/22.86 Derived: -real_normed_field(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(5098,a,5118,a)]. 22.87/22.86 Derived: -real_normed_field(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(5098,a,5119,b)]. 22.87/22.86 5120 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_4024_powser__insidea) # label(axiom). [clausify(3059)]. 22.87/22.86 Derived: -real_normed_field(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(5120,b,5098,a)]. 22.87/22.86 5121 -banach(A) | -real_normed_field(A) | one_one(A) = hAPP(A,A,exp(A),zero_zero(A)) # label(fact_1773_exp__zero) # label(axiom). [clausify(3080)]. 22.87/22.86 Derived: -real_normed_field(complex) | one_one(complex) = hAPP(complex,complex,exp(complex),zero_zero(complex)). [resolve(5121,a,5098,a)]. 22.87/22.86 5122 -banach(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f552(A,C,D,B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | 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))) # label(fact_4044_summable__norm__comparison__test) # label(axiom). [clausify(3118)]. 22.87/22.86 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f552(complex,B,C,A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | 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))). [resolve(5122,a,5098,a)]. 23.03/22.97 5123 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,B,f552(A,B,C,D)))),hAPP(nat,real,C,f552(A,B,C,D)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),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)),B))) # label(fact_4044_summable__norm__comparison__test) # label(axiom). [clausify(3118)]. 23.03/22.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,A,f552(complex,A,B,C)))),hAPP(nat,real,B,f552(complex,A,B,C)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),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)),A))). [resolve(5123,a,5098,a)]. 23.03/22.97 5124 -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,A),bool,summable(A),B)) # label(fact_4032_summable__norm__cancel) # label(axiom). [clausify(3263)]. 23.03/22.97 Derived: -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,complex),bool,summable(complex),A)). [resolve(5124,a,5098,a)]. 23.03/22.97 5125 -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_4557_termdiffs__aux) # label(axiom). [clausify(3286)]. 23.03/22.97 Derived: -real_normed_field(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(5125,a,5098,a)]. 23.32/23.29 5126 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),exp(A)),B),hAPP(A,A,exp(A),B))) # label(fact_2645_DERIV__exp) # label(axiom). [clausify(3368)]. 23.32/23.29 Derived: -real_normed_field(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(5126,b,5098,a)]. 23.32/23.29 5127 -banach(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f639(A,B))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4314_summable__Cauchy) # label(axiom). [clausify(3574)]. 23.32/23.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f639(complex,A))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5127,a,5098,a)]. 23.32/23.29 5128 -banach(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f640(A,C,B))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) # label(fact_4314_summable__Cauchy) # label(axiom). [clausify(3574)]. 23.42/23.33 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f640(complex,B,A))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)). [resolve(5128,a,5098,a)]. 23.42/23.33 5129 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(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),f640(A,B,C)),f641(A,B,C))))),f639(A,B))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4314_summable__Cauchy) # label(axiom). [clausify(3574)]. 23.42/23.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(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),f640(complex,A,B)),f641(complex,A,B))))),f639(complex,A))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5129,a,5098,a)]. 23.42/23.33 5130 -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f642(A,C,B)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(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),D),E)))),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) # label(fact_4314_summable__Cauchy) # label(axiom). [clausify(3574)]. 23.42/23.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f642(complex,B,A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),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),C),D)))),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)). [resolve(5130,a,5098,a)]. 23.42/23.33 5131 banach(real) # label(arity_RealDef_Oreal___SEQ_Obanach) # label(axiom). [assumption]. 23.42/23.33 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f3(real,B,C,A))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5131,a,5099,a)]. 23.42/23.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,A,hAPP(nat,nat,suc,f3(real,A,B,C))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,norm_norm(real),hAPP(nat,real,A,f3(real,A,B,C)))))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5131,a,5100,a)]. 23.42/23.33 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f21(real,B,C,A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),B)). [resolve(5131,a,5101,a)]. 23.42/23.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,A,f21(real,A,B,C)))),hAPP(nat,real,B,f21(real,A,B,C)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5131,a,5102,a)]. 23.42/23.33 Derived: -real_normed_algebra(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(5131,a,5103,b)]. 23.42/23.33 Derived: -real_normed_field(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),exp(real)),A)). [resolve(5131,a,5104,b)]. 23.42/23.33 Derived: -real_normed_field(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(5131,a,5105,b)]. 23.42/23.33 Derived: -real_normed_field(real) | hAPP(real,real,of_real(real),hAPP(real,real,exp(real),A)) = hAPP(real,real,exp(real),hAPP(real,real,of_real(real),A)). [resolve(5131,a,5106,a)]. 23.42/23.33 Derived: -real_normed_field(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(5131,a,5107,a)]. 23.42/23.33 Derived: -real_n2089651433ebra_1(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)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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))))). [resolve(5131,a,5108,a)]. 23.42/23.33 Derived: -real_n2089651433ebra_1(real) | -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(5131,a,5109,b)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5111,b)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5112,b)]. 23.42/23.34 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f338(real,C,B,A))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),C)). [resolve(5131,a,5113,a)]. 23.42/23.34 Derived: -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_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,B,hAPP(nat,nat,suc,f338(real,B,C,A))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,norm_norm(real),hAPP(nat,real,B,f338(real,B,C,A)))))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),B)). [resolve(5131,a,5114,a)]. 23.42/23.34 Derived: -real_n2089651433ebra_1(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),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)))). [resolve(5131,a,5115,a)]. 23.42/23.34 Derived: -real_normed_field(real) | zero_zero(real) != hAPP(real,real,exp(real),A). [resolve(5131,a,5116,b)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5117,a)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5118,a)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5119,b)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5120,b)]. 23.42/23.34 Derived: -real_normed_field(real) | one_one(real) = hAPP(real,real,exp(real),zero_zero(real)). [resolve(5131,a,5121,a)]. 23.42/23.34 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f552(real,B,C,A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | 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))). [resolve(5131,a,5122,a)]. 23.42/23.34 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,A,f552(real,A,B,C)))),hAPP(nat,real,B,f552(real,A,B,C)))) | -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(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))). [resolve(5131,a,5123,a)]. 23.42/23.34 Derived: -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),A)). [resolve(5131,a,5124,a)]. 23.42/23.34 Derived: -real_normed_field(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(5131,a,5125,a)]. 23.49/23.42 Derived: -real_normed_field(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(5131,a,5126,b)]. 23.49/23.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f639(real,A))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5131,a,5127,a)]. 23.49/23.42 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f640(real,B,A))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),B)). [resolve(5131,a,5128,a)]. 23.49/23.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(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),f640(real,A,B)),f641(real,A,B))))),f639(real,A))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5131,a,5129,a)]. 23.49/23.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f642(real,B,A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(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),C),D)))),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)). [resolve(5131,a,5130,a)]. 23.49/23.42 5132 -banach(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | zero_zero(B) != ti(B,f669(A,B,E,D,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),hAPP(fun(B,fun(nat,A)),fun(B,A),hAPP(fun(fun(nat,A),A),fun(fun(B,fun(nat,A)),fun(B,A)),combb(fun(nat,A),A,B),suminf(A)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4650_lemma__termdiff5) # label(axiom). [clausify(3691)]. 23.49/23.42 Derived: -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(A) != ti(A,f669(complex,A,D,C,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),hAPP(fun(A,fun(nat,complex)),fun(A,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(A,fun(nat,complex)),fun(A,complex)),combb(fun(nat,complex),complex,A),suminf(complex)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5132,a,5098,a)]. 23.49/23.42 Derived: -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | zero_zero(A) != ti(A,f669(real,A,D,C,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),hAPP(fun(A,fun(nat,real)),fun(A,real),hAPP(fun(fun(nat,real),real),fun(fun(A,fun(nat,real)),fun(A,real)),combb(fun(nat,real),real,A),suminf(real)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5132,a,5131,a)]. 23.49/23.42 5133 -banach(A) | -real_normed_field(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(B,real,norm_norm(B),f669(A,B,E,D,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),hAPP(fun(B,fun(nat,A)),fun(B,A),hAPP(fun(fun(nat,A),A),fun(fun(B,fun(nat,A)),fun(B,A)),combb(fun(nat,A),A,B),suminf(A)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4650_lemma__termdiff5) # label(axiom). [clausify(3691)]. 23.49/23.42 Derived: -real_normed_field(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(A,real,norm_norm(A),f669(complex,A,D,C,B))),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),hAPP(fun(A,fun(nat,complex)),fun(A,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(A,fun(nat,complex)),fun(A,complex)),combb(fun(nat,complex),complex,A),suminf(complex)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5133,a,5098,a)]. 23.49/23.42 Derived: -real_normed_field(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(A,real,norm_norm(A),f669(real,A,D,C,B))),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),hAPP(fun(A,fun(nat,real)),fun(A,real),hAPP(fun(fun(nat,real),real),fun(fun(A,fun(nat,real)),fun(A,real)),combb(fun(nat,real),real,A),suminf(real)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5133,a,5131,a)]. 23.49/23.42 5134 -banach(A) | -real_normed_field(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(A,real,norm_norm(A),hAPP(nat,A,hAPP(B,fun(nat,A),E,f669(A,B,E,D,C)),f670(A,B,E,D,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,D,f670(A,B,E,D,C))),hAPP(B,real,norm_norm(B),f669(A,B,E,D,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),hAPP(fun(B,fun(nat,A)),fun(B,A),hAPP(fun(fun(nat,A),A),fun(fun(B,fun(nat,A)),fun(B,A)),combb(fun(nat,A),A,B),suminf(A)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4650_lemma__termdiff5) # label(axiom). [clausify(3691)]. 23.49/23.42 Derived: -real_normed_field(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(complex,real,norm_norm(complex),hAPP(nat,complex,hAPP(A,fun(nat,complex),D,f669(complex,A,D,C,B)),f670(complex,A,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f670(complex,A,D,C,B))),hAPP(A,real,norm_norm(A),f669(complex,A,D,C,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),hAPP(fun(A,fun(nat,complex)),fun(A,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(A,fun(nat,complex)),fun(A,complex)),combb(fun(nat,complex),complex,A),suminf(complex)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5134,a,5098,a)]. 23.49/23.42 Derived: -real_normed_field(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(real,real,norm_norm(real),hAPP(nat,real,hAPP(A,fun(nat,real),D,f669(real,A,D,C,B)),f670(real,A,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f670(real,A,D,C,B))),hAPP(A,real,norm_norm(A),f669(real,A,D,C,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),hAPP(fun(A,fun(nat,real)),fun(A,real),hAPP(fun(fun(nat,real),real),fun(fun(A,fun(nat,real)),fun(A,real)),combb(fun(nat,real),real,A),suminf(real)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),zero_zero(A)))). [resolve(5134,a,5131,a)]. 23.49/23.45 5135 -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_4648_Cauchy__product__sums) # label(axiom). [clausify(3725)]. 23.49/23.45 Derived: -real_normed_algebra(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(5135,b,5098,a)]. 24.09/24.04 Derived: -real_normed_algebra(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(5135,b,5131,a)]. 24.09/24.04 5136 -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_1775_exp__add) # label(axiom). [clausify(3914)]. 24.09/24.04 5137 -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_3884_DERIV__fun__exp) # label(axiom). [clausify(4055)]. 24.09/24.04 Derived: -real_normed_field(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(5137,a,5098,a)]. 24.09/24.04 Derived: -real_normed_field(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(5137,a,5131,a)]. 24.09/24.04 5138 -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(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(fun(nat,A),A,suminf(A),B))),hAPP(fun(nat,real),real,suminf(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)))) # label(fact_4050_summable__norm) # label(axiom). [clausify(4406)]. 25.39/25.31 Derived: -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(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(fun(nat,complex),complex,suminf(complex),A))),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),norm_norm(complex)),A)))). [resolve(5138,a,5098,a)]. 25.39/25.31 Derived: -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(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(fun(nat,real),real,suminf(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),norm_norm(real)),A)))). [resolve(5138,a,5131,a)]. 25.39/25.31 5139 -banach(A) | -real_normed_field(A) | exp(A) = ti(fun(A,A),exp(A)) # label(tsy_c_Transcendental_Oexp_res) # label(axiom). [clausify(4574)]. 25.39/25.31 Derived: -real_normed_field(complex) | exp(complex) = ti(fun(complex,complex),exp(complex)). [resolve(5139,a,5098,a)]. 25.39/25.31 Derived: -real_normed_field(real) | exp(real) = ti(fun(real,real),exp(real)). [resolve(5139,a,5131,a)]. 25.39/25.31 5140 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom). [assumption]. 25.39/25.31 5141 -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_2607_le__imp__inverse__le) # label(axiom). [clausify(14)]. 25.39/25.31 5142 -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_2628_one__le__inverse) # label(axiom). [clausify(102)]. 25.39/25.31 5143 -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_1885_gt__half__sum) # label(axiom). [clausify(125)]. 25.39/25.31 5144 -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_1875_divide__strict__left__mono) # label(axiom). [clausify(226)]. 25.39/25.31 5145 -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_1886_less__half__sum) # label(axiom). [clausify(362)]. 25.39/25.31 5146 -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_1866_divide__nonpos__neg) # label(axiom). [clausify(400)]. 25.39/25.31 5147 -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_1871_mult__imp__div__pos__less) # label(axiom). [clausify(421)]. 25.39/25.32 5148 -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_1862_frac__less2) # label(axiom). [clausify(631)]. 25.39/25.32 5149 -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_1823_pos__le__divide__eq) # label(axiom). [clausify(674)]. 25.39/25.32 5150 -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_1823_pos__le__divide__eq) # label(axiom). [clausify(674)]. 25.39/25.32 5151 -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_2589_less__imp__inverse__less) # label(axiom). [clausify(754)]. 25.39/25.32 5152 -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_2633_inv__of__nat__fact__gt__zero) # label(axiom). [clausify(784)]. 25.39/25.32 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(5140,a,5141,a)]. 25.39/25.32 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(5140,a,5142,a)]. 25.39/25.32 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(5140,a,5143,a)]. 25.39/25.32 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(5140,a,5144,a)]. 25.39/25.32 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(5140,a,5145,a)]. 25.44/25.37 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(5140,a,5146,a)]. 25.44/25.37 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)). [resolve(5140,a,5147,a)]. 25.44/25.37 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5140,a,5148,a)]. 25.44/25.37 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5140,a,5149,a)]. 25.44/25.37 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5140,a,5150,a)]. 25.44/25.37 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(5140,a,5151,a)]. 25.44/25.37 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(5140,a,5152,a)]. 25.44/25.37 5153 -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_2588_less__imp__inverse__less__neg) # label(axiom). [clausify(931)]. 25.44/25.37 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(5153,a,5140,a)]. 25.44/25.37 5154 -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_2586_inverse__less__imp__less) # label(axiom). [clausify(1083)]. 25.44/25.37 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(5154,a,5140,a)]. 25.56/25.53 5155 -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_1861_divide__nonneg__neg) # label(axiom). [clausify(1090)]. 25.56/25.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5155,a,5140,a)]. 25.56/25.53 5156 -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_1890_neg__divide__le__eq) # label(axiom). [clausify(1374)]. 25.56/25.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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(5156,a,5140,a)]. 25.56/25.53 5157 -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_1890_neg__divide__le__eq) # label(axiom). [clausify(1374)]. 25.56/25.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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(5157,a,5140,a)]. 25.56/25.53 5158 -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_1893_mult__imp__div__pos__le) # label(axiom). [clausify(1573)]. 25.56/25.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C)). [resolve(5158,a,5140,a)]. 25.56/25.53 5159 -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_1842_divide__pos__pos) # label(axiom). [clausify(1597)]. 25.56/25.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5159,a,5140,a)]. 25.56/25.53 5160 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),B)) # label(fact_1858_nonzero__abs__divide) # label(axiom). [clausify(1654)]. 25.56/25.53 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),A)). [resolve(5160,a,5140,a)]. 25.56/25.54 5161 linordered_field(rat) # label(arity_Rat_Orat___Fields_Olinordered__field) # label(axiom). [assumption]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5161,a,5141,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),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(5161,a,5142,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5161,a,5143,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5161,a,5144,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5161,a,5145,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5161,a,5146,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5161,a,5147,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5161,a,5148,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),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(5161,a,5149,a)]. 25.56/25.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),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(5161,a,5150,a)]. 25.65/25.56 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(5161,a,5151,a)]. 25.65/25.56 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(5161,a,5152,a)]. 25.65/25.56 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(5161,a,5153,a)]. 25.65/25.56 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(5161,a,5154,a)]. 25.65/25.56 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(5161,a,5155,a)]. 25.65/25.56 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(5161,a,5156,a)]. 25.65/25.56 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(5161,a,5157,a)]. 25.65/25.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)). [resolve(5161,a,5158,a)]. 25.65/25.56 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(5161,a,5159,a)]. 25.65/25.56 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5161,a,5160,a)]. 25.65/25.56 5162 -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_1872_mult__imp__less__div__pos) # label(axiom). [clausify(1666)]. 25.65/25.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5162,a,5140,a)]. 25.65/25.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5162,a,5161,a)]. 25.82/25.75 5163 -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_1839_divide__neg__neg) # label(axiom). [clausify(1903)]. 25.82/25.75 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(5163,a,5140,a)]. 25.82/25.75 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(5163,a,5161,a)]. 25.82/25.75 5164 -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_1824_pos__divide__le__eq) # label(axiom). [clausify(1938)]. 25.82/25.75 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(5164,a,5140,a)]. 25.82/25.75 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(5164,a,5161,a)]. 25.82/25.75 5165 -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_1824_pos__divide__le__eq) # label(axiom). [clausify(1938)]. 25.82/25.75 5166 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2591_inverse__positive__imp__positive) # label(axiom). [clausify(1958)]. 25.82/25.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5166,a,5140,a)]. 25.82/25.75 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5166,a,5161,a)]. 25.82/25.75 5167 -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_1841_divide__pos__neg) # label(axiom). [clausify(2179)]. 26.02/26.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5167,a,5140,a)]. 26.02/26.00 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(5167,a,5161,a)]. 26.02/26.00 5168 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f417(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1897_field__le__epsilon) # label(axiom). [clausify(2440)]. 26.02/26.00 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f417(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5168,a,5140,a)]. 26.02/26.00 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f417(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5168,a,5161,a)]. 26.02/26.00 5169 -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),f417(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1897_field__le__epsilon) # label(axiom). [clausify(2440)]. 26.02/26.00 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),f417(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5169,a,5140,a)]. 26.02/26.00 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),f417(rat,A,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5169,a,5161,a)]. 26.02/26.00 5170 -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_1863_frac__less) # label(axiom). [clausify(2651)]. 26.02/26.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5170,a,5140,a)]. 26.02/26.00 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(5170,a,5161,a)]. 26.02/26.00 5171 -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_1874_neg__divide__less__eq) # label(axiom). [clausify(2724)]. 26.02/26.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5171,a,5140,a)]. 26.31/26.23 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(5171,a,5161,a)]. 26.31/26.23 5172 -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_1874_neg__divide__less__eq) # label(axiom). [clausify(2724)]. 26.31/26.24 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(5172,a,5140,a)]. 26.31/26.24 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(5172,a,5161,a)]. 26.31/26.24 5173 -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_2590_negative__imp__inverse__negative) # label(axiom). [clausify(2744)]. 26.31/26.24 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(5173,a,5140,a)]. 26.31/26.24 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(5173,a,5161,a)]. 26.31/26.24 5174 -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_1889_divide__left__mono) # label(axiom). [clausify(2997)]. 26.31/26.24 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5174,a,5140,a)]. 26.31/26.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_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(5174,a,5161,a)]. 26.72/26.64 5175 -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_1840_divide__neg__pos) # label(axiom). [clausify(3012)]. 26.72/26.64 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(5175,a,5140,a)]. 26.72/26.64 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(5175,a,5161,a)]. 26.72/26.64 5176 -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_1892_mult__imp__le__div__pos) # label(axiom). [clausify(3061)]. 26.72/26.64 5177 -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_1837_divide__strict__right__mono__neg) # label(axiom). [clausify(3212)]. 26.72/26.64 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(5177,a,5140,a)]. 26.72/26.64 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(5177,a,5161,a)]. 26.72/26.64 5178 -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_1838_divide__strict__right__mono) # label(axiom). [clausify(3268)]. 26.72/26.64 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(5178,a,5140,a)]. 26.72/26.64 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(5178,a,5161,a)]. 26.72/26.64 5179 -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_2632_inv__of__nat__fact__ge__zero) # label(axiom). [clausify(3421)]. 26.72/26.64 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(5179,a,5140,a)]. 26.72/26.67 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(5179,a,5161,a)]. 26.72/26.67 5180 -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_1891_neg__le__divide__eq) # label(axiom). [clausify(3445)]. 26.72/26.67 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(5180,a,5140,a)]. 26.72/26.67 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(5180,a,5161,a)]. 26.72/26.67 5181 -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_1891_neg__le__divide__eq) # label(axiom). [clausify(3445)]. 26.72/26.67 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(5181,a,5140,a)]. 26.72/26.67 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(5181,a,5161,a)]. 26.72/26.67 5182 -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_1869_pos__less__divide__eq) # label(axiom). [clausify(3460)]. 26.72/26.67 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),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(5182,a,5140,a)]. 26.72/26.67 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),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(5182,a,5161,a)]. 26.72/26.67 5183 -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_1869_pos__less__divide__eq) # label(axiom). [clausify(3460)]. 26.94/26.90 5184 -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_1864_frac__le) # label(axiom). [clausify(3624)]. 26.94/26.90 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(5184,a,5140,a)]. 26.94/26.90 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(5184,a,5161,a)]. 26.94/26.90 5185 -linordered_field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) # label(fact_2601_nonzero__abs__inverse) # label(axiom). [clausify(3704)]. 26.94/26.90 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)). [resolve(5185,a,5140,a)]. 26.94/26.90 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5185,a,5161,a)]. 26.94/26.90 5186 -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_2608_le__imp__inverse__le__neg) # label(axiom). [clausify(3749)]. 26.94/26.90 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(5186,a,5140,a)]. 26.94/26.90 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),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(5186,a,5161,a)]. 26.94/26.90 5187 -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_1873_neg__less__divide__eq) # label(axiom). [clausify(3770)]. 26.94/26.90 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(5187,a,5140,a)]. 27.25/27.22 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(5187,a,5161,a)]. 27.25/27.22 5188 -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_1873_neg__less__divide__eq) # label(axiom). [clausify(3770)]. 27.25/27.22 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(5188,a,5140,a)]. 27.25/27.22 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(5188,a,5161,a)]. 27.25/27.22 5189 -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_2614_one__less__inverse) # label(axiom). [clausify(3897)]. 27.25/27.22 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(5189,a,5140,a)]. 27.25/27.22 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(5189,a,5161,a)]. 27.25/27.22 5190 -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_2585_inverse__less__imp__less__neg) # label(axiom). [clausify(3965)]. 27.25/27.22 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(5190,a,5140,a)]. 27.25/27.22 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5190,a,5161,a)]. 27.25/27.22 5191 -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_1860_divide__nonneg__pos) # label(axiom). [clausify(4158)]. 27.25/27.22 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(5191,a,5140,a)]. 27.56/27.52 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(5191,a,5161,a)]. 27.56/27.52 5192 -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_2610_inverse__le__imp__le__neg) # label(axiom). [clausify(4174)]. 27.56/27.52 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(5192,a,5140,a)]. 27.56/27.52 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(5192,a,5161,a)]. 27.56/27.52 5193 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2587_inverse__negative__imp__negative) # label(axiom). [clausify(4336)]. 27.56/27.52 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5193,a,5140,a)]. 27.56/27.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5193,a,5161,a)]. 27.56/27.52 5194 -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_2592_positive__imp__inverse__positive) # label(axiom). [clausify(4442)]. 27.56/27.52 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(5194,a,5140,a)]. 27.56/27.52 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(5194,a,5161,a)]. 27.56/27.52 5195 -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_3975_abs__setprod) # label(axiom). [clausify(4532)]. 27.56/27.52 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(5195,a,5140,a)]. 27.56/27.52 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(5195,a,5161,a)]. 27.86/27.82 5196 -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_2609_inverse__le__imp__le) # label(axiom). [clausify(4675)]. 27.86/27.82 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(5196,a,5140,a)]. 27.86/27.82 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(5196,a,5161,a)]. 27.86/27.82 5197 -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),inverse_divide(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),times_times(A),D),B))) # label(fact_1870_pos__divide__less__eq) # label(axiom). [clausify(4696)]. 27.86/27.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5197,a,5140,a)]. 27.86/27.82 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5197,a,5161,a)]. 27.86/27.82 5198 -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),inverse_divide(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),times_times(A),D),B))) # label(fact_1870_pos__divide__less__eq) # label(axiom). [clausify(4696)]. 27.86/27.82 5199 -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_1865_divide__nonpos__pos) # label(axiom). [clausify(4828)]. 27.86/27.82 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(5199,a,5140,a)]. 27.86/27.82 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(5199,a,5161,a)]. 27.86/27.82 5200 -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_1876_divide__strict__left__mono__neg) # label(axiom). [clausify(4895)]. 28.96/28.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5200,a,5140,a)]. 28.96/28.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5200,a,5161,a)]. 28.96/28.85 5201 ordere779506340up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 28.96/28.85 5202 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_212_add__left__mono) # label(axiom). [clausify(19)]. 28.96/28.85 5203 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f63(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4370_setsum__mono) # label(axiom). [clausify(463)]. 28.96/28.85 5204 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f63(B,A,C,D,E))),hAPP(B,A,D,f63(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4370_setsum__mono) # label(axiom). [clausify(463)]. 28.96/28.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(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(5201,a,5202,a)]. 28.96/28.85 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(5201,a,5203,b)]. 28.96/28.85 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f63(A,rat,B,C,D))),hAPP(A,rat,C,f63(A,rat,B,C,D)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D))). [resolve(5201,a,5204,b)]. 28.96/28.85 5205 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f138(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4335_setsum__nonpos) # label(axiom). [clausify(889)]. 28.96/28.85 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))). [resolve(5205,b,5201,a)]. 29.05/28.97 5206 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f138(B,A,C,D))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4335_setsum__nonpos) # label(axiom). [clausify(889)]. 29.05/28.97 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f138(A,rat,B,C))),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)),zero_zero(rat))). [resolve(5206,b,5201,a)]. 29.05/28.97 5207 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f146(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4319_setsum__mono3) # label(axiom). [clausify(921)]. 29.05/28.97 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(5207,a,5201,a)]. 29.05/28.97 5208 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f146(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4319_setsum__mono3) # label(axiom). [clausify(921)]. 29.05/28.97 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f146(A,rat,D,C,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(5208,a,5201,a)]. 29.05/28.97 5209 -ordere779506340up_add(A) | -semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f222(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_4323_setsum__bounded) # label(axiom). [clausify(1330)]. 29.05/28.97 Derived: -semiring_1(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,rat,B,C,D)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5209,a,5201,a)]. 29.41/29.32 5210 -ordere779506340up_add(A) | -semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f222(B,A,C,D,E))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,finite_card(B),E))),D))) # label(fact_4323_setsum__bounded) # label(axiom). [clausify(1330)]. 29.41/29.32 Derived: -semiring_1(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f222(A,rat,B,C,D))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5210,a,5201,a)]. 29.41/29.32 5211 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_213_add__right__mono) # label(axiom). [clausify(2108)]. 29.41/29.32 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),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(5211,a,5201,a)]. 29.41/29.32 5212 ordere779506340up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 29.41/29.32 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),plus_plus(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))). [resolve(5212,a,5202,a)]. 29.41/29.32 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(5212,a,5203,b)]. 29.41/29.32 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f63(A,real,B,C,D))),hAPP(A,real,C,f63(A,real,B,C,D)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D))). [resolve(5212,a,5204,b)]. 29.41/29.32 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))). [resolve(5212,a,5205,b)]. 29.41/29.32 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f138(A,real,B,C))),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)),zero_zero(real))). [resolve(5212,a,5206,b)]. 29.41/29.32 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(5212,a,5207,a)]. 29.65/29.60 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f146(A,real,D,C,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(5212,a,5208,a)]. 29.65/29.60 Derived: -semiring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5212,a,5209,a)]. 29.65/29.60 Derived: -semiring_1(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f222(A,real,B,C,D))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5212,a,5210,a)]. 29.65/29.60 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),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(5212,a,5211,a)]. 29.65/29.60 5213 ordere779506340up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 29.65/29.60 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),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(5213,a,5202,a)]. 29.65/29.60 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(5213,a,5203,b)]. 29.65/29.60 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f63(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f63(A,code_code_numeral,B,C,D)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D))). [resolve(5213,a,5204,b)]. 29.65/29.61 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))). [resolve(5213,a,5205,b)]. 29.65/29.61 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f138(A,code_code_numeral,B,C))),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C)),zero_zero(code_code_numeral))). [resolve(5213,a,5206,b)]. 29.65/29.61 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,code_code_numeral,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(5213,a,5207,a)]. 29.65/29.61 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,D,f146(A,code_code_numeral,D,C,B)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),C)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),D),B))). [resolve(5213,a,5208,a)]. 29.65/29.61 Derived: -semiring_1(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,code_code_numeral,B,C,D)),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),hAPP(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(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5213,a,5209,a)]. 29.65/29.61 Derived: -semiring_1(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(A,code_code_numeral,B,f222(A,code_code_numeral,B,C,D))),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),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(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5213,a,5210,a)]. 30.18/30.10 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),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(5213,a,5211,a)]. 30.18/30.10 5214 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_211_add__mono) # label(axiom). [clausify(3103)]. 30.18/30.10 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),plus_plus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),D))). [resolve(5214,a,5201,a)]. 30.18/30.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(5214,a,5212,a)]. 30.18/30.10 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_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),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(5214,a,5213,a)]. 30.18/30.10 5215 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 30.18/30.10 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,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(5215,a,5202,a)]. 30.18/30.10 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(5215,a,5203,b)]. 30.18/30.10 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f63(A,int,B,C,D))),hAPP(A,int,C,f63(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(5215,a,5204,b)]. 30.18/30.10 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)),zero_zero(int))). [resolve(5215,a,5205,b)]. 30.76/30.67 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f138(A,int,B,C))),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)),zero_zero(int))). [resolve(5215,a,5206,b)]. 30.76/30.67 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(5215,a,5207,a)]. 30.76/30.67 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f146(A,int,D,C,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(5215,a,5208,a)]. 30.76/30.67 Derived: -semiring_1(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5215,a,5209,a)]. 30.76/30.67 Derived: -semiring_1(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f222(A,int,B,C,D))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5215,a,5210,a)]. 30.76/30.67 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),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(5215,a,5211,a)]. 30.76/30.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(5215,a,5214,a)]. 30.76/30.67 5216 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f689(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4336_setsum__nonneg) # label(axiom). [clausify(3815)]. 30.76/30.67 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(A,rat,B,C)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))). [resolve(5216,b,5201,a)]. 30.76/30.67 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(A,real,B,C)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))). [resolve(5216,b,5212,a)]. 31.28/31.19 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(A,code_code_numeral,B,C)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))). [resolve(5216,b,5213,a)]. 31.28/31.19 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(A,int,B,C)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))). [resolve(5216,b,5215,a)]. 31.28/31.19 5217 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f689(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4336_setsum__nonneg) # label(axiom). [clausify(3815)]. 31.28/31.19 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f689(A,rat,B,C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C))). [resolve(5217,b,5201,a)]. 31.28/31.19 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f689(A,real,B,C)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C))). [resolve(5217,b,5212,a)]. 31.28/31.19 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(A,code_code_numeral,B,f689(A,code_code_numeral,B,C)))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),C))). [resolve(5217,b,5213,a)]. 31.28/31.19 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f689(A,int,B,C)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C))). [resolve(5217,b,5215,a)]. 31.28/31.19 5218 ordere779506340up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 31.28/31.19 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),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(5218,a,5202,a)]. 31.28/31.19 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(5218,a,5203,b)]. 31.28/31.20 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f63(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f63(A,quickcheck_code_int,B,C,D)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D))). [resolve(5218,a,5204,b)]. 31.28/31.20 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))). [resolve(5218,a,5205,b)]. 31.28/31.20 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f138(A,quickcheck_code_int,B,C))),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C)),zero_zero(quickcheck_code_int))). [resolve(5218,a,5206,b)]. 31.28/31.20 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,quickcheck_code_int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(5218,a,5207,a)]. 31.28/31.20 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,D,f146(A,quickcheck_code_int,D,C,B)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),C)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),D),B))). [resolve(5218,a,5208,a)]. 31.28/31.20 Derived: -semiring_1(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,quickcheck_code_int,B,C,D)),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),hAPP(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(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5218,a,5209,a)]. 31.28/31.21 Derived: -semiring_1(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(A,quickcheck_code_int,B,f222(A,quickcheck_code_int,B,C,D))),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),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(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5218,a,5210,a)]. 31.28/31.21 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),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(5218,a,5211,a)]. 31.28/31.21 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),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(5218,a,5214,a)]. 31.28/31.21 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(A,quickcheck_code_int,B,C)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))). [resolve(5218,a,5216,b)]. 31.28/31.21 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f689(A,quickcheck_code_int,B,C)))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),C))). [resolve(5218,a,5217,b)]. 31.28/31.21 5219 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 31.28/31.21 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),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(5219,a,5202,a)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f63(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(5219,a,5203,b)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f63(A,nat,B,C,D))),hAPP(A,nat,C,f63(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(5219,a,5204,b)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f138(A,nat,B,C)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)),zero_zero(nat))). [resolve(5219,a,5205,b)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f138(A,nat,B,C))),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),C)),zero_zero(nat))). [resolve(5219,a,5206,b)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f146(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(5219,a,5207,a)]. 31.28/31.21 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f146(A,nat,D,C,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(5219,a,5208,a)]. 31.28/31.21 Derived: -semiring_1(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f222(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5219,a,5209,a)]. 31.28/31.21 Derived: -semiring_1(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f222(A,nat,B,C,D))),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,finite_card(A),D))),C))). [resolve(5219,a,5210,a)]. 31.28/31.21 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),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(5219,a,5211,a)]. 31.28/31.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(5219,a,5214,a)]. 32.71/32.66 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f689(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_co1399186613setsum(A,nat),B),C))). [resolve(5219,a,5216,b)]. 32.71/32.66 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f689(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_co1399186613setsum(A,nat),B),C))). [resolve(5219,a,5217,b)]. 32.71/32.66 5220 number_semiring(rat) # label(arity_Rat_Orat___Int_Onumber__semiring) # label(axiom). [assumption]. 32.71/32.66 5221 -number_semiring(A) | one_one(A) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) # label(fact_104_semiring__numeral__1__eq__1) # label(axiom). [clausify(22)]. 32.71/32.66 5222 -number_semiring(A) | 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)))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_544_semiring__mult__2__right) # label(axiom). [clausify(93)]. 32.71/32.66 5223 -number_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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),plus_plus(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_575_power2__sum) # label(axiom). [clausify(216)]. 32.71/32.66 Derived: one_one(rat) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)). [resolve(5220,a,5221,a)]. 32.71/32.66 Derived: 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)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(5220,a,5222,a)]. 32.71/32.66 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(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),plus_plus(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5220,a,5223,a)]. 32.71/32.66 5224 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption]. 32.71/32.66 Derived: 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)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(5224,a,5222,a)]. 32.71/32.66 Derived: 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),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),plus_plus(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5224,a,5223,a)]. 34.00/33.91 5225 -number_semiring(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(int,A,number_number_of(A),hAPP(nat,int,semiring_1_of_nat(int),B)) # label(fact_97_number__of__int) # label(axiom). [clausify(1656)]. 34.00/33.91 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(int,rat,number_number_of(rat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5225,a,5220,a)]. 34.00/33.91 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5225,a,5224,a)]. 34.00/33.91 5226 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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,succ,B)) # label(fact_270_semiring__number__of__add__1) # label(axiom). [clausify(2347)]. 34.00/33.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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,succ,A)). [resolve(5226,a,5220,a)]. 34.00/33.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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,succ,A)). [resolve(5226,a,5224,a)]. 34.00/33.91 5227 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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_271_semiring__1__add__number__of) # label(axiom). [clausify(2467)]. 34.00/33.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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(5227,a,5220,a)]. 34.00/33.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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(5227,a,5224,a)]. 34.00/33.91 5228 -number_semiring(A) | zero_zero(A) = hAPP(int,A,number_number_of(A),pls) # label(fact_84_semiring__numeral__0__eq__0) # label(axiom). [clausify(2924)]. 34.00/33.91 Derived: zero_zero(rat) = hAPP(int,rat,number_number_of(rat),pls). [resolve(5228,a,5220,a)]. 34.00/33.91 Derived: zero_zero(int) = hAPP(int,int,number_number_of(int),pls). [resolve(5228,a,5224,a)]. 34.00/33.91 5229 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom). [assumption]. 34.00/33.91 Derived: one_one(real) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)). [resolve(5229,a,5221,a)]. 34.00/33.91 Derived: 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)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(5229,a,5222,a)]. 34.00/33.91 Derived: 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),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),plus_plus(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5229,a,5223,a)]. 34.46/34.41 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5229,a,5225,a)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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,succ,A)). [resolve(5229,a,5226,a)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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(5229,a,5227,a)]. 34.46/34.41 Derived: zero_zero(real) = hAPP(int,real,number_number_of(real),pls). [resolve(5229,a,5228,a)]. 34.46/34.41 5230 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | 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_305_semiring__add__number__of) # label(axiom). [clausify(3720)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5230,a,5220,a)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5230,a,5224,a)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5230,a,5229,a)]. 34.46/34.41 5231 -number_semiring(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_9_semiring__one__add__one__is__two) # label(axiom). [clausify(4135)]. 34.46/34.41 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(5231,a,5220,a)]. 34.46/34.41 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(5231,a,5224,a)]. 34.46/34.41 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(5231,a,5229,a)]. 34.46/34.41 5232 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | 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_422_semiring__mult__number__of) # label(axiom). [clausify(4205)]. 34.46/34.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5232,a,5220,a)]. 34.54/34.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5232,a,5224,a)]. 34.54/34.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5232,a,5229,a)]. 34.54/34.47 5233 -number_semiring(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) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_546_semiring__mult__2) # label(axiom). [clausify(4278)]. 34.54/34.47 Derived: 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) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(5233,a,5220,a)]. 34.54/34.47 Derived: 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) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(5233,a,5224,a)]. 34.54/34.47 Derived: 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) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(5233,a,5229,a)]. 34.54/34.47 5234 number_semiring(complex) # label(arity_Complex_Ocomplex___Int_Onumber__semiring) # label(axiom). [assumption]. 34.54/34.47 Derived: one_one(complex) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)). [resolve(5234,a,5221,a)]. 34.54/34.47 Derived: 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)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(5234,a,5222,a)]. 34.54/34.47 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(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),plus_plus(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5234,a,5223,a)]. 34.54/34.47 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5234,a,5225,a)]. 34.54/34.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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,succ,A)). [resolve(5234,a,5226,a)]. 34.54/34.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | 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(5234,a,5227,a)]. 34.94/34.86 Derived: zero_zero(complex) = hAPP(int,complex,number_number_of(complex),pls). [resolve(5234,a,5228,a)]. 34.94/34.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5234,a,5230,a)]. 34.94/34.86 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(5234,a,5231,a)]. 34.94/34.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | 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(5234,a,5232,a)]. 34.94/34.86 Derived: 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) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(5234,a,5233,a)]. 34.94/34.86 5235 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption]. 34.94/34.86 Derived: one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)). [resolve(5235,a,5221,a)]. 34.94/34.86 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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),plus_plus(nat),A),A). [resolve(5235,a,5222,a)]. 34.94/34.86 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),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)))))),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),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A)),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5235,a,5223,a)]. 34.94/34.86 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(int,nat,number_number_of(nat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5235,a,5225,a)]. 34.94/34.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)). [resolve(5235,a,5226,a)]. 34.94/34.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)). [resolve(5235,a,5227,a)]. 34.94/34.86 Derived: zero_zero(nat) = hAPP(int,nat,number_number_of(nat),pls). [resolve(5235,a,5228,a)]. 34.94/34.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)). [resolve(5235,a,5230,a)]. 36.01/35.93 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). [resolve(5235,a,5231,a)]. 36.01/35.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5235,a,5232,a)]. 36.01/35.93 Derived: 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) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(5235,a,5233,a)]. 36.01/35.93 5236 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.93 5237 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 36.01/35.93 5238 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5238,a,5237,a)]. 36.01/35.93 5239 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))). [resolve(5239,a,5237,a)]. 36.01/35.93 5240 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.93 5241 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.93 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5241,a,5237,a)]. 36.01/35.93 5242 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_425_mult__le__0__iff) # label(axiom). [clausify(314)]. 36.01/35.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5242,a,5237,a)]. 36.01/35.97 5243 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_456_mult__strict__left__mono__neg) # label(axiom). [clausify(378)]. 36.01/35.97 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),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(5243,a,5237,a)]. 36.01/35.97 5244 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.01/35.97 5245 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.01/35.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5245,a,5237,a)]. 36.01/35.97 5246 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.01/35.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(5246,a,5237,a)]. 36.01/35.97 5247 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.01/35.97 5248 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.01/35.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5248,a,5237,a)]. 36.71/36.63 5249 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_424_zero__le__mult__iff) # label(axiom). [clausify(647)]. 36.71/36.63 5250 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_449_mult__less__cancel__left__neg) # label(axiom). [clausify(673)]. 36.71/36.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(5250,a,5237,a)]. 36.71/36.63 5251 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_449_mult__less__cancel__left__neg) # label(axiom). [clausify(673)]. 36.71/36.63 5252 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_443_mult__less__cancel__left__pos) # label(axiom). [clausify(1286)]. 36.71/36.63 5253 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_443_mult__less__cancel__left__pos) # label(axiom). [clausify(1286)]. 36.71/36.63 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),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5253,a,5237,a)]. 36.71/36.63 5254 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_451_mult__neg__neg) # label(axiom). [clausify(1294)]. 36.71/36.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(5254,a,5237,a)]. 36.71/36.63 5255 linord581940658strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 36.71/36.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5255,a,5238,a)]. 36.71/36.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))). [resolve(5255,a,5239,a)]. 36.77/36.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5255,a,5241,a)]. 36.77/36.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5255,a,5242,a)]. 36.77/36.69 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),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5255,a,5243,a)]. 36.77/36.69 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5255,a,5245,a)]. 36.77/36.69 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(5255,a,5246,a)]. 36.77/36.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -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),A),zero_zero(rat))). [resolve(5255,a,5248,a)]. 36.77/36.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),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_eq(rat),zero_zero(rat)),A)). [resolve(5255,a,5249,a)]. 36.77/36.69 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),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(rat),C),B)). [resolve(5255,a,5250,a)]. 36.77/36.69 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),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))). [resolve(5255,a,5252,a)]. 36.77/36.69 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),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))). [resolve(5255,a,5253,a)]. 36.77/36.69 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),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(5255,a,5254,a)]. 36.77/36.69 5256 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 36.77/36.70 5257 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 36.77/36.70 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(5257,a,5237,a)]. 36.77/36.70 5258 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 36.77/36.70 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5258,a,5237,a)]. 36.77/36.70 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),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(5258,a,5255,a)]. 36.77/36.70 5259 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 36.77/36.70 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5259,a,5237,a)]. 36.77/36.70 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(5259,a,5255,a)]. 36.77/36.70 5260 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 36.77/36.70 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(5260,a,5237,a)]. 36.77/36.70 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)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5260,a,5255,a)]. 37.01/36.93 5261 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_442_mult__less__cancel__left__disj) # label(axiom). [clausify(2878)]. 37.01/36.93 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(5261,a,5237,a)]. 37.01/36.93 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(5261,a,5255,a)]. 37.01/36.93 5262 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_487_sum__squares__le__zero__iff) # label(axiom). [clausify(3088)]. 37.01/36.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(5262,a,5237,a)]. 37.01/36.93 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(5262,a,5255,a)]. 37.01/36.93 5263 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,C) # label(fact_487_sum__squares__le__zero__iff) # label(axiom). [clausify(3088)]. 37.01/36.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,B). [resolve(5263,a,5237,a)]. 37.01/36.93 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,B). [resolve(5263,a,5255,a)]. 37.01/36.93 5264 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_487_sum__squares__le__zero__iff) # label(axiom). [clausify(3088)]. 37.01/36.93 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(5264,a,5237,a)]. 37.01/36.93 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B))),zero_zero(rat))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(5264,a,5255,a)]. 37.35/37.29 5265 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_484_mult__le__cancel__left__neg) # label(axiom). [clausify(3218)]. 37.35/37.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)). [resolve(5265,a,5237,a)]. 37.35/37.29 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),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),C),B)). [resolve(5265,a,5255,a)]. 37.35/37.29 5266 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_484_mult__le__cancel__left__neg) # label(axiom). [clausify(3218)]. 37.35/37.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)). [resolve(5266,a,5237,a)]. 37.35/37.29 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),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),C),B)). [resolve(5266,a,5255,a)]. 37.35/37.29 5267 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_489_sum__squares__gt__zero__iff) # label(axiom). [clausify(3472)]. 37.35/37.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(5267,a,5237,a)]. 37.35/37.29 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(5267,a,5255,a)]. 37.35/37.29 5268 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) = ti(A,B) # label(fact_489_sum__squares__gt__zero__iff) # label(axiom). [clausify(3472)]. 37.35/37.29 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) = ti(int,A). [resolve(5268,a,5237,a)]. 37.35/37.29 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) = ti(rat,A). [resolve(5268,a,5255,a)]. 37.47/37.36 5269 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) = ti(A,C) # label(fact_489_sum__squares__gt__zero__iff) # label(axiom). [clausify(3472)]. 37.47/37.36 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) = ti(int,B). [resolve(5269,a,5237,a)]. 37.47/37.36 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)))) | zero_zero(rat) = ti(rat,B). [resolve(5269,a,5255,a)]. 37.47/37.36 5270 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(5270,a,5237,a)]. 37.47/37.36 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(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(5270,a,5255,a)]. 37.47/37.36 5271 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(5271,a,5237,a)]. 37.47/37.36 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(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(5271,a,5255,a)]. 37.47/37.36 5272 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(5272,a,5237,a)]. 37.47/37.38 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(5272,a,5255,a)]. 37.47/37.38 5273 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(5273,a,5237,a)]. 37.47/37.38 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(5273,a,5255,a)]. 37.47/37.38 5274 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.38 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). [resolve(5274,a,5237,a)]. 37.47/37.38 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),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),zero_zero(rat)),B)). [resolve(5274,a,5255,a)]. 37.47/37.38 5275 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_441_mult__less__cancel__right__disj) # label(axiom). [clausify(3576)]. 37.47/37.38 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(5275,a,5237,a)]. 37.47/37.38 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(5275,a,5255,a)]. 37.47/37.38 5276 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_485_mult__le__cancel__left__pos) # label(axiom). [clausify(3591)]. 38.34/38.26 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5276,a,5237,a)]. 38.34/38.26 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(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))). [resolve(5276,a,5255,a)]. 38.34/38.26 5277 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_485_mult__le__cancel__left__pos) # label(axiom). [clausify(3591)]. 38.34/38.26 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(5277,a,5237,a)]. 38.34/38.26 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(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))). [resolve(5277,a,5255,a)]. 38.34/38.26 5278 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_455_mult__strict__right__mono__neg) # label(axiom). [clausify(4550)]. 38.34/38.26 5279 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 38.34/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5279,a,5238,a)]. 38.34/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(5279,a,5239,a)]. 38.34/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5279,a,5241,a)]. 38.34/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5279,a,5242,a)]. 38.34/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5279,a,5243,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5279,a,5245,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(5279,a,5246,a)]. 38.36/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -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),A),zero_zero(real))). [resolve(5279,a,5248,a)]. 38.36/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),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_eq(real),zero_zero(real)),A)). [resolve(5279,a,5249,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(5279,a,5250,a)]. 38.36/38.26 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5252,a)]. 38.36/38.26 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5253,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(5279,a,5254,a)]. 38.36/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5258,a)]. 38.36/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5259,a)]. 38.36/38.26 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)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5279,a,5260,a)]. 38.36/38.26 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(5279,a,5261,a)]. 38.36/38.26 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(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(5279,a,5262,a)]. 38.36/38.26 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(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(5279,a,5263,a)]. 38.36/38.26 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(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(5279,a,5264,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(5279,a,5265,a)]. 38.36/38.26 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(5279,a,5266,a)]. 38.36/38.26 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(5279,a,5267,a)]. 38.36/38.26 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,A). [resolve(5279,a,5268,a)]. 38.36/38.26 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,B). [resolve(5279,a,5269,a)]. 38.36/38.26 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(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(5279,a,5270,a)]. 38.36/38.26 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(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(5279,a,5271,a)]. 38.53/38.48 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(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(5279,a,5272,a)]. 38.53/38.48 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(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(5279,a,5273,a)]. 38.53/38.48 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(real),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5279,a,5274,a)]. 38.53/38.48 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(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(5279,a,5275,a)]. 38.53/38.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5276,a)]. 38.53/38.48 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(5279,a,5277,a)]. 38.53/38.48 5280 -linord581940658strict(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) | zero_zero(A) = ti(A,C) # label(fact_457_sum__squares__eq__zero__iff) # label(axiom). [clausify(4908)]. 38.53/38.48 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) | zero_zero(int) = ti(int,B). [resolve(5280,a,5237,a)]. 38.53/38.48 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) | zero_zero(rat) = ti(rat,B). [resolve(5280,a,5255,a)]. 38.53/38.48 Derived: 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),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) | zero_zero(real) = ti(real,B). [resolve(5280,a,5279,a)]. 38.53/38.48 5281 -linord581940658strict(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) | zero_zero(A) = ti(A,B) # label(fact_457_sum__squares__eq__zero__iff) # label(axiom). [clausify(4908)]. 38.53/38.48 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) | zero_zero(int) = ti(int,A). [resolve(5281,a,5237,a)]. 38.53/38.48 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) | zero_zero(rat) = ti(rat,A). [resolve(5281,a,5255,a)]. 39.62/39.51 Derived: 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),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) | zero_zero(real) = ti(real,A). [resolve(5281,a,5279,a)]. 39.62/39.51 5282 -linord581940658strict(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) | zero_zero(A) != ti(A,C) | zero_zero(A) != ti(A,B) # label(fact_457_sum__squares__eq__zero__iff) # label(axiom). [clausify(4908)]. 39.62/39.51 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) | zero_zero(int) != ti(int,B) | zero_zero(int) != ti(int,A). [resolve(5282,a,5237,a)]. 39.62/39.51 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) != ti(rat,A). [resolve(5282,a,5255,a)]. 39.62/39.51 Derived: 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),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) | zero_zero(real) != ti(real,B) | zero_zero(real) != ti(real,A). [resolve(5282,a,5279,a)]. 39.62/39.51 5283 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption]. 39.62/39.51 5284 -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_310_power__strict__mono) # label(axiom). [clausify(32)]. 39.62/39.51 5285 -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_492_power__gt1__lemma) # label(axiom). [clausify(333)]. 39.62/39.51 5286 -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_239_power__increasing__iff) # label(axiom). [clausify(356)]. 39.62/39.51 5287 -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_239_power__increasing__iff) # label(axiom). [clausify(356)]. 39.62/39.51 5288 -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_172_of__nat__less__imp__less) # label(axiom). [clausify(369)]. 39.62/39.51 5289 -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_1457_power__Suc__less__one) # label(axiom). [clausify(383)]. 39.62/39.51 5290 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_249_not__one__le__zero) # label(axiom). [clausify(443)]. 39.62/39.52 5291 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f68(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_4176_setprod__pos) # label(axiom). [clausify(498)]. 39.62/39.52 5292 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(B,A,C,f68(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_4176_setprod__pos) # label(axiom). [clausify(498)]. 39.62/39.52 5293 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f79(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_4177_setprod__mono) # label(axiom). [clausify(533)]. 39.62/39.52 5294 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f79(B,A,D,C,E))),hAPP(B,A,D,f79(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,f79(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_4177_setprod__mono) # label(axiom). [clausify(533)]. 39.62/39.52 5295 -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_1456_realpow__Suc__le__self) # label(axiom). [clausify(648)]. 39.62/39.52 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(5283,a,5284,a)]. 39.62/39.52 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(5283,a,5285,a)]. 39.62/39.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,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_eq(nat),B),C)). [resolve(5283,a,5286,a)]. 39.62/39.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,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_eq(nat),B),C)). [resolve(5283,a,5287,a)]. 39.62/39.52 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(5283,a,5289,a)]. 39.62/39.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(5283,a,5290,a)]. 39.62/39.52 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5283,a,5291,a)]. 39.67/39.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,B,f68(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(5283,a,5292,a)]. 39.67/39.57 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5283,a,5293,a)]. 39.67/39.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f79(A,int,C,B,D))),hAPP(A,int,C,f79(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,f79(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(5283,a,5294,a)]. 39.67/39.57 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(5283,a,5295,a)]. 39.67/39.57 5296 -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_189_of__nat__less__0__iff) # label(axiom). [clausify(762)]. 39.67/39.57 5297 -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_332_power2__less__imp__less) # label(axiom). [clausify(869)]. 39.67/39.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),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(int),A),B)). [resolve(5297,a,5283,a)]. 39.67/39.57 5298 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_208_of__nat__le__iff) # label(axiom). [clausify(905)]. 39.67/39.57 5299 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_208_of__nat__le__iff) # label(axiom). [clausify(905)]. 39.67/39.57 5300 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(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),D) | C = D # label(fact_184_power__inject__exp) # label(axiom). [clausify(933)]. 39.67/39.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(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),C) | B = C. [resolve(5300,a,5283,a)]. 39.67/39.64 5301 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(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),D) | C != D # label(fact_184_power__inject__exp) # label(axiom). [clausify(933)]. 39.67/39.64 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(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),C) | B != C. [resolve(5301,a,5283,a)]. 39.67/39.64 5302 -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_170_of__nat__less__iff) # label(axiom). [clausify(945)]. 39.67/39.64 5303 -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_170_of__nat__less__iff) # label(axiom). [clausify(945)]. 39.67/39.64 5304 -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_182_zero__less__power) # label(axiom). [clausify(1046)]. 39.67/39.64 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(5304,a,5283,a)]. 39.67/39.64 5305 -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_314_power2__le__imp__le) # label(axiom). [clausify(1184)]. 39.67/39.64 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),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(5305,a,5283,a)]. 39.67/39.64 5306 -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_1425_power__le__imp__le__base) # label(axiom). [clausify(1198)]. 39.67/39.64 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),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(5306,a,5283,a)]. 39.67/39.64 5307 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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_4300_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(1255)]. 39.88/39.78 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5307,a,5283,a)]. 39.88/39.78 5308 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,B,f208(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_4300_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(1255)]. 39.88/39.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,A,f208(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(5308,a,5283,a)]. 39.88/39.78 5309 -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_255_zero__le__imp__of__nat) # label(axiom). [clausify(1544)]. 39.88/39.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(5309,a,5283,a)]. 39.88/39.78 5310 -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_237_power__decreasing) # label(axiom). [clausify(1587)]. 39.88/39.78 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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(5310,a,5283,a)]. 39.88/39.78 5311 -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_171_less__imp__of__nat__less) # label(axiom). [clausify(1670)]. 39.88/39.78 5312 -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_216_power__increasing) # label(axiom). [clausify(1759)]. 39.88/39.78 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(5312,a,5283,a)]. 40.06/39.99 5313 -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_111_one__less__power) # label(axiom). [clausify(1795)]. 40.06/39.99 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(5313,a,5283,a)]. 40.06/39.99 5314 -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_253_one__le__power) # label(axiom). [clausify(2133)]. 40.06/39.99 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(5314,a,5283,a)]. 40.06/39.99 5315 -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_459_less__1__mult) # label(axiom). [clausify(2142)]. 40.06/39.99 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(5315,a,5283,a)]. 40.06/39.99 5316 -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_186_power__less__imp__less__exp) # label(axiom). [clausify(2195)]. 40.06/39.99 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(5316,a,5283,a)]. 40.06/39.99 5317 -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_313_power2__eq__imp__eq) # label(axiom). [clausify(2242)]. 40.06/39.99 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(5317,a,5283,a)]. 40.06/39.99 5318 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f392(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_4178_setprod__nonneg) # label(axiom). [clausify(2294)]. 40.18/40.13 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f392(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(5318,a,5283,a)]. 40.18/40.13 5319 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f392(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_4178_setprod__nonneg) # label(axiom). [clausify(2294)]. 40.18/40.13 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f392(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(5319,a,5283,a)]. 40.18/40.13 5320 -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_252_zero__le__power) # label(axiom). [clausify(2502)]. 40.18/40.13 5321 -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_114_zero__less__two) # label(axiom). [clausify(2560)]. 40.18/40.13 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(5321,a,5283,a)]. 40.18/40.13 5322 -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_538_power__Suc__less) # label(axiom). [clausify(2571)]. 40.18/40.13 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(5322,a,5283,a)]. 40.18/40.13 5323 -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_1430_power__gt1) # label(axiom). [clausify(2583)]. 40.18/40.13 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(5323,a,5283,a)]. 40.18/40.13 5324 -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_2550_of__nat__fact__gt__zero) # label(axiom). [clausify(2600)]. 40.18/40.13 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(5324,a,5283,a)]. 40.18/40.13 5325 -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_251_power__mono) # label(axiom). [clausify(2628)]. 40.18/40.14 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(5325,a,5283,a)]. 40.18/40.14 5326 linordered_semidom(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semidom) # label(axiom). [assumption]. 40.18/40.14 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),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(5326,a,5284,a)]. 40.18/40.14 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(5326,a,5285,a)]. 40.18/40.14 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_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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5326,a,5286,a)]. 40.18/40.14 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_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))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5326,a,5287,a)]. 40.18/40.14 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(5326,a,5288,a)]. 40.18/40.14 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(5326,a,5289,a)]. 40.18/40.14 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(5326,a,5290,a)]. 40.18/40.15 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5326,a,5291,a)]. 40.18/40.15 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,f68(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(5326,a,5292,a)]. 40.18/40.15 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5326,a,5293,a)]. 40.18/40.15 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,f79(A,code_code_numeral,C,B,D))),hAPP(A,code_code_numeral,C,f79(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,f79(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(5326,a,5294,a)]. 40.18/40.15 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(5326,a,5295,a)]. 40.18/40.15 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(5326,a,5296,a)]. 40.18/40.15 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),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(code_code_numeral),A),B)). [resolve(5326,a,5297,a)]. 40.26/40.16 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),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(5326,a,5298,a)]. 40.26/40.16 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),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(5326,a,5299,a)]. 40.26/40.16 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)) | 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) | B = C. [resolve(5326,a,5300,a)]. 40.26/40.16 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)) | 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) | B != C. [resolve(5326,a,5301,a)]. 40.26/40.16 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(5326,a,5303,a)]. 40.26/40.16 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(5326,a,5304,a)]. 40.26/40.16 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(5326,a,5305,a)]. 40.26/40.16 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(5326,a,5306,a)]. 40.26/40.16 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5326,a,5307,a)]. 40.26/40.16 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,f208(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(5326,a,5308,a)]. 40.26/40.16 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(5326,a,5309,a)]. 40.26/40.16 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(5326,a,5310,a)]. 40.26/40.16 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(5326,a,5312,a)]. 40.26/40.16 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(5326,a,5313,a)]. 40.26/40.16 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(5326,a,5314,a)]. 40.26/40.17 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(5326,a,5315,a)]. 40.26/40.17 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(5326,a,5316,a)]. 40.26/40.17 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(5326,a,5317,a)]. 40.26/40.17 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f392(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(5326,a,5318,a)]. 40.26/40.17 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,f392(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(5326,a,5319,a)]. 40.26/40.17 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(5326,a,5320,a)]. 40.26/40.17 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(5326,a,5321,a)]. 40.46/40.41 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(5326,a,5322,a)]. 40.46/40.41 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(5326,a,5323,a)]. 40.46/40.41 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(5326,a,5324,a)]. 40.46/40.41 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(5326,a,5325,a)]. 40.46/40.41 5327 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_180_not__one__less__zero) # label(axiom). [clausify(2675)]. 40.46/40.41 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(5327,a,5283,a)]. 40.46/40.41 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(5327,a,5326,a)]. 40.46/40.41 5328 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom). [assumption]. 40.46/40.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5328,a,5284,a)]. 40.46/40.41 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(5328,a,5285,a)]. 40.46/40.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,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_eq(nat),B),C)). [resolve(5328,a,5286,a)]. 40.46/40.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,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_eq(nat),B),C)). [resolve(5328,a,5287,a)]. 40.46/40.42 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(5328,a,5288,a)]. 40.46/40.42 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(5328,a,5289,a)]. 40.46/40.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))). [resolve(5328,a,5290,a)]. 40.46/40.42 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5328,a,5291,a)]. 40.46/40.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(A,real,B,f68(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(5328,a,5292,a)]. 40.46/40.42 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5328,a,5293,a)]. 40.46/40.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f79(A,real,C,B,D))),hAPP(A,real,C,f79(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,f79(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(5328,a,5294,a)]. 40.46/40.42 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(5328,a,5295,a)]. 40.46/40.42 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(5328,a,5296,a)]. 40.46/40.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),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(real),A),B)). [resolve(5328,a,5297,a)]. 40.46/40.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))). [resolve(5328,a,5298,a)]. 40.46/40.42 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))). [resolve(5328,a,5299,a)]. 40.54/40.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(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),C) | B = C. [resolve(5328,a,5300,a)]. 40.54/40.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(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),C) | B != C. [resolve(5328,a,5301,a)]. 40.54/40.43 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(5328,a,5303,a)]. 40.54/40.43 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),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(5328,a,5304,a)]. 40.54/40.43 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(5328,a,5305,a)]. 40.54/40.43 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(5328,a,5306,a)]. 40.54/40.43 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5328,a,5307,a)]. 40.54/40.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A,f208(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(5328,a,5308,a)]. 40.54/40.43 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(5328,a,5309,a)]. 40.54/40.43 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(5328,a,5310,a)]. 40.54/40.43 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(5328,a,5312,a)]. 40.54/40.44 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(5328,a,5313,a)]. 40.54/40.44 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(5328,a,5314,a)]. 40.54/40.44 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(5328,a,5315,a)]. 40.54/40.44 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(5328,a,5316,a)]. 40.54/40.44 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(5328,a,5317,a)]. 40.54/40.44 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f392(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(5328,a,5318,a)]. 40.54/40.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f392(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(5328,a,5319,a)]. 40.54/40.44 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(5328,a,5320,a)]. 40.54/40.44 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(5328,a,5321,a)]. 40.54/40.44 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(5328,a,5322,a)]. 40.54/40.44 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(5328,a,5323,a)]. 40.54/40.44 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(5328,a,5324,a)]. 40.60/40.53 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(5328,a,5325,a)]. 40.60/40.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))). [resolve(5328,a,5327,a)]. 40.60/40.53 5329 -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_110_of__nat__0__less__iff) # label(axiom). [clausify(2977)]. 40.60/40.53 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(5329,a,5326,a)]. 40.60/40.53 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(5329,a,5328,a)]. 40.60/40.53 5330 -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_110_of__nat__0__less__iff) # label(axiom). [clausify(2977)]. 40.60/40.53 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(5330,a,5326,a)]. 40.60/40.53 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(5330,a,5328,a)]. 40.60/40.53 5331 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 40.60/40.53 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(5331,a,5284,a)]. 40.60/40.53 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(5331,a,5285,a)]. 40.60/40.53 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,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_eq(nat),B),C)). [resolve(5331,a,5286,a)]. 40.60/40.53 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,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_eq(nat),B),C)). [resolve(5331,a,5287,a)]. 40.60/40.53 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(5331,a,5288,a)]. 40.66/40.55 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),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(5331,a,5289,a)]. 40.66/40.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(5331,a,5290,a)]. 40.66/40.55 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5331,a,5291,a)]. 40.66/40.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(A,nat,B,f68(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(5331,a,5292,a)]. 40.66/40.55 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5331,a,5293,a)]. 40.66/40.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f79(A,nat,C,B,D))),hAPP(A,nat,C,f79(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,f79(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(5331,a,5294,a)]. 40.66/40.55 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(5331,a,5295,a)]. 40.66/40.55 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),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(nat),A),B)). [resolve(5331,a,5297,a)]. 40.66/40.55 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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(5331,a,5298,a)]. 40.66/40.55 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),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(5331,a,5299,a)]. 40.66/40.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(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),C) | B = C. [resolve(5331,a,5300,a)]. 40.66/40.55 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(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),C) | B != C. [resolve(5331,a,5301,a)]. 40.66/40.55 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(5331,a,5303,a)]. 40.66/40.56 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(5331,a,5305,a)]. 40.66/40.56 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(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),A),C)). [resolve(5331,a,5306,a)]. 40.66/40.56 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5331,a,5307,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,A,f208(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(5331,a,5308,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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(5331,a,5310,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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(5331,a,5312,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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(5331,a,5313,a)]. 40.66/40.56 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(5331,a,5314,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(5331,a,5315,a)]. 40.66/40.56 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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(5331,a,5316,a)]. 40.68/40.57 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(5331,a,5317,a)]. 40.68/40.57 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(5331,a,5321,a)]. 40.68/40.57 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(5331,a,5322,a)]. 40.68/40.57 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(5331,a,5323,a)]. 40.68/40.57 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(5331,a,5324,a)]. 40.68/40.57 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(5331,a,5325,a)]. 40.68/40.57 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(5331,a,5329,a)]. 40.68/40.57 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(5331,a,5330,a)]. 40.68/40.57 5332 -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_304_power__eq__imp__eq__base) # label(axiom). [clausify(3070)]. 40.68/40.57 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(5332,a,5283,a)]. 40.68/40.57 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(5332,a,5326,a)]. 41.05/41.00 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(5332,a,5328,a)]. 41.05/41.00 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(5332,a,5331,a)]. 41.05/41.00 5333 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_248_zero__le__one) # label(axiom). [clausify(3220)]. 41.05/41.00 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(5333,a,5283,a)]. 41.05/41.00 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(5333,a,5326,a)]. 41.05/41.00 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))). [resolve(5333,a,5328,a)]. 41.05/41.00 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(5333,a,5331,a)]. 41.05/41.00 5334 -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_179_pos__add__strict) # label(axiom). [clausify(3468)]. 41.05/41.00 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(5334,a,5283,a)]. 41.05/41.00 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(5334,a,5326,a)]. 41.05/41.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5334,a,5328,a)]. 41.05/41.00 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(5334,a,5331,a)]. 41.05/41.00 5335 -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_187_power__strict__increasing) # label(axiom). [clausify(3555)]. 41.05/41.00 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(5335,a,5283,a)]. 41.53/41.42 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),one_one(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(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(5335,a,5326,a)]. 41.53/41.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),B))). [resolve(5335,a,5328,a)]. 41.53/41.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(5335,a,5331,a)]. 41.53/41.42 5336 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_181_zero__less__one) # label(axiom). [clausify(3776)]. 41.53/41.42 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(5336,a,5283,a)]. 41.53/41.42 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(5336,a,5326,a)]. 41.53/41.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))). [resolve(5336,a,5328,a)]. 41.53/41.42 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(5336,a,5331,a)]. 41.53/41.42 5337 -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_238_power__le__imp__le__exp) # label(axiom). [clausify(3800)]. 41.53/41.42 5338 -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_185_power__strict__increasing__iff) # label(axiom). [clausify(4018)]. 41.53/41.42 5339 -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_185_power__strict__increasing__iff) # label(axiom). [clausify(4018)]. 41.53/41.42 5340 linordered_semidom(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semidom) # label(axiom). [assumption]. 41.53/41.42 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(5340,a,5284,a)]. 41.53/41.42 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(5340,a,5285,a)]. 41.53/41.42 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_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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5340,a,5286,a)]. 41.53/41.42 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_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))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5340,a,5287,a)]. 41.53/41.42 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(5340,a,5288,a)]. 41.53/41.42 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(5340,a,5289,a)]. 41.53/41.42 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(5340,a,5290,a)]. 41.53/41.42 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5340,a,5291,a)]. 41.53/41.42 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,f68(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(5340,a,5292,a)]. 41.53/41.43 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5340,a,5293,a)]. 41.53/41.43 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,f79(A,quickcheck_code_int,C,B,D))),hAPP(A,quickcheck_code_int,C,f79(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,f79(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(5340,a,5294,a)]. 41.53/41.43 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(5340,a,5295,a)]. 41.53/41.43 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(5340,a,5296,a)]. 41.53/41.43 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),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(quickcheck_code_int),A),B)). [resolve(5340,a,5297,a)]. 41.53/41.43 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),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(5340,a,5298,a)]. 41.53/41.43 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),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(5340,a,5299,a)]. 41.53/41.43 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)) | 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) | B = C. [resolve(5340,a,5300,a)]. 41.53/41.43 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)) | 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) | B != C. [resolve(5340,a,5301,a)]. 41.53/41.43 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(5340,a,5303,a)]. 41.53/41.43 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(5340,a,5304,a)]. 41.53/41.43 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(5340,a,5305,a)]. 41.53/41.43 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(5340,a,5306,a)]. 41.53/41.43 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5340,a,5307,a)]. 41.53/41.44 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,f208(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(5340,a,5308,a)]. 41.53/41.44 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(5340,a,5309,a)]. 41.53/41.44 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(5340,a,5310,a)]. 41.53/41.44 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(5340,a,5312,a)]. 41.53/41.44 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(5340,a,5313,a)]. 41.53/41.44 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(5340,a,5314,a)]. 41.53/41.44 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(5340,a,5315,a)]. 41.53/41.44 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(5340,a,5316,a)]. 41.53/41.44 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(5340,a,5317,a)]. 41.53/41.44 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f392(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(5340,a,5318,a)]. 41.53/41.44 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,f392(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(5340,a,5319,a)]. 41.53/41.44 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(5340,a,5320,a)]. 41.53/41.44 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(5340,a,5321,a)]. 41.53/41.44 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(5340,a,5322,a)]. 41.53/41.44 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(5340,a,5323,a)]. 41.53/41.44 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(5340,a,5324,a)]. 41.53/41.44 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(5340,a,5325,a)]. 41.53/41.44 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(5340,a,5327,a)]. 41.53/41.44 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(5340,a,5329,a)]. 41.53/41.44 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(5340,a,5330,a)]. 41.53/41.44 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(5340,a,5332,a)]. 41.58/41.47 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(5340,a,5333,a)]. 41.58/41.47 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(5340,a,5334,a)]. 41.58/41.47 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),one_one(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(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(5340,a,5335,a)]. 41.58/41.47 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(5340,a,5336,a)]. 41.58/41.47 5341 -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_1424_power__inject__base) # label(axiom). [clausify(4125)]. 41.58/41.47 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(5341,a,5283,a)]. 41.58/41.47 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(5341,a,5326,a)]. 41.58/41.47 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(5341,a,5328,a)]. 41.58/41.47 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(5341,a,5331,a)]. 41.58/41.47 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(5341,a,5340,a)]. 41.84/41.73 5342 -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_254_of__nat__0__le__iff) # label(axiom). [clausify(4228)]. 41.84/41.73 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(5342,a,5331,a)]. 41.84/41.73 5343 -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_493_power__less__power__Suc) # label(axiom). [clausify(4329)]. 41.84/41.73 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(5343,a,5283,a)]. 41.84/41.73 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(5343,a,5326,a)]. 41.84/41.73 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(5343,a,5328,a)]. 41.84/41.73 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(5343,a,5331,a)]. 41.84/41.73 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(5343,a,5340,a)]. 41.84/41.73 5344 -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_183_less__add__one) # label(axiom). [clausify(4463)]. 41.84/41.73 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(5344,a,5283,a)]. 41.97/41.86 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(5344,a,5326,a)]. 41.97/41.86 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(5344,a,5328,a)]. 41.97/41.86 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(5344,a,5331,a)]. 41.97/41.86 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(5344,a,5340,a)]. 41.97/41.86 5345 -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_113_power__strict__decreasing) # label(axiom). [clausify(4611)]. 41.97/41.86 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(5345,a,5283,a)]. 41.97/41.86 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(5345,a,5326,a)]. 41.97/41.86 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(5345,a,5328,a)]. 41.97/41.86 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(5345,a,5331,a)]. 41.97/41.86 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(5345,a,5340,a)]. 42.08/41.96 5346 -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_2549_of__nat__fact__ge__zero) # label(axiom). [clausify(4641)]. 42.08/41.96 5347 -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_272_power__less__imp__less__base) # label(axiom). [clausify(4679)]. 42.08/41.96 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(5347,a,5283,a)]. 42.08/41.96 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(5347,a,5326,a)]. 42.08/41.96 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(5347,a,5328,a)]. 42.08/41.96 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(5347,a,5331,a)]. 42.08/41.96 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(5347,a,5340,a)]. 42.08/41.96 5348 linordered_semidom(rat) # label(arity_Rat_Orat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 42.08/41.96 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(5348,a,5284,a)]. 42.08/41.96 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(5348,a,5285,a)]. 42.08/41.96 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_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))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5348,a,5286,a)]. 42.08/41.96 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_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))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5348,a,5287,a)]. 42.08/41.96 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(5348,a,5288,a)]. 42.08/41.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5348,a,5289,a)]. 42.08/41.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),zero_zero(rat))). [resolve(5348,a,5290,a)]. 42.08/41.96 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f68(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(5348,a,5291,a)]. 42.08/41.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(A,rat,B,f68(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(5348,a,5292,a)]. 42.08/41.96 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f79(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(5348,a,5293,a)]. 42.08/41.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f79(A,rat,C,B,D))),hAPP(A,rat,C,f79(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,f79(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(5348,a,5294,a)]. 42.08/41.96 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(5348,a,5295,a)]. 42.08/41.96 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(5348,a,5296,a)]. 42.08/41.96 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),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(rat),A),B)). [resolve(5348,a,5297,a)]. 42.09/41.97 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),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))). [resolve(5348,a,5298,a)]. 42.09/41.97 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),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))). [resolve(5348,a,5299,a)]. 42.09/41.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(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),C) | B = C. [resolve(5348,a,5300,a)]. 42.09/41.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(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),C) | B != C. [resolve(5348,a,5301,a)]. 42.09/41.97 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(5348,a,5303,a)]. 42.09/41.97 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(5348,a,5304,a)]. 42.09/41.97 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(5348,a,5305,a)]. 42.09/41.97 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(5348,a,5306,a)]. 42.09/41.97 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f208(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(5348,a,5307,a)]. 42.09/41.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,A,f208(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(5348,a,5308,a)]. 42.09/41.97 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(5348,a,5309,a)]. 42.09/41.97 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(5348,a,5310,a)]. 42.09/41.97 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(5348,a,5312,a)]. 42.09/41.97 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(5348,a,5313,a)]. 42.09/41.97 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(5348,a,5314,a)]. 42.09/41.97 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(5348,a,5315,a)]. 42.09/41.97 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(5348,a,5316,a)]. 42.09/41.97 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(5348,a,5317,a)]. 42.09/41.97 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f392(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(5348,a,5318,a)]. 42.09/41.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f392(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(5348,a,5319,a)]. 42.09/41.97 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(5348,a,5320,a)]. 42.09/41.97 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(5348,a,5321,a)]. 42.09/41.97 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(5348,a,5322,a)]. 42.09/41.97 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(5348,a,5323,a)]. 42.09/41.98 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(5348,a,5324,a)]. 42.09/41.98 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(5348,a,5325,a)]. 42.09/41.98 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),zero_zero(rat))). [resolve(5348,a,5327,a)]. 42.09/41.98 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(5348,a,5329,a)]. 42.09/41.98 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(5348,a,5330,a)]. 42.09/41.98 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(5348,a,5332,a)]. 42.09/41.98 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),one_one(rat))). [resolve(5348,a,5333,a)]. 42.09/41.98 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5348,a,5334,a)]. 42.09/41.98 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),one_one(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5348,a,5335,a)]. 42.09/41.98 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),one_one(rat))). [resolve(5348,a,5336,a)]. 42.09/41.98 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(5348,a,5341,a)]. 42.09/41.98 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(5348,a,5343,a)]. 42.09/41.98 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(5348,a,5344,a)]. 42.09/41.98 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(5348,a,5345,a)]. 42.09/41.98 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(5348,a,5347,a)]. 43.41/43.31 5349 comm_semiring_1(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 43.41/43.31 5350 -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_730_dvd__add) # label(axiom). [clausify(34)]. 43.41/43.31 5351 -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_296_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(101)]. 43.41/43.31 5352 -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),f23(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_3992_setprod__dvd__setprod__subset2) # label(axiom). [clausify(134)]. 43.41/43.31 5353 -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,f23(B,A,E,F,D,C))),hAPP(B,A,F,f23(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_3992_setprod__dvd__setprod__subset2) # label(axiom). [clausify(134)]. 43.41/43.31 5354 -comm_semiring_1(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) # label(fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(137)]. 43.41/43.31 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(5349,a,5350,a)]. 43.41/43.31 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(5349,a,5351,a)]. 43.41/43.31 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),f23(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(5349,a,5352,a)]. 43.41/43.31 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,f23(A,code_code_numeral,D,E,C,B))),hAPP(A,code_code_numeral,E,f23(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(5349,a,5353,a)]. 43.47/43.36 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),zero_zero(code_code_numeral)). [resolve(5349,a,5354,a)]. 43.47/43.36 5355 -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_301_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(387)]. 43.47/43.36 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),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(5355,a,5349,a)]. 43.47/43.36 5356 -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_293_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(399)]. 43.47/43.36 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),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(5356,a,5349,a)]. 43.47/43.36 5357 -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_723_dvd__mult__left) # label(axiom). [clausify(401)]. 43.47/43.36 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(5357,a,5349,a)]. 43.47/43.36 5358 -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_365_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(696)]. 43.47/43.36 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(5358,a,5349,a)]. 43.54/43.42 5359 -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_750_le__imp__power__dvd) # label(axiom). [clausify(738)]. 43.54/43.42 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(5359,a,5349,a)]. 43.54/43.42 5360 -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_748_power__le__dvd) # label(axiom). [clausify(767)]. 43.54/43.42 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(5360,a,5349,a)]. 43.54/43.42 5361 -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_749_dvd__power__le) # label(axiom). [clausify(877)]. 43.54/43.42 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(5361,a,5349,a)]. 43.54/43.42 5362 -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_359_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(991)]. 43.54/43.42 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(5362,a,5349,a)]. 43.59/43.50 5363 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),B)) # label(fact_713_dvd__refl) # label(axiom). [clausify(1170)]. 43.59/43.50 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),A)). [resolve(5363,a,5349,a)]. 43.59/43.50 5364 -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_362_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(1298)]. 43.59/43.50 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(5364,a,5349,a)]. 43.59/43.50 5365 comm_semiring_1(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 43.59/43.50 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(5365,a,5350,a)]. 43.59/43.50 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(5365,a,5351,a)]. 43.59/43.50 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),f23(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(5365,a,5352,a)]. 43.59/43.50 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(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(A,quickcheck_code_int,D,f23(A,quickcheck_code_int,D,E,C,B))),hAPP(A,quickcheck_code_int,E,f23(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(5365,a,5353,a)]. 43.59/43.51 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),zero_zero(quickcheck_code_int)). [resolve(5365,a,5354,a)]. 43.59/43.51 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(5365,a,5355,a)]. 43.59/43.51 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(5365,a,5356,a)]. 43.59/43.51 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(5365,a,5357,a)]. 43.59/43.51 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(5365,a,5358,a)]. 43.59/43.51 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(5365,a,5359,a)]. 43.59/43.51 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(5365,a,5360,a)]. 43.68/43.58 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(5365,a,5361,a)]. 43.68/43.58 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(5365,a,5362,a)]. 43.68/43.58 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),A)). [resolve(5365,a,5363,a)]. 43.68/43.58 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(5365,a,5364,a)]. 43.68/43.58 5366 -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_1367_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom). [clausify(1371)]. 43.68/43.58 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(5366,a,5349,a)]. 43.68/43.58 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(5366,a,5365,a)]. 43.68/43.58 5367 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),one_one(A)),B)) # label(fact_731_one__dvd) # label(axiom). [clausify(1429)]. 43.68/43.58 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(5367,a,5349,a)]. 43.68/43.58 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(5367,a,5365,a)]. 43.68/43.58 5368 comm_semiring_1(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 43.68/43.59 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(5368,a,5350,a)]. 43.68/43.59 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(5368,a,5351,a)]. 43.68/43.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f23(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(5368,a,5352,a)]. 43.68/43.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,f23(A,rat,D,E,C,B))),hAPP(A,rat,E,f23(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(5368,a,5353,a)]. 43.68/43.59 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),zero_zero(rat)). [resolve(5368,a,5354,a)]. 43.68/43.59 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(5368,a,5355,a)]. 43.68/43.59 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(5368,a,5356,a)]. 43.68/43.59 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(5368,a,5357,a)]. 43.68/43.59 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(5368,a,5358,a)]. 43.68/43.59 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(5368,a,5359,a)]. 43.68/43.59 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(5368,a,5360,a)]. 43.68/43.59 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(5368,a,5361,a)]. 43.68/43.59 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(5368,a,5362,a)]. 43.79/43.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),A)). [resolve(5368,a,5363,a)]. 43.79/43.67 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(5368,a,5364,a)]. 43.79/43.67 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(5368,a,5366,a)]. 43.79/43.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),one_one(rat)),A)). [resolve(5368,a,5367,a)]. 43.79/43.67 5369 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_391_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(1636)]. 43.79/43.67 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(5369,a,5349,a)]. 43.79/43.67 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(5369,a,5365,a)]. 43.79/43.67 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),one_one(rat)). [resolve(5369,a,5368,a)]. 43.79/43.67 5370 -comm_semiring_1(A) | -no_zero_divisors(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) | zero_zero(A) = hAPP(B,A,D,f273(B,A,D,C)) # label(fact_3977_setprod__zero__iff) # label(axiom). [clausify(1679)]. 43.79/43.67 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(code_code_numeral) != hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) | zero_zero(code_code_numeral) = hAPP(A,code_code_numeral,C,f273(A,code_code_numeral,C,B)). [resolve(5370,a,5349,a)]. 43.79/43.67 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(quickcheck_code_int) != hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) | zero_zero(quickcheck_code_int) = hAPP(A,quickcheck_code_int,C,f273(A,quickcheck_code_int,C,B)). [resolve(5370,a,5365,a)]. 43.79/43.67 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) | zero_zero(rat) = hAPP(A,rat,C,f273(A,rat,C,B)). [resolve(5370,a,5368,a)]. 43.79/43.67 5371 -comm_semiring_1(A) | -no_zero_divisors(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) != hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f273(B,A,D,C)),C)) # label(fact_3977_setprod__zero__iff) # label(axiom). [clausify(1679)]. 43.79/43.67 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(code_code_numeral) != hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,code_code_numeral,C,B)),B)). [resolve(5371,a,5349,a)]. 43.79/43.67 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(quickcheck_code_int) != hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,quickcheck_code_int,C,B)),B)). [resolve(5371,a,5365,a)]. 43.79/43.70 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(rat) != hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,rat,C,B)),B)). [resolve(5371,a,5368,a)]. 43.79/43.70 5372 -comm_semiring_1(A) | -no_zero_divisors(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) | zero_zero(A) != hAPP(B,A,D,E) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) # label(fact_3977_setprod__zero__iff) # label(axiom). [clausify(1679)]. 43.79/43.70 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5372,a,5349,a)]. 43.79/43.70 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5372,a,5365,a)]. 43.79/43.70 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) | zero_zero(rat) != hAPP(A,rat,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5372,a,5368,a)]. 43.79/43.70 5373 -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_473_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(1746)]. 43.79/43.70 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(5373,a,5349,a)]. 43.79/43.70 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(5373,a,5365,a)]. 43.79/43.70 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(5373,a,5368,a)]. 43.88/43.76 5374 -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_466_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(1751)]. 43.88/43.76 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(5374,a,5349,a)]. 43.88/43.76 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(5374,a,5365,a)]. 43.88/43.76 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(5374,a,5368,a)]. 43.88/43.76 5375 -comm_semiring_1(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),zero_zero(nat)) # label(fact_196_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(1845)]. 43.88/43.76 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(5375,a,5349,a)]. 43.88/43.76 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(5375,a,5365,a)]. 43.88/43.76 Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),zero_zero(nat)). [resolve(5375,a,5368,a)]. 43.88/43.76 5376 -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_712_dvd__trans) # label(axiom). [clausify(1900)]. 43.88/43.76 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(5376,a,5349,a)]. 43.88/43.76 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(5376,a,5365,a)]. 43.88/43.76 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(5376,a,5368,a)]. 43.96/43.88 5377 -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_725_mult__dvd__mono) # label(axiom). [clausify(1917)]. 43.96/43.88 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(5377,a,5349,a)]. 43.96/43.88 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(5377,a,5365,a)]. 43.96/43.88 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),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(5377,a,5368,a)]. 43.96/43.88 5378 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_384_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(2164)]. 43.96/43.88 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),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),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(5378,a,5349,a)]. 43.96/43.88 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),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),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(5378,a,5365,a)]. 43.96/43.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(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),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(5378,a,5368,a)]. 44.01/43.93 5379 -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_395_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(2183)]. 44.01/43.93 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(5379,a,5349,a)]. 44.01/43.93 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(5379,a,5365,a)]. 44.01/43.93 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(5379,a,5368,a)]. 44.01/43.93 5380 -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_728_dvd__triv__right) # label(axiom). [clausify(2211)]. 44.01/43.93 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(5380,a,5349,a)]. 44.01/43.93 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(5380,a,5365,a)]. 44.01/43.93 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(5380,a,5368,a)]. 44.01/43.93 5381 comm_semiring_1(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 44.01/43.93 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(5381,a,5350,a)]. 44.01/43.93 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(5381,a,5351,a)]. 44.01/43.94 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),f23(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(5381,a,5352,a)]. 44.01/43.94 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(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,D,f23(A,complex,D,E,C,B))),hAPP(A,complex,E,f23(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(5381,a,5353,a)]. 44.01/43.94 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),zero_zero(complex)). [resolve(5381,a,5354,a)]. 44.01/43.94 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(5381,a,5355,a)]. 44.01/43.94 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(5381,a,5356,a)]. 44.01/43.94 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(5381,a,5357,a)]. 44.01/43.94 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(5381,a,5358,a)]. 44.01/43.94 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(5381,a,5359,a)]. 44.01/43.94 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(5381,a,5360,a)]. 44.01/43.94 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(5381,a,5361,a)]. 44.07/43.95 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(5381,a,5362,a)]. 44.07/43.95 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),A)). [resolve(5381,a,5363,a)]. 44.07/43.95 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(5381,a,5364,a)]. 44.07/43.95 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(5381,a,5366,a)]. 44.07/43.95 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),one_one(complex)),A)). [resolve(5381,a,5367,a)]. 44.07/43.95 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),one_one(complex)). [resolve(5381,a,5369,a)]. 44.07/43.95 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(complex) != hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) | zero_zero(complex) = hAPP(A,complex,C,f273(A,complex,C,B)). [resolve(5381,a,5370,a)]. 44.07/43.95 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(complex) != hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,complex,C,B)),B)). [resolve(5381,a,5371,a)]. 44.07/43.95 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) | zero_zero(complex) != hAPP(A,complex,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5381,a,5372,a)]. 44.07/43.95 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(5381,a,5373,a)]. 44.07/43.95 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(5381,a,5374,a)]. 44.07/43.95 Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),zero_zero(nat)). [resolve(5381,a,5375,a)]. 44.07/43.95 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(5381,a,5376,a)]. 44.07/43.95 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(5381,a,5377,a)]. 44.09/43.99 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(5381,a,5378,a)]. 44.09/43.99 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),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(5381,a,5379,a)]. 44.09/43.99 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(5381,a,5380,a)]. 44.09/43.99 5382 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(2266)]. 44.09/43.99 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(5382,a,5349,a)]. 44.09/43.99 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(5382,a,5365,a)]. 44.09/43.99 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),A). [resolve(5382,a,5368,a)]. 44.09/43.99 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),A). [resolve(5382,a,5381,a)]. 44.09/43.99 5383 -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_1504_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom). [clausify(2309)]. 44.09/43.99 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),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(5383,a,5349,a)]. 44.09/43.99 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(5383,a,5365,a)]. 44.28/44.16 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(5383,a,5368,a)]. 44.28/44.16 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(5383,a,5381,a)]. 44.28/44.16 5384 -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_299_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(2339)]. 44.28/44.16 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),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(5384,a,5349,a)]. 44.28/44.16 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),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(5384,a,5365,a)]. 44.28/44.16 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(5384,a,5368,a)]. 44.28/44.16 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(5384,a,5381,a)]. 44.28/44.16 5385 -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_4642_gauss__sum) # label(axiom). [clausify(2673)]. 44.28/44.16 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(5385,a,5349,a)]. 44.28/44.17 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(5385,a,5365,a)]. 44.28/44.17 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(5385,a,5368,a)]. 44.28/44.17 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(5385,a,5381,a)]. 44.28/44.17 5386 -comm_semiring_1(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) # label(fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(2682)]. 44.28/44.17 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(5386,a,5349,a)]. 44.28/44.17 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(5386,a,5365,a)]. 44.39/44.26 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),zero_zero(rat)),A). [resolve(5386,a,5368,a)]. 44.39/44.26 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),zero_zero(complex)),A). [resolve(5386,a,5381,a)]. 44.39/44.26 5387 -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_1369_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom). [clausify(2691)]. 44.39/44.26 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(5387,a,5349,a)]. 44.39/44.26 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(5387,a,5365,a)]. 44.39/44.26 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(5387,a,5368,a)]. 44.39/44.26 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(5387,a,5381,a)]. 44.39/44.26 5388 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(2743)]. 44.39/44.26 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(5388,a,5349,a)]. 44.39/44.26 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(5388,a,5365,a)]. 44.39/44.26 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),one_one(rat)),A). [resolve(5388,a,5368,a)]. 44.39/44.26 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),one_one(complex)),A). [resolve(5388,a,5381,a)]. 44.39/44.26 5389 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(2757)]. 44.39/44.26 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(5389,a,5349,a)]. 44.39/44.26 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(5389,a,5365,a)]. 44.39/44.26 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),zero_zero(rat)). [resolve(5389,a,5368,a)]. 44.39/44.26 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),zero_zero(complex)). [resolve(5389,a,5381,a)]. 44.39/44.26 5390 -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_358_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(2838)]. 44.56/44.48 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(5390,a,5349,a)]. 44.56/44.48 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(5390,a,5365,a)]. 44.56/44.48 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(5390,a,5368,a)]. 44.56/44.48 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(5390,a,5381,a)]. 44.56/44.48 5391 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_462_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(2897)]. 44.56/44.48 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))),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),A). [resolve(5391,a,5349,a)]. 44.56/44.48 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))),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),A). [resolve(5391,a,5365,a)]. 44.56/44.48 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))),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A). [resolve(5391,a,5368,a)]. 44.56/44.48 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))),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A). [resolve(5391,a,5381,a)]. 44.56/44.48 5392 -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_722_dvd__mult__right) # label(axiom). [clausify(3035)]. 44.56/44.48 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(5392,a,5349,a)]. 44.56/44.48 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(5392,a,5365,a)]. 44.73/44.60 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(5392,a,5368,a)]. 44.73/44.60 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(5392,a,5381,a)]. 44.73/44.60 5393 -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_732_dvd__power__same) # label(axiom). [clausify(3173)]. 44.73/44.60 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(5393,a,5349,a)]. 44.73/44.60 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(5393,a,5365,a)]. 44.73/44.60 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(5393,a,5368,a)]. 44.73/44.60 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(5393,a,5381,a)]. 44.73/44.60 5394 -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_298_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(3179)]. 44.73/44.60 5395 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_464_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(3196)]. 44.73/44.60 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),A),one_one(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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B). [resolve(5395,a,5349,a)]. 44.73/44.60 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),A),one_one(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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B). [resolve(5395,a,5365,a)]. 44.78/44.71 Derived: 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) = 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). [resolve(5395,a,5368,a)]. 44.78/44.71 Derived: 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) = 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). [resolve(5395,a,5381,a)]. 44.78/44.71 5396 -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_729_dvd__triv__left) # label(axiom). [clausify(3240)]. 44.78/44.71 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(5396,a,5349,a)]. 44.78/44.71 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(5396,a,5365,a)]. 44.78/44.71 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(5396,a,5368,a)]. 44.78/44.71 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(5396,a,5381,a)]. 44.78/44.71 5397 -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_548_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(3274)]. 44.78/44.71 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(5397,a,5349,a)]. 44.78/44.71 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(5397,a,5365,a)]. 44.78/44.71 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(5397,a,5368,a)]. 44.78/44.71 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(5397,a,5381,a)]. 44.78/44.71 5398 -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_364_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(3356)]. 44.99/44.93 5399 -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_785_dvd__power) # label(axiom). [clausify(3357)]. 44.99/44.93 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(5399,a,5349,a)]. 44.99/44.93 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(5399,a,5365,a)]. 44.99/44.93 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(5399,a,5368,a)]. 44.99/44.93 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(5399,a,5381,a)]. 44.99/44.93 5400 -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_785_dvd__power) # label(axiom). [clausify(3357)]. 44.99/44.93 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(5400,a,5349,a)]. 44.99/44.93 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(5400,a,5365,a)]. 44.99/44.93 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(5400,a,5368,a)]. 44.99/44.93 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(5400,a,5381,a)]. 44.99/44.93 5401 -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_300_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(3492)]. 44.99/44.93 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(5401,a,5349,a)]. 44.99/44.93 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(5401,a,5365,a)]. 45.07/44.98 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(5401,a,5368,a)]. 45.07/44.98 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(5401,a,5381,a)]. 45.07/44.98 5402 -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_3980_dvd__setprod) # label(axiom). [clausify(3511)]. 45.07/44.98 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(5402,a,5349,a)]. 45.07/44.98 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(5402,a,5365,a)]. 45.07/44.98 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(5402,a,5368,a)]. 45.07/44.98 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(5402,a,5381,a)]. 45.07/44.98 5403 -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_726_dvd__mult) # label(axiom). [clausify(3548)]. 45.07/44.98 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(5403,a,5349,a)]. 45.07/44.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),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(5403,a,5365,a)]. 45.07/44.98 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(5403,a,5368,a)]. 45.29/45.23 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(5403,a,5381,a)]. 45.29/45.23 5404 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_463_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(3629)]. 45.29/45.23 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),A),one_one(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),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),B)). [resolve(5404,a,5349,a)]. 45.29/45.23 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),A),one_one(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),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),B)). [resolve(5404,a,5365,a)]. 45.29/45.23 Derived: 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) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(5404,a,5368,a)]. 45.29/45.23 Derived: 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) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(5404,a,5381,a)]. 45.29/45.23 5405 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),zero_zero(A)),B)) | zero_zero(A) = ti(A,B) # label(fact_721_dvd__0__left) # label(axiom). [clausify(3632)]. 45.29/45.23 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)) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(5405,a,5349,a)]. 45.29/45.23 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)) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(5405,a,5365,a)]. 45.29/45.23 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),zero_zero(rat)),A)) | zero_zero(rat) = ti(rat,A). [resolve(5405,a,5368,a)]. 45.29/45.23 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),zero_zero(complex)),A)) | zero_zero(complex) = ti(complex,A). [resolve(5405,a,5381,a)]. 45.29/45.23 5406 -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_1368_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom). [clausify(3649)]. 45.29/45.23 5407 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(3862)]. 45.66/45.55 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(5407,a,5349,a)]. 45.66/45.55 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(5407,a,5365,a)]. 45.66/45.55 Derived: ti(rat,A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),one_one(nat)). [resolve(5407,a,5368,a)]. 45.66/45.55 Derived: ti(complex,A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),one_one(nat)). [resolve(5407,a,5381,a)]. 45.66/45.55 5408 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 45.66/45.55 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(5408,a,5350,a)]. 45.66/45.55 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(5408,a,5351,a)]. 45.66/45.55 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),f23(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(5408,a,5352,a)]. 45.66/45.55 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,f23(A,nat,D,E,C,B))),hAPP(A,nat,E,f23(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(5408,a,5353,a)]. 45.66/45.55 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)). [resolve(5408,a,5354,a)]. 45.66/45.55 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(5408,a,5355,a)]. 45.66/45.55 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(5408,a,5356,a)]. 45.66/45.55 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(5408,a,5357,a)]. 45.66/45.55 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(5408,a,5358,a)]. 45.66/45.55 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),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(5408,a,5359,a)]. 45.66/45.55 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(5408,a,5360,a)]. 45.66/45.55 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(5408,a,5361,a)]. 45.66/45.55 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(5408,a,5362,a)]. 45.66/45.55 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),A)). [resolve(5408,a,5363,a)]. 45.66/45.55 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(5408,a,5364,a)]. 45.66/45.55 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(5408,a,5366,a)]. 45.66/45.55 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A)). [resolve(5408,a,5367,a)]. 45.66/45.55 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)). [resolve(5408,a,5369,a)]. 45.66/45.55 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(nat) != hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) | zero_zero(nat) = hAPP(A,nat,C,f273(A,nat,C,B)). [resolve(5408,a,5370,a)]. 45.66/45.55 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(nat) != hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,nat,C,B)),B)). [resolve(5408,a,5371,a)]. 45.66/45.55 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) | zero_zero(nat) != hAPP(A,nat,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5408,a,5372,a)]. 45.66/45.55 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(5408,a,5373,a)]. 45.66/45.55 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(5408,a,5374,a)]. 45.66/45.55 Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),zero_zero(nat)). [resolve(5408,a,5375,a)]. 45.66/45.55 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(5408,a,5376,a)]. 45.66/45.55 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(5408,a,5377,a)]. 45.66/45.55 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(5408,a,5378,a)]. 45.66/45.56 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(5408,a,5379,a)]. 45.66/45.56 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(5408,a,5380,a)]. 45.66/45.56 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A). [resolve(5408,a,5382,a)]. 45.66/45.56 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(5408,a,5383,a)]. 45.66/45.56 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(5408,a,5384,a)]. 45.66/45.56 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(5408,a,5385,a)]. 45.66/45.56 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A). [resolve(5408,a,5386,a)]. 45.66/45.56 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(5408,a,5387,a)]. 45.66/45.56 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A). [resolve(5408,a,5388,a)]. 45.66/45.56 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)). [resolve(5408,a,5389,a)]. 45.66/45.56 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(5408,a,5390,a)]. 45.66/45.56 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(5408,a,5391,a)]. 45.66/45.56 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(5408,a,5392,a)]. 45.66/45.56 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(5408,a,5393,a)]. 45.66/45.56 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(5408,a,5395,a)]. 45.66/45.56 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(5408,a,5396,a)]. 45.79/45.65 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(5408,a,5397,a)]. 45.79/45.65 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(5408,a,5399,a)]. 45.79/45.65 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(5408,a,5400,a)]. 45.79/45.65 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(5408,a,5402,a)]. 45.79/45.65 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(5408,a,5403,a)]. 45.79/45.65 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(5408,a,5404,a)]. 45.79/45.65 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A)) | zero_zero(nat) = ti(nat,A). [resolve(5408,a,5405,a)]. 45.79/45.65 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)). [resolve(5408,a,5407,a)]. 45.79/45.65 5409 -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_607_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(4309)]. 45.79/45.65 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(5409,a,5349,a)]. 45.79/45.65 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(5409,a,5365,a)]. 45.79/45.65 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(5409,a,5368,a)]. 45.79/45.65 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(5409,a,5381,a)]. 45.79/45.65 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(5409,a,5408,a)]. 45.79/45.65 5410 -comm_semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f762(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_4798_dvd__setsum) # label(axiom). [clausify(4350)]. 45.79/45.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5410,a,5349,a)]. 45.79/45.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5410,a,5365,a)]. 45.79/45.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5410,a,5368,a)]. 45.79/45.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5410,a,5381,a)]. 45.79/45.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5410,a,5408,a)]. 45.79/45.66 5411 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(C,A,D,f762(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_4798_dvd__setsum) # label(axiom). [clausify(4350)]. 45.79/45.66 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,f762(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(5411,a,5349,a)]. 45.79/45.66 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,f762(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(5411,a,5365,a)]. 45.79/45.66 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(B,rat,C,f762(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(5411,a,5368,a)]. 45.79/45.66 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(B,complex,C,f762(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(5411,a,5381,a)]. 45.79/45.66 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(B,nat,C,f762(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(5411,a,5408,a)]. 45.79/45.66 5412 -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_727_dvd__mult2) # label(axiom). [clausify(4352)]. 45.81/45.67 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(5412,a,5349,a)]. 45.81/45.67 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(5412,a,5365,a)]. 45.81/45.67 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(5412,a,5368,a)]. 45.81/45.67 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(5412,a,5381,a)]. 45.81/45.67 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(5412,a,5408,a)]. 45.81/45.67 5413 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 45.81/45.67 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(5413,a,5350,a)]. 45.81/45.67 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(5413,a,5351,a)]. 45.81/45.67 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),f23(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(5413,a,5352,a)]. 45.81/45.67 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,f23(A,real,D,E,C,B))),hAPP(A,real,E,f23(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(5413,a,5353,a)]. 45.81/45.67 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)). [resolve(5413,a,5354,a)]. 45.81/45.67 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(5413,a,5355,a)]. 45.81/45.67 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(5413,a,5356,a)]. 45.81/45.68 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(5413,a,5357,a)]. 45.81/45.68 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(5413,a,5358,a)]. 45.81/45.68 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(5413,a,5359,a)]. 45.81/45.68 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(5413,a,5360,a)]. 45.81/45.68 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(5413,a,5361,a)]. 45.81/45.68 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(5413,a,5362,a)]. 45.81/45.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),A)). [resolve(5413,a,5363,a)]. 45.81/45.68 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(5413,a,5364,a)]. 45.81/45.68 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(5413,a,5366,a)]. 45.81/45.68 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),one_one(real)),A)). [resolve(5413,a,5367,a)]. 45.81/45.68 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)). [resolve(5413,a,5369,a)]. 45.81/45.68 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) | zero_zero(real) = hAPP(A,real,C,f273(A,real,C,B)). [resolve(5413,a,5370,a)]. 45.81/45.68 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(real) != hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,real,C,B)),B)). [resolve(5413,a,5371,a)]. 45.81/45.68 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) | zero_zero(real) != hAPP(A,real,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5413,a,5372,a)]. 45.81/45.68 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(5413,a,5373,a)]. 45.81/45.69 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(5413,a,5374,a)]. 45.81/45.69 Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),zero_zero(nat)). [resolve(5413,a,5375,a)]. 45.81/45.69 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(5413,a,5376,a)]. 45.81/45.69 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(5413,a,5377,a)]. 45.81/45.69 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(5413,a,5379,a)]. 45.81/45.69 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(5413,a,5380,a)]. 45.81/45.69 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A). [resolve(5413,a,5382,a)]. 45.81/45.69 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(5413,a,5383,a)]. 45.81/45.69 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(5413,a,5384,a)]. 45.81/45.69 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(5413,a,5385,a)]. 45.81/45.69 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A). [resolve(5413,a,5386,a)]. 45.81/45.69 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(5413,a,5387,a)]. 45.81/45.69 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A). [resolve(5413,a,5388,a)]. 45.81/45.69 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)). [resolve(5413,a,5389,a)]. 45.81/45.69 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(5413,a,5390,a)]. 45.81/45.69 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))),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(5413,a,5391,a)]. 45.81/45.69 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(5413,a,5392,a)]. 45.81/45.69 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(5413,a,5393,a)]. 45.81/45.69 Derived: 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) = 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). [resolve(5413,a,5395,a)]. 45.81/45.69 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(5413,a,5396,a)]. 45.81/45.69 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(5413,a,5397,a)]. 45.81/45.69 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(5413,a,5399,a)]. 45.81/45.69 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(5413,a,5400,a)]. 45.81/45.69 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(5413,a,5401,a)]. 45.81/45.69 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(5413,a,5402,a)]. 45.81/45.69 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(5413,a,5403,a)]. 45.81/45.69 Derived: 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) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(5413,a,5404,a)]. 45.81/45.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),zero_zero(real)),A)) | zero_zero(real) = ti(real,A). [resolve(5413,a,5405,a)]. 45.81/45.69 Derived: ti(real,A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),one_one(nat)). [resolve(5413,a,5407,a)]. 45.81/45.69 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(5413,a,5409,a)]. 45.81/45.69 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5413,a,5410,a)]. 45.81/45.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(B,real,C,f762(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(5413,a,5411,a)]. 45.89/45.76 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(5413,a,5412,a)]. 45.89/45.76 5414 -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)) | zero_zero(A) != hAPP(B,A,E,D) | zero_zero(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_3976_setprod__zero) # label(axiom). [clausify(4381)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(code_code_numeral) != hAPP(A,code_code_numeral,D,C) | zero_zero(code_code_numeral) = hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),D),B). [resolve(5414,a,5349,a)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,C) | zero_zero(quickcheck_code_int) = hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),D),B). [resolve(5414,a,5365,a)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(rat) != hAPP(A,rat,D,C) | zero_zero(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),D),B). [resolve(5414,a,5368,a)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(complex) != hAPP(A,complex,D,C) | zero_zero(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),D),B). [resolve(5414,a,5381,a)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(nat) != hAPP(A,nat,D,C) | zero_zero(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B). [resolve(5414,a,5408,a)]. 45.89/45.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | zero_zero(real) != hAPP(A,real,D,C) | zero_zero(real) = hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),D),B). [resolve(5414,a,5413,a)]. 45.89/45.76 5415 -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_4351_arith__series__general) # label(axiom). [clausify(4433)]. 45.89/45.76 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(5415,a,5349,a)]. 45.89/45.76 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(5415,a,5365,a)]. 45.89/45.77 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(5415,a,5368,a)]. 45.89/45.77 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(5415,a,5381,a)]. 45.89/45.77 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(5415,a,5408,a)]. 45.89/45.77 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(5415,a,5413,a)]. 45.89/45.79 5416 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_385_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(4441)]. 45.89/45.79 5417 -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_366_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(4466)]. 45.89/45.79 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),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(5417,a,5349,a)]. 45.89/45.79 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(5417,a,5365,a)]. 45.89/45.79 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),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(5417,a,5368,a)]. 45.89/45.79 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(5417,a,5381,a)]. 45.89/45.82 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(5417,a,5408,a)]. 45.89/45.82 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(5417,a,5413,a)]. 45.89/45.82 5418 -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_363_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(4485)]. 45.89/45.82 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(5418,a,5349,a)]. 45.89/45.82 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(5418,a,5365,a)]. 45.89/45.82 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(5418,a,5368,a)]. 45.89/45.82 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(5418,a,5381,a)]. 45.89/45.82 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(5418,a,5408,a)]. 45.89/45.82 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(5418,a,5413,a)]. 45.89/45.82 5419 -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_360_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(4490)]. 46.12/46.00 5420 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_382_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(4501)]. 46.12/46.00 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),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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(5420,a,5349,a)]. 46.12/46.00 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),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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(5420,a,5365,a)]. 46.12/46.00 Derived: 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)) = 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)). [resolve(5420,a,5368,a)]. 46.12/46.00 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)). [resolve(5420,a,5381,a)]. 46.12/46.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(5420,a,5413,a)]. 46.12/46.00 5421 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))) # label(fact_706_dvd__0__right) # label(axiom). [clausify(4701)]. 46.12/46.00 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(5421,a,5349,a)]. 46.12/46.00 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(5421,a,5365,a)]. 46.12/46.00 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),zero_zero(rat))). [resolve(5421,a,5368,a)]. 46.12/46.00 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),zero_zero(complex))). [resolve(5421,a,5381,a)]. 46.12/46.00 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),zero_zero(nat))). [resolve(5421,a,5408,a)]. 46.29/46.14 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),zero_zero(real))). [resolve(5421,a,5413,a)]. 46.29/46.14 5422 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 46.29/46.14 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(5422,a,5350,a)]. 46.29/46.14 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(5422,a,5351,a)]. 46.29/46.14 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),f23(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(5422,a,5352,a)]. 46.29/46.14 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,f23(A,int,D,E,C,B))),hAPP(A,int,E,f23(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(5422,a,5353,a)]. 46.29/46.14 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)). [resolve(5422,a,5354,a)]. 46.29/46.14 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(5422,a,5355,a)]. 46.29/46.14 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(5422,a,5356,a)]. 46.29/46.14 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(5422,a,5357,a)]. 46.29/46.14 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(5422,a,5358,a)]. 46.29/46.14 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(5422,a,5359,a)]. 46.29/46.14 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(5422,a,5360,a)]. 46.29/46.14 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(5422,a,5361,a)]. 46.29/46.14 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(5422,a,5362,a)]. 46.29/46.14 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),A)). [resolve(5422,a,5363,a)]. 46.29/46.14 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(5422,a,5364,a)]. 46.29/46.14 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(5422,a,5366,a)]. 46.29/46.14 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),one_one(int)),A)). [resolve(5422,a,5367,a)]. 46.29/46.14 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)). [resolve(5422,a,5369,a)]. 46.29/46.14 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) | zero_zero(int) = hAPP(A,int,C,f273(A,int,C,B)). [resolve(5422,a,5370,a)]. 46.29/46.14 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(int) != hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f273(A,int,C,B)),B)). [resolve(5422,a,5371,a)]. 46.29/46.14 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) | zero_zero(int) != hAPP(A,int,C,D) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)). [resolve(5422,a,5372,a)]. 46.29/46.14 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(5422,a,5373,a)]. 46.29/46.14 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(5422,a,5374,a)]. 46.29/46.14 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),zero_zero(nat)). [resolve(5422,a,5375,a)]. 46.29/46.14 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(5422,a,5376,a)]. 46.29/46.14 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(5422,a,5377,a)]. 46.29/46.14 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(5422,a,5378,a)]. 46.29/46.14 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(5422,a,5379,a)]. 46.29/46.15 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(5422,a,5380,a)]. 46.29/46.15 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A). [resolve(5422,a,5382,a)]. 46.29/46.15 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(5422,a,5383,a)]. 46.29/46.15 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(5422,a,5384,a)]. 46.29/46.15 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(5422,a,5385,a)]. 46.29/46.15 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A). [resolve(5422,a,5386,a)]. 46.29/46.15 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(5422,a,5387,a)]. 46.29/46.15 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A). [resolve(5422,a,5388,a)]. 46.29/46.15 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)). [resolve(5422,a,5389,a)]. 46.29/46.15 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(5422,a,5390,a)]. 46.29/46.15 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(5422,a,5391,a)]. 46.29/46.15 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(5422,a,5392,a)]. 46.29/46.15 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(5422,a,5393,a)]. 46.29/46.15 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B). [resolve(5422,a,5395,a)]. 46.29/46.15 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(5422,a,5396,a)]. 46.29/46.15 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(5422,a,5397,a)]. 46.29/46.15 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(5422,a,5399,a)]. 46.29/46.15 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(5422,a,5400,a)]. 46.29/46.15 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(5422,a,5401,a)]. 46.29/46.15 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)) | 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(5422,a,5402,a)]. 46.29/46.15 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(5422,a,5403,a)]. 46.29/46.15 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(5422,a,5404,a)]. 46.29/46.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),zero_zero(int)),A)) | zero_zero(int) = ti(int,A). [resolve(5422,a,5405,a)]. 46.29/46.15 Derived: ti(int,A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)). [resolve(5422,a,5407,a)]. 46.29/46.15 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(5422,a,5409,a)]. 46.29/46.15 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f762(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(5422,a,5410,a)]. 46.29/46.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(B,int,C,f762(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(5422,a,5411,a)]. 46.29/46.15 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(5422,a,5412,a)]. 46.29/46.15 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)) | zero_zero(int) != hAPP(A,int,D,C) | zero_zero(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B). [resolve(5422,a,5414,a)]. 46.29/46.15 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(5422,a,5415,a)]. 46.29/46.15 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(5422,a,5417,a)]. 47.75/47.64 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(5422,a,5418,a)]. 47.75/47.64 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(5422,a,5420,a)]. 47.75/47.64 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),zero_zero(int))). [resolve(5422,a,5421,a)]. 47.75/47.64 5423 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.75/47.64 5424 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom). [assumption]. 47.75/47.64 5425 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.75/47.64 5426 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.75/47.64 5427 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.75/47.64 5428 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.75/47.64 5429 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.82/47.69 5430 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.82/47.69 5431 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.82/47.69 5432 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),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),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.82/47.69 5433 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),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),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1801_divide__le__eq__number__of1) # label(axiom). [clausify(59)]. 47.82/47.69 5434 -number(A) | -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_460_right__distrib__number__of) # label(axiom). [clausify(227)]. 47.82/47.69 5435 number(complex) # label(arity_Complex_Ocomplex___Int_Onumber) # label(axiom). [assumption]. 47.82/47.69 5436 number(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Int_Onumber) # label(axiom). [assumption]. 47.82/47.69 5437 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.82/47.69 5438 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5439 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5440 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5441 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5442 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5443 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5444 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5445 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),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),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.85/47.70 5446 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),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),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1794_divide__less__eq__number__of) # label(axiom). [clausify(645)]. 47.99/47.86 5447 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom). [assumption]. 47.99/47.86 5448 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_756_right__diff__distrib__number__of) # label(axiom). [clausify(1381)]. 47.99/47.86 Derived: -ring(complex) | 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),minus_minus(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(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),A)),C)). [resolve(5448,a,5435,a)]. 47.99/47.86 Derived: -ring(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)),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)) = 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)). [resolve(5448,a,5436,a)]. 47.99/47.86 5449 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.86 5450 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.86 5451 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5452 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5453 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),D))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5454 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5455 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5456 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5457 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),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),D))) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 47.99/47.88 5458 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) # label(fact_1804_le__divide__eq__number__of1) # label(axiom). [clausify(1431)]. 48.05/47.95 5459 -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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5460 -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),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),B),zero_zero(A))) | 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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5461 -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),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)),zero_zero(A))) | 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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5462 -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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5463 -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),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(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5464 -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),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5465 -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),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)),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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.05/47.95 5466 -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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.15/48.01 5467 -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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.15/48.01 5468 -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_1803_le__divide__eq__number__of) # label(axiom). [clausify(1575)]. 48.15/48.01 5469 -field_inverse_zero(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | zero_zero(A) = ti(A,C) | 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_1778_divide__eq__eq__number__of) # label(axiom). [clausify(1748)]. 48.15/48.01 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) | zero_zero(nat) = ti(nat,B) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B). [resolve(5469,b,5424,a)]. 48.15/48.01 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) | zero_zero(complex) = ti(complex,B) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B). [resolve(5469,b,5435,a)]. 48.15/48.01 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) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | 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(5469,b,5436,a)]. 48.15/48.01 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) | zero_zero(int) = ti(int,B) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B). [resolve(5469,b,5447,a)]. 48.15/48.01 5470 -field_inverse_zero(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) != hAPP(int,A,number_number_of(A),D) | zero_zero(A) != ti(A,C) | zero_zero(A) = hAPP(int,A,number_number_of(A),D) # label(fact_1778_divide__eq__eq__number__of) # label(axiom). [clausify(1748)]. 48.15/48.01 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) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C). [resolve(5470,b,5424,a)]. 48.15/48.01 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) | zero_zero(complex) != ti(complex,B) | zero_zero(complex) = hAPP(int,complex,number_number_of(complex),C). [resolve(5470,b,5435,a)]. 48.15/48.02 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) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,B) | zero_zero(quickcheck_code_int) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C). [resolve(5470,b,5436,a)]. 48.15/48.02 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) | zero_zero(int) != ti(int,B) | zero_zero(int) = hAPP(int,int,number_number_of(int),C). [resolve(5470,b,5447,a)]. 48.15/48.02 5471 -field_inverse_zero(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | zero_zero(A) != ti(A,C) | zero_zero(A) != hAPP(int,A,number_number_of(A),D) # label(fact_1778_divide__eq__eq__number__of) # label(axiom). [clausify(1748)]. 48.15/48.02 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) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),C). [resolve(5471,b,5424,a)]. 48.15/48.02 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) | zero_zero(complex) != ti(complex,B) | zero_zero(complex) != hAPP(int,complex,number_number_of(complex),C). [resolve(5471,b,5435,a)]. 48.15/48.02 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) | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,B) | zero_zero(quickcheck_code_int) != hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C). [resolve(5471,b,5436,a)]. 48.15/48.02 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) | zero_zero(int) != ti(int,B) | zero_zero(int) != hAPP(int,int,number_number_of(int),C). [resolve(5471,b,5447,a)]. 48.15/48.02 5472 -field_inverse_zero(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) | zero_zero(A) = ti(A,C) # label(fact_1778_divide__eq__eq__number__of) # label(axiom). [clausify(1748)]. 48.15/48.02 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,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B) | zero_zero(nat) = ti(nat,B). [resolve(5472,b,5424,a)]. 48.15/48.02 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,A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B) | zero_zero(complex) = ti(complex,B). [resolve(5472,b,5435,a)]. 48.15/48.02 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,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) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B). [resolve(5472,b,5436,a)]. 48.20/48.06 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,A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B) | zero_zero(int) = ti(int,B). [resolve(5472,b,5447,a)]. 48.20/48.06 5473 -field_inverse_zero(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(int,A,number_number_of(A),D) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C) | zero_zero(A) != hAPP(int,A,number_number_of(A),D) # label(fact_1778_divide__eq__eq__number__of) # label(axiom). [clausify(1748)]. 48.20/48.06 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,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),C)),B) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),C). [resolve(5473,b,5424,a)]. 48.20/48.06 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,A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),C)),B) | zero_zero(complex) != hAPP(int,complex,number_number_of(complex),C). [resolve(5473,b,5435,a)]. 48.20/48.06 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,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) | zero_zero(quickcheck_code_int) != hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C). [resolve(5473,b,5436,a)]. 48.20/48.06 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,A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),C)),B) | zero_zero(int) != hAPP(int,int,number_number_of(int),C). [resolve(5473,b,5447,a)]. 48.20/48.06 5474 -field_inverse_zero(A) | -number(A) | zero_zero(A) = hAPP(int,A,number_number_of(A),B) | 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_1776_eq__divide__eq__number__of1) # label(axiom). [clausify(1879)]. 48.20/48.06 Derived: -field_inverse_zero(nat) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | 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(5474,b,5424,a)]. 48.20/48.06 Derived: -field_inverse_zero(complex) | zero_zero(complex) = hAPP(int,complex,number_number_of(complex),A) | 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(5474,b,5435,a)]. 48.20/48.06 Derived: -field_inverse_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),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),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(5474,b,5436,a)]. 48.20/48.07 Derived: -field_inverse_zero(int) | zero_zero(int) = hAPP(int,int,number_number_of(int),A) | 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(5474,b,5447,a)]. 48.20/48.07 5475 -field_inverse_zero(A) | -number(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != hAPP(int,A,number_number_of(A),C) | 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_1776_eq__divide__eq__number__of1) # label(axiom). [clausify(1879)]. 48.20/48.07 Derived: -field_inverse_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),B)). [resolve(5475,b,5424,a)]. 48.20/48.07 Derived: -field_inverse_zero(complex) | zero_zero(complex) != ti(complex,A) | zero_zero(complex) != hAPP(int,complex,number_number_of(complex),B) | ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),B)). [resolve(5475,b,5435,a)]. 48.20/48.07 Derived: -field_inverse_zero(quickcheck_code_int) | zero_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) | 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(5475,b,5436,a)]. 48.20/48.07 Derived: -field_inverse_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != hAPP(int,int,number_number_of(int),B) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),B)). [resolve(5475,b,5447,a)]. 48.20/48.07 5476 -field_inverse_zero(A) | -number(A) | zero_zero(A) != ti(A,B) | 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_1776_eq__divide__eq__number__of1) # label(axiom). [clausify(1879)]. 48.20/48.07 5477 -field_inverse_zero(A) | -number(A) | zero_zero(A) != hAPP(int,A,number_number_of(A),B) | zero_zero(A) = ti(A,C) | 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_1776_eq__divide__eq__number__of1) # label(axiom). [clausify(1879)]. 48.20/48.07 Derived: -field_inverse_zero(nat) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),A) | zero_zero(nat) = ti(nat,B) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),inverse_divide(nat),C),hAPP(int,nat,number_number_of(nat),A)). [resolve(5477,b,5424,a)]. 48.20/48.07 Derived: -field_inverse_zero(complex) | zero_zero(complex) != hAPP(int,complex,number_number_of(complex),A) | zero_zero(complex) = ti(complex,B) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)). [resolve(5477,b,5435,a)]. 48.20/48.07 Derived: -field_inverse_zero(quickcheck_code_int) | zero_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) | 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(5477,b,5436,a)]. 48.20/48.07 Derived: -field_inverse_zero(int) | zero_zero(int) != hAPP(int,int,number_number_of(int),A) | zero_zero(int) = ti(int,B) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),inverse_divide(int),C),hAPP(int,int,number_number_of(int),A)). [resolve(5477,b,5447,a)]. 48.30/48.21 5478 -field_inverse_zero(A) | -number(A) | zero_zero(A) = hAPP(int,A,number_number_of(A),B) | 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_1776_eq__divide__eq__number__of1) # label(axiom). [clausify(1879)]. 48.30/48.21 Derived: -field_inverse_zero(nat) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | 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(5478,b,5424,a)]. 48.30/48.21 Derived: -field_inverse_zero(complex) | zero_zero(complex) = hAPP(int,complex,number_number_of(complex),A) | 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(5478,b,5435,a)]. 48.30/48.21 Derived: -field_inverse_zero(quickcheck_code_int) | zero_zero(quickcheck_code_int) = hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),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),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(5478,b,5436,a)]. 48.30/48.21 Derived: -field_inverse_zero(int) | zero_zero(int) = hAPP(int,int,number_number_of(int),A) | 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(5478,b,5447,a)]. 48.30/48.21 5479 number(real) # label(arity_RealDef_Oreal___Int_Onumber) # label(axiom). [assumption]. 48.30/48.21 Derived: -linord1117847801e_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)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))). [resolve(5479,a,5439,b)]. 48.30/48.21 Derived: -linord1117847801e_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)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))). [resolve(5479,a,5440,b)]. 48.30/48.21 Derived: -linord1117847801e_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)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))). [resolve(5479,a,5442,b)]. 48.30/48.21 Derived: -linord1117847801e_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)),hAPP(int,real,number_number_of(real),C))) | -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),C)),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))). [resolve(5479,a,5444,b)]. 48.37/48.24 Derived: -ring(real) | 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),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(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),A)),C)). [resolve(5479,a,5448,a)]. 48.37/48.24 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) | zero_zero(real) = ti(real,B) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B). [resolve(5479,a,5469,b)]. 48.37/48.24 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) | zero_zero(real) != ti(real,B) | zero_zero(real) = hAPP(int,real,number_number_of(real),C). [resolve(5479,a,5470,b)]. 48.37/48.24 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) | zero_zero(real) != ti(real,B) | zero_zero(real) != hAPP(int,real,number_number_of(real),C). [resolve(5479,a,5471,b)]. 48.37/48.24 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,A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B) | zero_zero(real) = ti(real,B). [resolve(5479,a,5472,b)]. 48.37/48.24 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,A) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B) | zero_zero(real) != hAPP(int,real,number_number_of(real),C). [resolve(5479,a,5473,b)]. 48.37/48.24 Derived: -field_inverse_zero(real) | zero_zero(real) = hAPP(int,real,number_number_of(real),A) | 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(5479,a,5474,b)]. 48.37/48.24 Derived: -field_inverse_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != hAPP(int,real,number_number_of(real),B) | ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),B)). [resolve(5479,a,5475,b)]. 48.37/48.24 Derived: -field_inverse_zero(real) | zero_zero(real) != hAPP(int,real,number_number_of(real),A) | zero_zero(real) = ti(real,B) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)). [resolve(5479,a,5477,b)]. 48.37/48.24 Derived: -field_inverse_zero(real) | zero_zero(real) = hAPP(int,real,number_number_of(real),A) | 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(5479,a,5478,b)]. 48.37/48.24 5480 -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),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_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5481 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_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_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5482 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(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),hAPP(int,A,number_number_of(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),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5483 -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(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),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5484 -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(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5485 -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),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5486 -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),zero_zero(A)),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),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(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.37/48.25 5487 -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(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_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.41/48.27 5488 -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),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_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.41/48.27 5489 -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),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_1802_divide__le__eq__number__of) # label(axiom). [clausify(2197)]. 48.41/48.27 5490 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.27 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(5490,b,5424,a)]. 48.41/48.27 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(5490,b,5435,a)]. 48.41/48.27 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(5490,b,5436,a)]. 48.41/48.27 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),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(5490,b,5447,a)]. 48.41/48.27 5491 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.27 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(5491,b,5424,a)]. 48.41/48.27 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(5491,b,5435,a)]. 48.41/48.27 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(5491,b,5436,a)]. 48.41/48.27 Derived: -linord1117847801e_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),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(5491,b,5447,a)]. 48.41/48.27 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(5491,b,5479,a)]. 48.41/48.27 5492 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.27 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(5492,b,5435,a)]. 48.41/48.28 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),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(5492,b,5436,a)]. 48.41/48.28 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(5492,b,5447,a)]. 48.41/48.28 5493 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.28 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(5493,b,5435,a)]. 48.41/48.28 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),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(5493,b,5436,a)]. 48.41/48.29 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(5493,b,5447,a)]. 48.41/48.29 5494 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.29 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(5494,b,5435,a)]. 48.41/48.29 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),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(5494,b,5436,a)]. 48.41/48.29 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(5494,b,5447,a)]. 48.41/48.29 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(5494,b,5479,a)]. 48.41/48.30 5495 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.30 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(5495,b,5435,a)]. 48.41/48.30 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(5495,b,5436,a)]. 48.41/48.30 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,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(5495,b,5447,a)]. 48.41/48.30 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(5495,b,5479,a)]. 48.41/48.30 5496 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.31 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(5496,b,5424,a)]. 48.41/48.31 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(5496,b,5435,a)]. 48.41/48.31 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(5496,b,5436,a)]. 48.41/48.31 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(5496,b,5447,a)]. 48.41/48.31 5497 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.31 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(5497,b,5435,a)]. 48.41/48.31 5498 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.41/48.31 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(5498,b,5435,a)]. 48.41/48.31 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(5498,b,5436,a)]. 48.41/48.31 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(5498,b,5447,a)]. 48.41/48.31 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(5498,b,5479,a)]. 48.41/48.31 5499 -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)),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_1793_less__divide__eq__number__of) # label(axiom). [clausify(2205)]. 48.54/48.43 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(5499,b,5435,a)]. 48.54/48.43 5500 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_757_left__diff__distrib__number__of) # label(axiom). [clausify(2409)]. 48.54/48.43 Derived: -ring(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),hAPP(int,complex,number_number_of(complex),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),C))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),C))). [resolve(5500,a,5435,a)]. 48.54/48.43 Derived: -ring(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),minus_minus(quickcheck_code_int),A),B)),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),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),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),C))). [resolve(5500,a,5436,a)]. 48.54/48.43 Derived: -ring(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),C))). [resolve(5500,a,5447,a)]. 48.54/48.43 Derived: -ring(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(int,real,number_number_of(real),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))). [resolve(5500,a,5479,a)]. 48.54/48.43 5501 -monoid_mult(A) | -number(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_551_power2__eq__square__number__of) # label(axiom). [clausify(2489)]. 48.71/48.64 5502 -semiring(A) | -number(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_461_left__distrib__number__of) # label(axiom). [clausify(2614)]. 48.71/48.64 5503 -field_inverse_zero(A) | -number(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) | zero_zero(A) = hAPP(int,A,number_number_of(A),D) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom). [clausify(2671)]. 48.71/48.64 5504 -field_inverse_zero(A) | -number(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) | zero_zero(A) != hAPP(int,A,number_number_of(A),D) | zero_zero(A) = ti(A,B) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom). [clausify(2671)]. 48.71/48.64 5505 -field_inverse_zero(A) | -number(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) | zero_zero(A) != hAPP(int,A,number_number_of(A),D) | zero_zero(A) != ti(A,B) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom). [clausify(2671)]. 48.71/48.64 5506 -field_inverse_zero(A) | -number(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)) | zero_zero(A) = hAPP(int,A,number_number_of(A),D) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom). [clausify(2671)]. 48.71/48.64 5507 -field_inverse_zero(A) | -number(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)) | zero_zero(A) != ti(A,B) # label(fact_1779_divide__eq__eq__number__of1) # label(axiom). [clausify(2671)]. 48.71/48.64 5508 -semiring_div(A) | -number(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(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),dvd_dvd(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1409_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(2717)]. 48.71/48.64 5509 -semiring_div(A) | -number(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(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),dvd_dvd(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_1409_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(2717)]. 48.71/48.64 5510 -number(A) | -field_inverse_zero(A) | zero_zero(A) = ti(A,B) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) = hAPP(int,A,number_number_of(A),D) # label(fact_1777_eq__divide__eq__number__of) # label(axiom). [clausify(2877)]. 48.71/48.64 5511 -number(A) | -field_inverse_zero(A) | zero_zero(A) != hAPP(int,A,number_number_of(A),B) | zero_zero(A) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C) = hAPP(int,A,number_number_of(A),B) # label(fact_1777_eq__divide__eq__number__of) # label(axiom). [clausify(2877)]. 48.71/48.64 5512 -number(A) | -field_inverse_zero(A) | zero_zero(A) != hAPP(int,A,number_number_of(A),B) | ti(A,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),inverse_divide(A),C),D) = hAPP(int,A,number_number_of(A),B) # label(fact_1777_eq__divide__eq__number__of) # label(axiom). [clausify(2877)]. 48.71/48.64 5513 -number(A) | -field_inverse_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(int,A,number_number_of(A),C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) != hAPP(int,A,number_number_of(A),C) # label(fact_1777_eq__divide__eq__number__of) # label(axiom). [clausify(2877)]. 48.92/48.80 5514 -number(A) | -field_inverse_zero(A) | zero_zero(A) = ti(A,B) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) != hAPP(int,A,number_number_of(A),D) # label(fact_1777_eq__divide__eq__number__of) # label(axiom). [clausify(2877)]. 48.92/48.80 5515 -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(2892)]. 48.92/48.80 Derived: number_number_of(nat) = ti(fun(int,nat),number_number_of(nat)). [resolve(5515,a,5424,a)]. 48.92/48.80 Derived: number_number_of(complex) = ti(fun(int,complex),number_number_of(complex)). [resolve(5515,a,5435,a)]. 48.92/48.80 Derived: number_number_of(quickcheck_code_int) = ti(fun(int,quickcheck_code_int),number_number_of(quickcheck_code_int)). [resolve(5515,a,5436,a)]. 48.92/48.80 Derived: number_number_of(int) = ti(fun(int,int),number_number_of(int)). [resolve(5515,a,5447,a)]. 48.92/48.80 Derived: number_number_of(real) = ti(fun(int,real),number_number_of(real)). [resolve(5515,a,5479,a)]. 48.92/48.80 5516 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.92/48.80 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(5516,b,5424,a)]. 48.92/48.80 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(5516,b,5435,a)]. 48.92/48.80 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(5516,b,5436,a)]. 48.92/48.80 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(5516,b,5447,a)]. 48.92/48.81 5517 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),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),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),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.92/48.81 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),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),A))) | 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(5517,b,5435,a)]. 48.92/48.81 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),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),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),inverse_divide(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)))). [resolve(5517,b,5436,a)]. 48.92/48.81 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),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),A))) | 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(5517,b,5447,a)]. 48.92/48.81 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(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),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),hAPP(int,real,number_number_of(real),A)))). [resolve(5517,b,5479,a)]. 48.92/48.81 5518 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),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),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.82 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),B),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),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),hAPP(int,complex,number_number_of(complex),A)))). [resolve(5518,b,5435,a)]. 48.96/48.82 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),B),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),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(5518,b,5436,a)]. 48.96/48.82 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),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),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(5518,b,5447,a)]. 48.96/48.82 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(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),hAPP(int,real,number_number_of(real),A)))). [resolve(5518,b,5479,a)]. 48.96/48.82 5519 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),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),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.82 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),B),hAPP(int,complex,number_number_of(complex),C)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),C)),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),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),A),hAPP(int,complex,number_number_of(complex),C)))). [resolve(5519,b,5435,a)]. 48.96/48.82 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),B),hAPP(int,quickcheck_code_int,number_number_of(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),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),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),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),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)))). [resolve(5519,b,5436,a)]. 48.96/48.82 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),B),hAPP(int,int,number_number_of(int),C)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),C)),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),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),A),hAPP(int,int,number_number_of(int),C)))). [resolve(5519,b,5447,a)]. 48.96/48.82 5520 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.82 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),B),hAPP(int,complex,number_number_of(complex),C)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(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),B),hAPP(int,complex,number_number_of(complex),C))),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),C)))). [resolve(5520,b,5435,a)]. 48.96/48.82 5521 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.83 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),B),hAPP(int,complex,number_number_of(complex),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(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),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),A),hAPP(int,complex,number_number_of(complex),C)))). [resolve(5521,b,5435,a)]. 48.96/48.83 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),B),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),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(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),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),A),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),C)))). [resolve(5521,b,5436,a)]. 48.96/48.83 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),B),hAPP(int,int,number_number_of(int),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(int),zero_zero(int)),hAPP(int,int,number_number_of(int),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),A),hAPP(int,int,number_number_of(int),C)))). [resolve(5521,b,5447,a)]. 48.96/48.83 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),B),hAPP(int,real,number_number_of(real),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),C)))). [resolve(5521,b,5479,a)]. 48.96/48.83 5522 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),D)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.83 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),B),hAPP(int,complex,number_number_of(complex),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(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(int,complex,number_number_of(complex),C))),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),hAPP(int,complex,number_number_of(complex),C)))). [resolve(5522,b,5435,a)]. 48.96/48.84 5523 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 48.96/48.84 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(5523,b,5435,a)]. 48.96/48.84 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(5523,b,5436,a)]. 48.96/48.84 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(5523,b,5447,a)]. 48.96/48.84 5524 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 49.01/48.84 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(5524,b,5424,a)]. 49.01/48.84 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(5524,b,5435,a)]. 49.01/48.84 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(5524,b,5436,a)]. 49.01/48.84 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(5524,b,5447,a)]. 49.01/48.84 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(5524,b,5479,a)]. 49.01/48.84 5525 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1792_less__divide__eq__number__of1) # label(axiom). [clausify(2978)]. 49.41/49.27 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(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(5525,b,5424,a)]. 49.41/49.27 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(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(5525,b,5435,a)]. 49.41/49.27 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(5525,b,5436,a)]. 49.41/49.27 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,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(5525,b,5447,a)]. 49.41/49.27 5526 number(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Int_Onumber) # label(axiom). [assumption]. 49.41/49.27 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),inverse_divide(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),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(5526,a,5423,a)]. 49.41/49.27 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),inverse_divide(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(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(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))),A)). [resolve(5526,a,5425,a)]. 49.41/49.27 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),inverse_divide(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(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),zero_zero(code_code_numeral)),C)). [resolve(5526,a,5426,a)]. 49.41/49.27 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),inverse_divide(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(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),zero_zero(code_code_numeral)),C)). [resolve(5526,a,5427,a)]. 49.41/49.27 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),inverse_divide(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),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))),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))). [resolve(5526,a,5428,a)]. 49.41/49.28 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),inverse_divide(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),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))),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)). [resolve(5526,a,5429,a)]. 49.41/49.28 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),inverse_divide(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),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)))) | -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))). [resolve(5526,a,5430,a)]. 49.41/49.28 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),inverse_divide(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),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)))) | 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),zero_zero(code_code_numeral)),C)). [resolve(5526,a,5431,a)]. 49.41/49.28 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),inverse_divide(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),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)))) | -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),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(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))). [resolve(5526,a,5432,a)]. 49.41/49.28 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),inverse_divide(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),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)))) | -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),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),zero_zero(code_code_numeral)),C)). [resolve(5526,a,5433,a)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(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(5526,a,5437,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)),B)),A)). [resolve(5526,a,5438,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(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),C))). [resolve(5526,a,5439,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(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),C))). [resolve(5526,a,5440,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(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),C)),B)),A)) | -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))). [resolve(5526,a,5441,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(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),C)),B)),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),C))). [resolve(5526,a,5442,b)]. 49.41/49.28 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(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),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))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)). [resolve(5526,a,5443,b)]. 49.41/49.29 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),inverse_divide(code_code_numeral),A),B)),hAPP(int,code_code_numeral,number_number_of(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),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))) | 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),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C))). [resolve(5526,a,5444,b)]. 49.41/49.29 Derived: -ring(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)),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)) = 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)). [resolve(5526,a,5448,a)]. 49.41/49.29 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) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | 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(5526,a,5469,b)]. 49.41/49.29 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) | zero_zero(code_code_numeral) != ti(code_code_numeral,B) | zero_zero(code_code_numeral) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C). [resolve(5526,a,5470,b)]. 49.41/49.29 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) | zero_zero(code_code_numeral) != ti(code_code_numeral,B) | zero_zero(code_code_numeral) != hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C). [resolve(5526,a,5471,b)]. 49.41/49.29 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,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) | zero_zero(code_code_numeral) = ti(code_code_numeral,B). [resolve(5526,a,5472,b)]. 49.41/49.29 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,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) | zero_zero(code_code_numeral) != hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C). [resolve(5526,a,5473,b)]. 49.41/49.29 Derived: -field_inverse_zero(code_code_numeral) | zero_zero(code_code_numeral) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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),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(5526,a,5474,b)]. 49.41/49.29 Derived: -field_inverse_zero(code_code_numeral) | zero_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) | 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(5526,a,5475,b)]. 49.41/49.29 Derived: -field_inverse_zero(code_code_numeral) | zero_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) | 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(5526,a,5477,b)]. 49.41/49.29 Derived: -field_inverse_zero(code_code_numeral) | zero_zero(code_code_numeral) = hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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),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(5526,a,5478,b)]. 49.41/49.29 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(5526,a,5480,a)]. 49.41/49.29 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),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(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),inverse_divide(code_code_numeral),C),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(5526,a,5481,a)]. 49.41/49.30 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),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),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(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(5526,a,5482,a)]. 49.41/49.30 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(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),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))). [resolve(5526,a,5483,a)]. 49.41/49.30 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(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))). [resolve(5526,a,5484,a)]. 49.46/49.30 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),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),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),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))). [resolve(5526,a,5485,a)]. 49.46/49.30 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),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),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(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(code_code_numeral),C),B)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A))). [resolve(5526,a,5486,a)]. 49.46/49.30 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(5526,a,5487,a)]. 49.46/49.30 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(5526,a,5488,a)]. 49.46/49.30 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(5526,a,5489,a)]. 49.46/49.30 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(5526,a,5490,b)]. 49.46/49.31 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(5526,a,5491,b)]. 49.46/49.31 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(5526,a,5492,b)]. 49.46/49.31 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(5526,a,5493,b)]. 49.46/49.31 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(5526,a,5494,b)]. 49.46/49.31 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(5526,a,5495,b)]. 49.46/49.31 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(5526,a,5496,b)]. 49.46/49.31 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(5526,a,5498,b)]. 49.46/49.32 Derived: -ring(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),minus_minus(code_code_numeral),A),B)),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),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),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),C))). [resolve(5526,a,5500,a)]. 49.46/49.32 Derived: number_number_of(code_code_numeral) = ti(fun(int,code_code_numeral),number_number_of(code_code_numeral)). [resolve(5526,a,5515,a)]. 49.46/49.32 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(5526,a,5516,b)]. 49.46/49.32 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),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),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),inverse_divide(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)))). [resolve(5526,a,5517,b)]. 49.46/49.32 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),B),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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(5526,a,5518,b)]. 49.46/49.32 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),B),hAPP(int,code_code_numeral,number_number_of(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),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),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)))). [resolve(5526,a,5519,b)]. 49.46/49.32 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),B),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),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),A),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),C)))). [resolve(5526,a,5521,b)]. 49.46/49.32 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(5526,a,5523,b)]. 49.53/49.42 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(5526,a,5524,b)]. 49.53/49.42 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(5526,a,5525,b)]. 49.53/49.42 5527 number(rat) # label(arity_Rat_Orat___Int_Onumber) # label(axiom). [assumption]. 49.53/49.42 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),inverse_divide(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(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(5527,a,5426,a)]. 49.53/49.42 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),inverse_divide(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(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(5527,a,5427,a)]. 49.53/49.42 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),inverse_divide(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_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(5527,a,5429,a)]. 49.53/49.42 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),inverse_divide(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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B)))) | 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),zero_zero(rat)),C)). [resolve(5527,a,5431,a)]. 49.53/49.43 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),inverse_divide(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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),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),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(5527,a,5433,a)]. 49.53/49.43 Derived: -linord1117847801e_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)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5439,b)]. 49.53/49.43 Derived: -linord1117847801e_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)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5440,b)]. 49.53/49.43 Derived: -linord1117847801e_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)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5442,b)]. 49.53/49.43 Derived: -linord1117847801e_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)),hAPP(int,rat,number_number_of(rat),C))) | -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),C)),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5444,b)]. 49.53/49.43 Derived: -ring(rat) | 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)) = 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)). [resolve(5527,a,5448,a)]. 49.53/49.43 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),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5527,a,5450,a)]. 49.53/49.44 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),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(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),C))). [resolve(5527,a,5453,a)]. 49.53/49.44 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),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_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),times_times(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)). [resolve(5527,a,5454,a)]. 49.53/49.44 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),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),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),A),hAPP(int,rat,number_number_of(rat),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),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5457,a)]. 49.53/49.44 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),inverse_divide(rat),B),hAPP(int,rat,number_number_of(rat),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),A),hAPP(int,rat,number_number_of(rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),C))),B)). [resolve(5527,a,5458,a)]. 49.53/49.44 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(5527,a,5459,a)]. 49.53/49.44 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),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),C)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5527,a,5461,a)]. 49.53/49.44 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),hAPP(int,rat,number_number_of(rat),A)),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_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),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(5527,a,5463,a)]. 49.53/49.45 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),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)),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(5527,a,5465,a)]. 49.53/49.45 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(5527,a,5468,a)]. 49.53/49.45 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) | zero_zero(rat) = ti(rat,B) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B). [resolve(5527,a,5469,b)]. 49.53/49.45 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) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) = hAPP(int,rat,number_number_of(rat),C). [resolve(5527,a,5470,b)]. 49.53/49.45 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) | zero_zero(rat) != ti(rat,B) | zero_zero(rat) != hAPP(int,rat,number_number_of(rat),C). [resolve(5527,a,5471,b)]. 49.53/49.45 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,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B) | zero_zero(rat) = ti(rat,B). [resolve(5527,a,5472,b)]. 49.53/49.45 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,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B) | zero_zero(rat) != hAPP(int,rat,number_number_of(rat),C). [resolve(5527,a,5473,b)]. 49.53/49.45 Derived: -field_inverse_zero(rat) | zero_zero(rat) = hAPP(int,rat,number_number_of(rat),A) | 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(5527,a,5474,b)]. 49.53/49.45 Derived: -field_inverse_zero(rat) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != hAPP(int,rat,number_number_of(rat),B) | ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),B)). [resolve(5527,a,5475,b)]. 49.53/49.45 Derived: -field_inverse_zero(rat) | zero_zero(rat) != hAPP(int,rat,number_number_of(rat),A) | zero_zero(rat) = ti(rat,B) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)). [resolve(5527,a,5477,b)]. 49.53/49.45 Derived: -field_inverse_zero(rat) | zero_zero(rat) = hAPP(int,rat,number_number_of(rat),A) | 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(5527,a,5478,b)]. 49.53/49.45 Derived: -linord1117847801e_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),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5527,a,5481,a)]. 49.53/49.46 Derived: -linord1117847801e_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),zero_zero(rat)),hAPP(int,rat,number_number_of(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),hAPP(int,rat,number_number_of(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),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5527,a,5482,a)]. 49.53/49.46 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),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5527,a,5485,a)]. 49.53/49.46 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),zero_zero(rat)),hAPP(int,rat,number_number_of(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),hAPP(int,rat,number_number_of(rat),A)),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5527,a,5486,a)]. 49.53/49.46 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(5527,a,5488,a)]. 49.53/49.46 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(5527,a,5491,b)]. 49.53/49.46 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(5527,a,5494,b)]. 49.53/49.46 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(5527,a,5495,b)]. 49.67/49.51 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(5527,a,5498,b)]. 49.67/49.51 Derived: -ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(int,rat,number_number_of(rat),C)) = 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),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C))). [resolve(5527,a,5500,a)]. 49.67/49.52 Derived: number_number_of(rat) = ti(fun(int,rat),number_number_of(rat)). [resolve(5527,a,5515,a)]. 49.67/49.52 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(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),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),hAPP(int,rat,number_number_of(rat),A)))). [resolve(5527,a,5517,b)]. 49.67/49.52 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(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),A))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),hAPP(int,rat,number_number_of(rat),A)))). [resolve(5527,a,5518,b)]. 49.67/49.52 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),B),hAPP(int,rat,number_number_of(rat),C)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),C)))). [resolve(5527,a,5521,b)]. 49.67/49.52 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(5527,a,5524,b)]. 49.67/49.52 5528 -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_3934_power__number__of__odd__number__of) # label(axiom). [clausify(3661)]. 49.77/49.63 5529 -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_3934_power__number__of__odd__number__of) # label(axiom). [clausify(3661)]. 49.77/49.63 5530 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.77/49.63 Derived: -linord1117847801e_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),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),times_times(nat),C),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5530,a,5424,a)]. 49.77/49.63 Derived: -linord1117847801e_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),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),times_times(complex),C),hAPP(int,complex,number_number_of(complex),B)))). [resolve(5530,a,5435,a)]. 49.77/49.63 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(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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),times_times(quickcheck_code_int),C),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)))). [resolve(5530,a,5436,a)]. 49.77/49.63 Derived: -linord1117847801e_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),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),times_times(int),C),hAPP(int,int,number_number_of(int),B)))). [resolve(5530,a,5447,a)]. 49.77/49.63 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(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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),times_times(code_code_numeral),C),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)))). [resolve(5530,a,5526,a)]. 49.77/49.64 5531 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.77/49.64 Derived: -linord1117847801e_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),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(int,complex,number_number_of(complex),B)),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),C),hAPP(int,complex,number_number_of(complex),B))),A)). [resolve(5531,a,5435,a)]. 49.77/49.64 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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(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),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))),A)). [resolve(5531,a,5436,a)]. 49.77/49.64 Derived: -linord1117847801e_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),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,number_number_of(int),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),B))),A)). [resolve(5531,a,5447,a)]. 49.77/49.64 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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(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),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))),A)). [resolve(5531,a,5526,a)]. 49.77/49.64 5532 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.77/49.64 Derived: -linord1117847801e_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),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(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)),C)). [resolve(5532,a,5424,a)]. 49.77/49.64 Derived: -linord1117847801e_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),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(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)),C)). [resolve(5532,a,5435,a)]. 49.77/49.64 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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(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)),C)). [resolve(5532,a,5436,a)]. 49.77/49.64 Derived: -linord1117847801e_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),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,number_number_of(int),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)). [resolve(5532,a,5447,a)]. 49.77/49.65 Derived: -linord1117847801e_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),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(int,real,number_number_of(real),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5532,a,5479,a)]. 49.77/49.65 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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(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)),C)). [resolve(5532,a,5526,a)]. 49.77/49.65 Derived: -linord1117847801e_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),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(int,rat,number_number_of(rat),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(5532,a,5527,a)]. 49.77/49.65 5533 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.77/49.65 Derived: -linord1117847801e_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),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(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)),C)). [resolve(5533,a,5424,a)]. 49.77/49.65 Derived: -linord1117847801e_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),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(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)),C)). [resolve(5533,a,5435,a)]. 49.77/49.65 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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(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)),C)). [resolve(5533,a,5436,a)]. 49.77/49.65 Derived: -linord1117847801e_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),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,number_number_of(int),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)). [resolve(5533,a,5447,a)]. 49.77/49.65 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),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(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5533,a,5479,a)]. 49.77/49.65 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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(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)),C)). [resolve(5533,a,5526,a)]. 49.77/49.65 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),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(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(5533,a,5527,a)]. 49.77/49.65 5534 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.77/49.66 Derived: -linord1117847801e_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),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),C),hAPP(int,complex,number_number_of(complex),B))),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))). [resolve(5534,a,5435,a)]. 49.77/49.66 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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),times_times(quickcheck_code_int),C),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(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),zero_zero(quickcheck_code_int))). [resolve(5534,a,5436,a)]. 49.77/49.66 Derived: -linord1117847801e_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),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),times_times(int),C),hAPP(int,int,number_number_of(int),B))),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),zero_zero(int))). [resolve(5534,a,5447,a)]. 49.77/49.66 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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),times_times(code_code_numeral),C),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(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),zero_zero(code_code_numeral))). [resolve(5534,a,5526,a)]. 49.77/49.66 5535 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.84/49.66 Derived: -linord1117847801e_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),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),times_times(nat),C),hAPP(int,nat,number_number_of(nat),B))),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)). [resolve(5535,a,5424,a)]. 49.84/49.66 Derived: -linord1117847801e_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),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),C),hAPP(int,complex,number_number_of(complex),B))),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)). [resolve(5535,a,5435,a)]. 49.84/49.66 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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),times_times(quickcheck_code_int),C),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(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)). [resolve(5535,a,5436,a)]. 49.84/49.66 Derived: -linord1117847801e_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),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),times_times(int),C),hAPP(int,int,number_number_of(int),B))),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)). [resolve(5535,a,5447,a)]. 49.84/49.66 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),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),times_times(real),C),hAPP(int,real,number_number_of(real),B))),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5535,a,5479,a)]. 49.84/49.66 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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),times_times(code_code_numeral),C),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(code_code_numeral),zero_zero(code_code_numeral)),C)). [resolve(5535,a,5526,a)]. 49.84/49.67 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),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),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B))),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(5535,a,5527,a)]. 49.84/49.67 5536 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.84/49.67 Derived: -linord1117847801e_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),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),B)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),B))). [resolve(5536,a,5424,a)]. 49.84/49.67 Derived: -linord1117847801e_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),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(int,complex,number_number_of(complex),B)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),hAPP(int,complex,number_number_of(complex),B))). [resolve(5536,a,5435,a)]. 49.84/49.67 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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),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(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),zero_zero(quickcheck_code_int)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B))). [resolve(5536,a,5436,a)]. 49.84/49.67 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),B)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))). [resolve(5536,a,5447,a)]. 49.84/49.67 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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),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(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),zero_zero(code_code_numeral)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B))). [resolve(5536,a,5526,a)]. 49.84/49.67 5537 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),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),zero_zero(A)),D)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.84/49.67 Derived: -linord1117847801e_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),hAPP(int,nat,number_number_of(nat),B))),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(int,nat,number_number_of(nat),B)))) | 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)),C)). [resolve(5537,a,5424,a)]. 49.84/49.67 Derived: -linord1117847801e_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),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),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),zero_zero(complex)),C)). [resolve(5537,a,5435,a)]. 49.84/49.67 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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),inverse_divide(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),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(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(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)),C)). [resolve(5537,a,5436,a)]. 49.84/49.68 Derived: -linord1117847801e_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),hAPP(int,int,number_number_of(int),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),B)))) | 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)),C)). [resolve(5537,a,5447,a)]. 49.84/49.68 Derived: -linord1117847801e_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),B))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(int,real,number_number_of(real),B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5537,a,5479,a)]. 49.84/49.68 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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),inverse_divide(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),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(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(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)),C)). [resolve(5537,a,5526,a)]. 49.84/49.68 Derived: -linord1117847801e_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(5537,a,5527,a)]. 49.84/49.68 5538 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 49.84/49.68 Derived: -linord1117847801e_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),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),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),C),hAPP(int,complex,number_number_of(complex),B))),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),hAPP(int,complex,number_number_of(complex),B)),zero_zero(complex))). [resolve(5538,a,5435,a)]. 50.30/50.13 5539 -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),inverse_divide(A),B),hAPP(int,A,number_number_of(A),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),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),D),hAPP(int,A,number_number_of(A),C))),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1795_divide__less__eq__number__of1) # label(axiom). [clausify(3823)]. 50.30/50.13 Derived: -linord1117847801e_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),hAPP(int,complex,number_number_of(complex),B))),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),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),C),hAPP(int,complex,number_number_of(complex),B))),A)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less(complex),zero_zero(complex)),C)). [resolve(5539,a,5435,a)]. 50.30/50.13 5540 -number(A) | -division_ring(A) | hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_2622_inverse__eq__divide__number__of) # label(axiom). [clausify(4414)]. 50.30/50.13 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(5540,a,5424,a)]. 50.30/50.13 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(5540,a,5435,a)]. 50.30/50.13 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(5540,a,5436,a)]. 50.30/50.13 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(5540,a,5447,a)]. 50.30/50.13 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(5540,a,5479,a)]. 50.30/50.13 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(5540,a,5526,a)]. 50.32/50.17 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(5540,a,5527,a)]. 50.32/50.17 5541 -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_3882_power__number__of__even__number__of) # label(axiom). [clausify(4458)]. 50.32/50.17 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(5541,a,5424,a)]. 50.32/50.17 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(5541,a,5435,a)]. 50.32/50.17 Derived: -monoid_mult(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5541,a,5436,a)]. 50.32/50.17 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(5541,a,5447,a)]. 50.32/50.17 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(5541,a,5479,a)]. 50.52/50.35 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(5541,a,5526,a)]. 50.52/50.35 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(5541,a,5527,a)]. 50.52/50.35 5542 -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_4856_min__number__of) # label(axiom). [clausify(4695)]. 50.52/50.35 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(5542,b,5424,a)]. 50.52/50.35 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(5542,b,5435,a)]. 50.52/50.35 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(5542,b,5436,a)]. 50.52/50.35 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(5542,b,5447,a)]. 50.52/50.35 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(5542,b,5479,a)]. 50.52/50.35 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(5542,b,5526,a)]. 50.52/50.35 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(5542,b,5527,a)]. 50.52/50.35 5543 -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_4856_min__number__of) # label(axiom). [clausify(4695)]. 50.52/50.35 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(5543,b,5424,a)]. 50.52/50.35 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(5543,b,5435,a)]. 50.52/50.35 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(5543,b,5436,a)]. 50.52/50.35 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(5543,b,5447,a)]. 50.52/50.35 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(5543,b,5479,a)]. 50.52/50.35 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(5543,b,5526,a)]. 52.42/52.33 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(5543,b,5527,a)]. 52.42/52.33 5544 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 52.42/52.33 5545 -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_3322_zero__less__ceiling) # label(axiom). [clausify(42)]. 52.42/52.33 5546 -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_3322_zero__less__ceiling) # label(axiom). [clausify(42)]. 52.42/52.33 5547 -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_3619_floor__add__of__int) # label(axiom). [clausify(105)]. 52.42/52.33 5548 -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_2905_floor__less__zero) # label(axiom). [clausify(128)]. 52.42/52.33 5549 -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_2905_floor__less__zero) # label(axiom). [clausify(128)]. 52.42/52.33 5550 -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_3329_ceiling__le__number__of) # label(axiom). [clausify(163)]. 52.42/52.33 5551 -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_3329_ceiling__le__number__of) # label(axiom). [clausify(163)]. 52.42/52.33 5552 -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_3328_number__of__less__ceiling) # label(axiom). [clausify(166)]. 52.42/52.33 5553 -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_3328_number__of__less__ceiling) # label(axiom). [clausify(166)]. 52.42/52.33 5554 -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_3306_ceiling__mono) # label(axiom). [clausify(283)]. 52.42/52.33 5555 -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_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2910_one__le__floor) # label(axiom). [clausify(303)]. 52.42/52.33 5556 -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_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2910_one__le__floor) # label(axiom). [clausify(303)]. 52.42/52.33 5557 -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_2873_one__less__floor) # label(axiom). [clausify(437)]. 52.42/52.33 5558 -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_2873_one__less__floor) # label(axiom). [clausify(437)]. 52.42/52.33 5559 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3324_ceiling__less__one) # label(axiom). [clausify(447)]. 52.42/52.33 5560 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3324_ceiling__less__one) # label(axiom). [clausify(447)]. 52.42/52.33 5561 -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_3318_floor__minus) # label(axiom). [clausify(477)]. 52.42/52.33 5562 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(A))) # label(fact_3327_ceiling__le__one) # label(axiom). [clausify(490)]. 52.42/52.33 5563 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(A))) # label(fact_3327_ceiling__le__one) # label(axiom). [clausify(490)]. 52.42/52.33 5564 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_2912_number__of__le__floor) # label(axiom). [clausify(583)]. 52.42/52.33 5565 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_2912_number__of__le__floor) # label(axiom). [clausify(583)]. 52.42/52.33 5566 -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)),B)) # label(fact_3335_zero__le__ceiling) # label(axiom). [clausify(841)]. 52.42/52.33 5567 -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)),B)) # label(fact_3335_zero__le__ceiling) # label(axiom). [clausify(841)]. 52.42/52.33 5568 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3637_le__ceiling__iff) # label(axiom). [clausify(848)]. 52.51/52.35 5569 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3637_le__ceiling__iff) # label(axiom). [clausify(848)]. 52.51/52.35 5570 -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,number_number_of(A),B)),one_one(A))),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,archimedean_ceiling(A),C))) # label(fact_3236_number__of__le__ceiling) # label(axiom). [clausify(897)]. 52.51/52.35 5571 -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,number_number_of(A),B)),one_one(A))),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,archimedean_ceiling(A),C))) # label(fact_3236_number__of__le__ceiling) # label(axiom). [clausify(897)]. 52.51/52.35 5572 -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_3310_ceiling__of__nat) # label(axiom). [clausify(997)]. 52.51/52.35 5573 -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_2898_floor__number__of) # label(axiom). [clausify(999)]. 52.51/52.35 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(5544,a,5545,a)]. 52.51/52.35 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(5544,a,5546,a)]. 52.51/52.35 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(5544,a,5547,a)]. 52.51/52.35 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(5544,a,5548,a)]. 52.51/52.35 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(5544,a,5549,a)]. 52.51/52.35 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(5544,a,5550,a)]. 52.51/52.35 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(5544,a,5551,a)]. 52.51/52.35 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(5544,a,5552,a)]. 52.51/52.35 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(5544,a,5553,a)]. 52.51/52.35 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(5544,a,5554,a)]. 52.51/52.37 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_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5544,a,5555,a)]. 52.51/52.37 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_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(5544,a,5556,a)]. 52.51/52.37 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(5544,a,5557,a)]. 52.51/52.37 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(5544,a,5558,a)]. 52.51/52.37 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))). [resolve(5544,a,5559,a)]. 52.51/52.37 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))). [resolve(5544,a,5560,a)]. 52.51/52.37 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(5544,a,5561,a)]. 52.51/52.37 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(real))). [resolve(5544,a,5562,a)]. 52.51/52.37 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(real))). [resolve(5544,a,5563,a)]. 52.51/52.37 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5544,a,5564,a)]. 52.51/52.37 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(5544,a,5565,a)]. 52.51/52.37 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)),A)). [resolve(5544,a,5566,a)]. 52.51/52.37 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)),A)). [resolve(5544,a,5567,a)]. 52.51/52.37 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5544,a,5568,a)]. 52.51/52.37 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(5544,a,5569,a)]. 52.56/52.44 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,number_number_of(real),A)),one_one(real))),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,archimedean_ceiling(real),B))). [resolve(5544,a,5570,a)]. 52.56/52.44 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,number_number_of(real),A)),one_one(real))),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,archimedean_ceiling(real),B))). [resolve(5544,a,5571,a)]. 52.56/52.44 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(5544,a,5572,a)]. 52.56/52.44 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5544,a,5573,a)]. 52.56/52.44 5574 -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_3332_ceiling__diff__one) # label(axiom). [clausify(1074)]. 52.56/52.44 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(5574,a,5544,a)]. 52.56/52.44 5575 -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_3330_ceiling__add__one) # label(axiom). [clausify(1117)]. 52.56/52.44 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(5575,a,5544,a)]. 52.56/52.44 5576 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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_2907_zero__less__floor) # label(axiom). [clausify(1234)]. 52.56/52.44 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(5576,a,5544,a)]. 52.56/52.44 5577 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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_2907_zero__less__floor) # label(axiom). [clausify(1234)]. 52.56/52.44 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(5577,a,5544,a)]. 52.56/52.44 5578 -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_2914_floor__add__number__of) # label(axiom). [clausify(1306)]. 52.56/52.44 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(5578,a,5544,a)]. 52.56/52.44 5579 -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_3620_less__ceiling__iff) # label(axiom). [clausify(1315)]. 52.72/52.59 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(5579,a,5544,a)]. 52.72/52.59 5580 -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_3620_less__ceiling__iff) # label(axiom). [clausify(1315)]. 52.72/52.59 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(5580,a,5544,a)]. 52.72/52.59 5581 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archimedean_ceiling(A),one_one(A)) # label(fact_3307_ceiling__one) # label(axiom). [clausify(1455)]. 52.72/52.59 Derived: one_one(int) = hAPP(real,int,archimedean_ceiling(real),one_one(real)). [resolve(5581,a,5544,a)]. 52.72/52.59 5582 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3613_ceiling__of__int) # label(axiom). [clausify(1521)]. 52.72/52.59 Derived: ti(int,A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5582,a,5544,a)]. 52.72/52.59 5583 -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_3631_ceiling__unique) # label(axiom). [clausify(1537)]. 52.72/52.59 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(5583,a,5544,a)]. 52.72/52.59 5584 -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_2872_floor__le__one) # label(axiom). [clausify(1733)]. 52.72/52.59 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(5584,a,5544,a)]. 52.72/52.59 5585 -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_2872_floor__le__one) # label(axiom). [clausify(1733)]. 52.72/52.59 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(5585,a,5544,a)]. 52.72/52.59 5586 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archim2085082626_floor(A),one_one(A)) # label(fact_2896_floor__one) # label(axiom). [clausify(1867)]. 52.72/52.59 Derived: one_one(int) = hAPP(real,int,archim2085082626_floor(real),one_one(real)). [resolve(5586,a,5544,a)]. 52.72/52.59 5587 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_3323_ceiling__le__zero) # label(axiom). [clausify(1873)]. 52.87/52.71 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5587,a,5544,a)]. 52.87/52.71 5588 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_3323_ceiling__le__zero) # label(axiom). [clausify(1873)]. 52.87/52.71 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5588,a,5544,a)]. 52.87/52.71 5589 -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_2915_floor__diff__one) # label(axiom). [clausify(1908)]. 52.87/52.71 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(5589,a,5544,a)]. 52.87/52.71 5590 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_2911_floor__less__number__of) # label(axiom). [clausify(1975)]. 52.87/52.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5590,a,5544,a)]. 52.87/52.71 5591 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_2911_floor__less__number__of) # label(axiom). [clausify(1975)]. 52.87/52.71 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5591,a,5544,a)]. 52.87/52.71 5592 -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_3635_floor__correct) # label(axiom). [clausify(2100)]. 52.87/52.71 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(5592,a,5544,a)]. 52.87/52.71 5593 -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_3635_floor__correct) # label(axiom). [clausify(2100)]. 52.87/52.71 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(5593,a,5544,a)]. 52.87/52.71 5594 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2909_floor__less__one) # label(axiom). [clausify(2203)]. 52.87/52.71 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5594,a,5544,a)]. 52.93/52.84 5595 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2909_floor__less__one) # label(axiom). [clausify(2203)]. 52.93/52.84 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5595,a,5544,a)]. 52.93/52.84 5596 -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_3325_one__le__ceiling) # label(axiom). [clausify(2209)]. 52.93/52.84 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(5596,a,5544,a)]. 52.93/52.84 5597 -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_3325_one__le__ceiling) # label(axiom). [clausify(2209)]. 52.93/52.84 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(5597,a,5544,a)]. 52.93/52.84 5598 -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_3331_ceiling__add__number__of) # label(axiom). [clausify(2350)]. 52.93/52.84 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(5598,a,5544,a)]. 52.93/52.84 5599 -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_3621_ceiling__le__iff) # label(axiom). [clausify(2421)]. 52.93/52.84 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(5599,a,5544,a)]. 52.93/52.84 5600 -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_3621_ceiling__le__iff) # label(axiom). [clausify(2421)]. 52.93/52.84 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(5600,a,5544,a)]. 52.93/52.84 5601 -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(2519)]. 52.93/52.84 Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)). [resolve(5601,a,5544,a)]. 52.93/52.84 5602 -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_3617_floor__less__iff) # label(axiom). [clausify(2530)]. 53.10/52.93 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(5602,a,5544,a)]. 53.10/52.93 5603 -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_3617_floor__less__iff) # label(axiom). [clausify(2530)]. 53.10/52.93 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(5603,a,5544,a)]. 53.10/52.93 5604 -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_3634_floor__le__iff) # label(axiom). [clausify(2558)]. 53.10/52.93 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(5604,a,5544,a)]. 53.10/52.93 5605 -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_3634_floor__le__iff) # label(axiom). [clausify(2558)]. 53.10/52.93 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(5605,a,5544,a)]. 53.10/52.93 5606 -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_3333_ceiling__diff__number__of) # label(axiom). [clausify(2589)]. 53.10/52.93 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(5606,a,5544,a)]. 53.10/52.93 5607 -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_2901_floor__of__nat) # label(axiom). [clausify(2595)]. 53.10/52.93 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(5607,a,5544,a)]. 53.10/52.93 5608 archim1727834104eiling(rat) # label(arity_Rat_Orat___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 53.10/52.93 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(5608,a,5545,a)]. 53.10/52.93 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(5608,a,5546,a)]. 53.10/52.93 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(5608,a,5547,a)]. 53.10/52.93 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(5608,a,5548,a)]. 53.11/52.95 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(5608,a,5549,a)]. 53.11/52.95 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(5608,a,5550,a)]. 53.11/52.95 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(5608,a,5551,a)]. 53.11/52.95 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(5608,a,5552,a)]. 53.11/52.95 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(5608,a,5553,a)]. 53.11/52.95 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(5608,a,5554,a)]. 53.11/52.95 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_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5608,a,5555,a)]. 53.11/52.95 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_eq(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(5608,a,5556,a)]. 53.11/52.95 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(5608,a,5557,a)]. 53.11/52.95 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(5608,a,5558,a)]. 53.11/52.95 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(5608,a,5559,a)]. 53.11/52.95 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(5608,a,5560,a)]. 53.11/52.95 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(5608,a,5561,a)]. 53.11/52.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(rat))). [resolve(5608,a,5562,a)]. 53.11/52.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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),one_one(rat))). [resolve(5608,a,5563,a)]. 53.11/52.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(5608,a,5564,a)]. 53.11/52.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)). [resolve(5608,a,5565,a)]. 53.11/52.97 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)),A)). [resolve(5608,a,5566,a)]. 53.11/52.97 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)),A)). [resolve(5608,a,5567,a)]. 53.11/52.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(5608,a,5568,a)]. 53.11/52.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(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,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(5608,a,5569,a)]. 53.11/52.97 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,number_number_of(rat),A)),one_one(rat))),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,archimedean_ceiling(rat),B))). [resolve(5608,a,5570,a)]. 53.11/52.97 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,number_number_of(rat),A)),one_one(rat))),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,archimedean_ceiling(rat),B))). [resolve(5608,a,5571,a)]. 53.11/52.97 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(5608,a,5572,a)]. 53.11/52.97 Derived: hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5608,a,5573,a)]. 53.11/52.97 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(5608,a,5574,a)]. 53.11/52.97 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)). [resolve(5608,a,5575,a)]. 53.11/52.97 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(5608,a,5576,a)]. 53.11/52.97 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(5608,a,5577,a)]. 53.11/52.97 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(5608,a,5578,a)]. 53.11/52.97 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(5608,a,5579,a)]. 53.11/52.98 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(5608,a,5580,a)]. 53.11/52.98 Derived: one_one(int) = hAPP(rat,int,archimedean_ceiling(rat),one_one(rat)). [resolve(5608,a,5581,a)]. 53.11/52.98 Derived: ti(int,A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(5608,a,5582,a)]. 53.11/52.98 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(5608,a,5583,a)]. 53.11/52.98 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(5608,a,5584,a)]. 53.11/52.98 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(5608,a,5585,a)]. 53.11/52.98 Derived: one_one(int) = hAPP(rat,int,archim2085082626_floor(rat),one_one(rat)). [resolve(5608,a,5586,a)]. 53.11/52.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5608,a,5587,a)]. 53.11/52.98 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5608,a,5588,a)]. 53.11/52.98 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(5608,a,5589,a)]. 53.11/52.98 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5608,a,5590,a)]. 53.11/52.98 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5608,a,5591,a)]. 53.11/52.98 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(5608,a,5592,a)]. 53.11/52.98 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(5608,a,5593,a)]. 53.11/52.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(5608,a,5594,a)]. 53.11/52.98 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(5608,a,5595,a)]. 53.11/52.98 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(5608,a,5596,a)]. 53.11/52.98 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(5608,a,5597,a)]. 53.34/53.17 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(5608,a,5598,a)]. 53.34/53.17 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(5608,a,5599,a)]. 53.34/53.17 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(5608,a,5600,a)]. 53.34/53.17 Derived: archim2085082626_floor(rat) = ti(fun(rat,int),archim2085082626_floor(rat)). [resolve(5608,a,5601,a)]. 53.34/53.17 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(5608,a,5602,a)]. 53.34/53.17 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(5608,a,5603,a)]. 53.34/53.17 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(5608,a,5604,a)]. 53.34/53.17 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(5608,a,5605,a)]. 53.34/53.17 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(5608,a,5606,a)]. 53.34/53.17 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(5608,a,5607,a)]. 53.34/53.17 5609 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2908_floor__le__zero) # label(axiom). [clausify(2952)]. 53.34/53.17 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))). [resolve(5609,a,5544,a)]. 53.34/53.17 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))). [resolve(5609,a,5608,a)]. 53.34/53.17 5610 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2908_floor__le__zero) # label(axiom). [clausify(2952)]. 53.34/53.17 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))). [resolve(5610,a,5544,a)]. 53.34/53.17 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))). [resolve(5610,a,5608,a)]. 53.54/53.40 5611 -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_2891_floor__mono) # label(axiom). [clausify(2965)]. 53.54/53.40 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(5611,a,5544,a)]. 53.54/53.40 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(5611,a,5608,a)]. 53.54/53.40 5612 -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_2913_floor__add__one) # label(axiom). [clausify(3024)]. 53.54/53.40 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(5612,a,5544,a)]. 53.54/53.40 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(5612,a,5608,a)]. 53.54/53.40 5613 -archim1727834104eiling(A) | zero_zero(int) = hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) # label(fact_3304_ceiling__zero) # label(axiom). [clausify(3273)]. 53.54/53.40 Derived: zero_zero(int) = hAPP(real,int,archimedean_ceiling(real),zero_zero(real)). [resolve(5613,a,5544,a)]. 53.54/53.40 Derived: zero_zero(int) = hAPP(rat,int,archimedean_ceiling(rat),zero_zero(rat)). [resolve(5613,a,5608,a)]. 53.54/53.40 5614 -archim1727834104eiling(A) | zero_zero(int) = hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) # label(fact_2889_floor__zero) # label(axiom). [clausify(3288)]. 53.54/53.40 Derived: zero_zero(int) = hAPP(real,int,archim2085082626_floor(real),zero_zero(real)). [resolve(5614,a,5544,a)]. 53.54/53.40 Derived: zero_zero(int) = hAPP(rat,int,archim2085082626_floor(rat),zero_zero(rat)). [resolve(5614,a,5608,a)]. 53.54/53.40 5615 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3336_ceiling__less__number__of) # label(axiom). [clausify(3311)]. 53.54/53.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5615,a,5544,a)]. 53.54/53.40 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5615,a,5608,a)]. 53.54/53.40 5616 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) # label(fact_3336_ceiling__less__number__of) # label(axiom). [clausify(3311)]. 53.54/53.40 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5616,a,5544,a)]. 53.84/53.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5616,a,5608,a)]. 53.84/53.69 5617 -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_3623_floor__diff__of__int) # label(axiom). [clausify(3474)]. 53.84/53.69 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(5617,a,5544,a)]. 53.84/53.69 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(5617,a,5608,a)]. 53.84/53.69 5618 -archim1727834104eiling(A) | archimedean_ceiling(A) = ti(fun(A,int),archimedean_ceiling(A)) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom). [clausify(3497)]. 53.84/53.69 Derived: archimedean_ceiling(real) = ti(fun(real,int),archimedean_ceiling(real)). [resolve(5618,a,5544,a)]. 53.84/53.69 Derived: archimedean_ceiling(rat) = ti(fun(rat,int),archimedean_ceiling(rat)). [resolve(5618,a,5608,a)]. 53.84/53.69 5619 -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_3624_ceiling__diff__of__int) # label(axiom). [clausify(3516)]. 53.84/53.69 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(5619,a,5544,a)]. 53.84/53.69 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(5619,a,5608,a)]. 53.84/53.69 5620 -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_3319_ceiling__minus) # label(axiom). [clausify(3531)]. 53.84/53.69 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(5620,a,5544,a)]. 53.84/53.69 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(5620,a,5608,a)]. 53.84/53.69 5621 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) # label(fact_3636_ceiling__less__iff) # label(axiom). [clausify(3589)]. 53.84/53.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)). [resolve(5621,a,5544,a)]. 54.03/53.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)). [resolve(5621,a,5608,a)]. 54.03/53.85 5622 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) # label(fact_3636_ceiling__less__iff) # label(axiom). [clausify(3589)]. 54.03/53.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)). [resolve(5622,a,5544,a)]. 54.03/53.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)). [resolve(5622,a,5608,a)]. 54.03/53.85 5623 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3326_one__less__ceiling) # label(axiom). [clausify(3797)]. 54.03/53.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(5623,a,5544,a)]. 54.03/53.85 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(5623,a,5608,a)]. 54.03/53.85 5624 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3326_one__less__ceiling) # label(axiom). [clausify(3797)]. 54.03/53.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(5624,a,5544,a)]. 54.03/53.85 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(5624,a,5608,a)]. 54.03/53.85 5625 -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_3622_ceiling__add__of__int) # label(axiom). [clausify(3805)]. 54.03/53.85 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(5625,a,5544,a)]. 54.03/53.85 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(5625,a,5608,a)]. 54.03/53.85 5626 -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_2890_floor__less__cancel) # label(axiom). [clausify(3807)]. 54.03/53.85 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(5626,a,5544,a)]. 54.21/54.05 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(5626,a,5608,a)]. 54.21/54.05 5627 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3597_floor__of__int) # label(axiom). [clausify(3835)]. 54.21/54.05 Derived: ti(int,A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5627,a,5544,a)]. 54.21/54.05 Derived: ti(int,A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(5627,a,5608,a)]. 54.21/54.05 5628 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3334_ceiling__less__zero) # label(axiom). [clausify(3994)]. 54.21/54.05 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5628,a,5544,a)]. 54.21/54.05 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5628,a,5608,a)]. 54.21/54.05 5629 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),min))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) # label(fact_3334_ceiling__less__zero) # label(axiom). [clausify(3994)]. 54.21/54.05 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),min))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))). [resolve(5629,a,5544,a)]. 54.21/54.05 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,number_number_of(rat),min))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),zero_zero(int))). [resolve(5629,a,5608,a)]. 54.21/54.05 5630 -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_3308_ceiling__number__of) # label(axiom). [clausify(4037)]. 54.21/54.05 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5630,a,5544,a)]. 54.21/54.05 Derived: hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5630,a,5608,a)]. 54.21/54.05 5631 -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_2919_number__of__less__floor) # label(axiom). [clausify(4053)]. 54.21/54.05 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(5631,a,5544,a)]. 54.21/54.05 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(5631,a,5608,a)]. 54.35/54.20 5632 -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_2919_number__of__less__floor) # label(axiom). [clausify(4053)]. 54.35/54.20 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(5632,a,5544,a)]. 54.35/54.20 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(5632,a,5608,a)]. 54.35/54.20 5633 -archim1727834104eiling(A) | hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(A,int,archimedean_ceiling(A),B))) = hAPP(A,int,archimedean_ceiling(A),B) # label(fact_3380_floor__ceiling) # label(axiom). [clausify(4098)]. 54.35/54.20 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),A))) = hAPP(real,int,archimedean_ceiling(real),A). [resolve(5633,a,5544,a)]. 54.35/54.20 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(rat,int,archimedean_ceiling(rat),A))) = hAPP(rat,int,archimedean_ceiling(rat),A). [resolve(5633,a,5608,a)]. 54.35/54.20 5634 -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_2916_floor__diff__number__of) # label(axiom). [clausify(4162)]. 54.35/54.20 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(5634,a,5544,a)]. 54.35/54.20 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(5634,a,5608,a)]. 54.35/54.20 5635 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2906_zero__le__floor) # label(axiom). [clausify(4247)]. 54.35/54.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5635,a,5544,a)]. 54.35/54.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5635,a,5608,a)]. 54.35/54.20 5636 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2906_zero__le__floor) # label(axiom). [clausify(4247)]. 54.35/54.20 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5636,a,5544,a)]. 54.57/54.41 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5636,a,5608,a)]. 54.57/54.41 5637 -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_3305_ceiling__less__cancel) # label(axiom). [clausify(4315)]. 54.57/54.41 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(5637,a,5544,a)]. 54.57/54.41 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(5637,a,5608,a)]. 54.57/54.41 5638 -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_2920_floor__le__number__of) # label(axiom). [clausify(4371)]. 54.57/54.41 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(5638,a,5544,a)]. 54.57/54.41 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(5638,a,5608,a)]. 54.57/54.41 5639 -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_2920_floor__le__number__of) # label(axiom). [clausify(4371)]. 54.57/54.41 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(5639,a,5544,a)]. 54.57/54.41 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(5639,a,5608,a)]. 54.57/54.41 5640 -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_le__of__int__ceiling) # label(axiom). [clausify(4373)]. 54.57/54.41 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(5640,a,5544,a)]. 54.57/54.41 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(5640,a,5608,a)]. 54.57/54.41 5641 -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,ring_1_of_int(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_3633_less__floor__iff) # label(axiom). [clausify(4509)]. 54.81/54.67 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5641,a,5544,a)]. 54.81/54.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5641,a,5608,a)]. 54.81/54.67 5642 -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,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_3633_less__floor__iff) # label(axiom). [clausify(4509)]. 54.81/54.67 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(5642,a,5544,a)]. 54.81/54.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(5642,a,5608,a)]. 54.81/54.67 5643 -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_3630_floor__unique) # label(axiom). [clausify(4631)]. 54.81/54.67 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(5643,a,5544,a)]. 54.81/54.67 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(5643,a,5608,a)]. 54.81/54.67 5644 -archim1727834104eiling(A) | hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(A,int,archim2085082626_floor(A),B))) = hAPP(A,int,archim2085082626_floor(A),B) # label(fact_3382_ceiling__floor) # label(axiom). [clausify(4653)]. 54.81/54.67 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),A))) = hAPP(real,int,archim2085082626_floor(real),A). [resolve(5644,a,5544,a)]. 54.81/54.67 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(rat,int,archim2085082626_floor(rat),A))) = hAPP(rat,int,archim2085082626_floor(rat),A). [resolve(5644,a,5608,a)]. 54.81/54.67 5645 -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_3610_of__int__floor__le) # label(axiom). [clausify(4686)]. 54.81/54.67 5646 -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_3320_ceiling__def) # label(axiom). [clausify(4827)]. 54.81/54.67 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(5646,a,5544,a)]. 56.64/56.55 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(5646,a,5608,a)]. 56.64/56.55 5647 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3618_le__floor__iff) # label(axiom). [clausify(4861)]. 56.64/56.55 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5647,a,5544,a)]. 56.64/56.55 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(5647,a,5608,a)]. 56.64/56.55 5648 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3618_le__floor__iff) # label(axiom). [clausify(4861)]. 56.64/56.55 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),B)). [resolve(5648,a,5544,a)]. 56.64/56.55 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),B)). [resolve(5648,a,5608,a)]. 56.64/56.55 5649 -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_3632_ceiling__correct) # label(axiom). [clausify(4868)]. 56.64/56.55 5650 -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_3632_ceiling__correct) # label(axiom). [clausify(4868)]. 56.64/56.55 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(5650,a,5544,a)]. 56.64/56.55 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(5650,a,5608,a)]. 56.64/56.55 5651 -real_normed_algebra(A) | -power(A) | -topological_space(B) | -hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),C),D)) | hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),hAPP(nat,fun(B,A),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),hAPP(fun(B,A),fun(B,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(B,A),fun(B,fun(nat,A))),combb(A,fun(nat,A),B),power_power(A)),C)),E)),D)) # label(fact_4917_isCont__power) # label(axiom). [clausify(234)]. 56.64/56.55 5652 power(real) # label(arity_RealDef_Oreal___Power_Opower) # label(axiom). [assumption]. 56.64/56.55 5653 power(rat) # label(arity_Rat_Orat___Power_Opower) # label(axiom). [assumption]. 56.64/56.55 Derived: -real_normed_algebra(real) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),D)),C)). [resolve(5651,b,5652,a)]. 56.64/56.55 Derived: -real_normed_algebra(rat) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,rat),fun(A,bool),isCont(A,rat),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,rat),fun(A,bool),isCont(A,rat),hAPP(nat,fun(A,rat),hAPP(fun(A,fun(nat,rat)),fun(nat,fun(A,rat)),combc(A,nat,rat),hAPP(fun(A,rat),fun(A,fun(nat,rat)),hAPP(fun(rat,fun(nat,rat)),fun(fun(A,rat),fun(A,fun(nat,rat))),combb(rat,fun(nat,rat),A),power_power(rat)),B)),D)),C)). [resolve(5651,b,5653,a)]. 56.77/56.63 5654 -power(A) | power_power(A) = ti(fun(A,fun(nat,A)),power_power(A)) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom). [clausify(293)]. 56.77/56.63 Derived: power_power(real) = ti(fun(real,fun(nat,real)),power_power(real)). [resolve(5654,a,5652,a)]. 56.77/56.63 Derived: power_power(rat) = ti(fun(rat,fun(nat,rat)),power_power(rat)). [resolve(5654,a,5653,a)]. 56.77/56.63 5655 -power(A) | zero_zero(nat) = B | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_924_realpow__num__eq__if) # label(axiom). [clausify(729)]. 56.77/56.63 Derived: zero_zero(nat) = A | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A). [resolve(5655,a,5652,a)]. 56.77/56.63 Derived: zero_zero(nat) = A | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A). [resolve(5655,a,5653,a)]. 56.77/56.63 5656 -power(A) | zero_zero(nat) != B | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_924_realpow__num__eq__if) # label(axiom). [clausify(729)]. 56.77/56.63 Derived: zero_zero(nat) != A | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A). [resolve(5656,a,5652,a)]. 56.77/56.63 Derived: zero_zero(nat) != A | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A). [resolve(5656,a,5653,a)]. 56.77/56.63 5657 power(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Power_Opower) # label(axiom). [assumption]. 56.77/56.63 Derived: -real_normed_algebra(code_code_numeral) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,code_code_numeral),fun(A,bool),isCont(A,code_code_numeral),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,code_code_numeral),fun(A,bool),isCont(A,code_code_numeral),hAPP(nat,fun(A,code_code_numeral),hAPP(fun(A,fun(nat,code_code_numeral)),fun(nat,fun(A,code_code_numeral)),combc(A,nat,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(nat,code_code_numeral)),hAPP(fun(code_code_numeral,fun(nat,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(nat,code_code_numeral))),combb(code_code_numeral,fun(nat,code_code_numeral),A),power_power(code_code_numeral)),B)),D)),C)). [resolve(5657,a,5651,b)]. 56.77/56.63 Derived: power_power(code_code_numeral) = ti(fun(code_code_numeral,fun(nat,code_code_numeral)),power_power(code_code_numeral)). [resolve(5657,a,5654,a)]. 56.77/56.63 Derived: zero_zero(nat) = A | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A). [resolve(5657,a,5655,a)]. 56.77/56.63 Derived: 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),B),A). [resolve(5657,a,5656,a)]. 56.77/56.63 5658 -power(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),zero_zero(nat)) # label(fact_190_power__0) # label(axiom). [clausify(862)]. 56.77/56.63 5659 -semiring_0(A) | -power(A) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B) | 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_11_power__0__left__number__of) # label(axiom). [clausify(927)]. 56.83/56.68 5660 -semiring_0(A) | -power(A) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | zero_zero(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_11_power__0__left__number__of) # label(axiom). [clausify(927)]. 56.83/56.68 Derived: -semiring_0(real) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5660,b,5652,a)]. 56.83/56.68 Derived: -semiring_0(rat) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5660,b,5653,a)]. 56.83/56.68 Derived: -semiring_0(code_code_numeral) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(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(5660,b,5657,a)]. 56.83/56.68 5661 -power(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(1037)]. 56.83/56.68 Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)). [resolve(5661,a,5652,a)]. 56.83/56.68 Derived: times_times(rat) = ti(fun(rat,fun(rat,rat)),times_times(rat)). [resolve(5661,a,5653,a)]. 56.83/56.68 Derived: times_times(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),times_times(code_code_numeral)). [resolve(5661,a,5657,a)]. 56.83/56.68 5662 -power(A) | power_power(A) = hAPP(fun(A,fun(A,A)),fun(A,fun(nat,A)),hAPP(A,fun(fun(A,fun(A,A)),fun(A,fun(nat,A))),power_1(A),one_one(A)),times_times(A)) # label(fact_2863_power__power__power) # label(axiom). [clausify(1089)]. 56.83/56.68 Derived: power_power(real) = hAPP(fun(real,fun(real,real)),fun(real,fun(nat,real)),hAPP(real,fun(fun(real,fun(real,real)),fun(real,fun(nat,real))),power_1(real),one_one(real)),times_times(real)). [resolve(5662,a,5652,a)]. 56.83/56.68 Derived: power_power(rat) = hAPP(fun(rat,fun(rat,rat)),fun(rat,fun(nat,rat)),hAPP(rat,fun(fun(rat,fun(rat,rat)),fun(rat,fun(nat,rat))),power_1(rat),one_one(rat)),times_times(rat)). [resolve(5662,a,5653,a)]. 56.83/56.68 Derived: power_power(code_code_numeral) = hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),hAPP(code_code_numeral,fun(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral))),power_1(code_code_numeral),one_one(code_code_numeral)),times_times(code_code_numeral)). [resolve(5662,a,5657,a)]. 56.83/56.68 5663 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) | zero_zero(nat) != C # label(fact_188_power__eq__0__iff) # label(axiom). [clausify(1094)]. 56.83/56.68 Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -mult_zero(real) | zero_zero(real) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) | zero_zero(nat) != B. [resolve(5663,a,5652,a)]. 56.83/56.68 Derived: -zero_neq_one(rat) | -no_zero_divisors(rat) | -mult_zero(rat) | zero_zero(rat) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) | zero_zero(nat) != B. [resolve(5663,a,5653,a)]. 56.83/56.68 Derived: -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -mult_zero(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) | zero_zero(nat) != B. [resolve(5663,a,5657,a)]. 56.83/56.68 5664 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) | zero_zero(A) = ti(A,B) # label(fact_188_power__eq__0__iff) # label(axiom). [clausify(1094)]. 56.83/56.68 Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -mult_zero(real) | zero_zero(real) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) | zero_zero(real) = ti(real,A). [resolve(5664,a,5652,a)]. 57.24/57.13 Derived: -zero_neq_one(rat) | -no_zero_divisors(rat) | -mult_zero(rat) | zero_zero(rat) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) | zero_zero(rat) = ti(rat,A). [resolve(5664,a,5653,a)]. 57.24/57.13 Derived: -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -mult_zero(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) | zero_zero(code_code_numeral) = ti(code_code_numeral,A). [resolve(5664,a,5657,a)]. 57.24/57.13 5665 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) | zero_zero(nat) = C | zero_zero(A) != ti(A,B) # label(fact_188_power__eq__0__iff) # label(axiom). [clausify(1094)]. 57.24/57.13 Derived: -zero_neq_one(real) | -no_zero_divisors(real) | -mult_zero(real) | zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) | zero_zero(nat) = B | zero_zero(real) != ti(real,A). [resolve(5665,a,5652,a)]. 57.24/57.13 Derived: -zero_neq_one(rat) | -no_zero_divisors(rat) | -mult_zero(rat) | zero_zero(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) | zero_zero(nat) = B | zero_zero(rat) != ti(rat,A). [resolve(5665,a,5653,a)]. 57.24/57.13 Derived: -zero_neq_one(code_code_numeral) | -no_zero_divisors(code_code_numeral) | -mult_zero(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) | zero_zero(nat) = B | zero_zero(code_code_numeral) != ti(code_code_numeral,A). [resolve(5665,a,5657,a)]. 57.24/57.13 5666 -power(A) | -semiring_0(A) | zero_zero(nat) = B | zero_zero(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) # label(fact_112_power__0__left) # label(axiom). [clausify(1602)]. 57.24/57.13 Derived: -semiring_0(real) | zero_zero(nat) = A | zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A). [resolve(5666,a,5652,a)]. 57.24/57.13 Derived: -semiring_0(rat) | zero_zero(nat) = A | zero_zero(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A). [resolve(5666,a,5653,a)]. 57.24/57.13 Derived: -semiring_0(code_code_numeral) | zero_zero(nat) = A | zero_zero(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(5666,a,5657,a)]. 57.24/57.13 5667 -power(A) | -semiring_0(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_112_power__0__left) # label(axiom). [clausify(1602)]. 57.24/57.13 5668 -power(A) | -semiring_0(A) | zero_zero(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(nat,nat,suc,B)) # label(fact_1364_power__0__Suc) # label(axiom). [clausify(1665)]. 57.24/57.13 Derived: -semiring_0(real) | zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(nat,nat,suc,A)). [resolve(5668,a,5652,a)]. 57.24/57.13 Derived: -semiring_0(rat) | zero_zero(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(nat,nat,suc,A)). [resolve(5668,a,5653,a)]. 57.24/57.13 Derived: -semiring_0(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),zero_zero(code_code_numeral)),hAPP(nat,nat,suc,A)). [resolve(5668,a,5657,a)]. 57.24/57.13 5669 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) | zero_zero(A) = ti(A,B) # label(fact_89_power__eq__0__iff__number__of) # label(axiom). [clausify(2597)]. 57.24/57.13 5670 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),C) # label(fact_89_power__eq__0__iff__number__of) # label(axiom). [clausify(2597)]. 57.61/57.42 5671 -power(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | zero_zero(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)) | zero_zero(A) != ti(A,B) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) # label(fact_89_power__eq__0__iff__number__of) # label(axiom). [clausify(2597)]. 57.61/57.42 5672 -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_4490_LIMSEQ__pow) # label(axiom). [clausify(2943)]. 57.61/57.42 Derived: -real_normed_algebra(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(5672,b,5652,a)]. 57.61/57.42 Derived: -real_normed_algebra(rat) | -hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(nat,fun(nat,rat),hAPP(fun(nat,fun(nat,rat)),fun(nat,fun(nat,rat)),combc(nat,nat,rat),hAPP(fun(nat,rat),fun(nat,fun(nat,rat)),hAPP(fun(rat,fun(nat,rat)),fun(fun(nat,rat),fun(nat,fun(nat,rat))),combb(rat,fun(nat,rat),nat),power_power(rat)),A)),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C)),sequentially)). [resolve(5672,b,5653,a)]. 57.61/57.42 Derived: -real_normed_algebra(code_code_numeral) | -hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(code_code_numeral,fun(filter(nat),bool),hAPP(fun(nat,code_code_numeral),fun(code_code_numeral,fun(filter(nat),bool)),tendsto(nat,code_code_numeral),hAPP(nat,fun(nat,code_code_numeral),hAPP(fun(nat,fun(nat,code_code_numeral)),fun(nat,fun(nat,code_code_numeral)),combc(nat,nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(nat,code_code_numeral)),hAPP(fun(code_code_numeral,fun(nat,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(nat,code_code_numeral))),combb(code_code_numeral,fun(nat,code_code_numeral),nat),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)),sequentially)). [resolve(5672,b,5657,a)]. 57.61/57.42 5673 power(complex) # label(arity_Complex_Ocomplex___Power_Opower) # label(axiom). [assumption]. 57.61/57.42 Derived: -real_normed_algebra(complex) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),D)),C)). [resolve(5673,a,5651,b)]. 57.61/57.45 Derived: power_power(complex) = ti(fun(complex,fun(nat,complex)),power_power(complex)). [resolve(5673,a,5654,a)]. 57.61/57.45 Derived: zero_zero(nat) = A | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A). [resolve(5673,a,5655,a)]. 57.61/57.45 Derived: zero_zero(nat) != A | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A). [resolve(5673,a,5656,a)]. 57.61/57.45 Derived: -semiring_0(complex) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5673,a,5660,b)]. 57.61/57.45 Derived: times_times(complex) = ti(fun(complex,fun(complex,complex)),times_times(complex)). [resolve(5673,a,5661,a)]. 57.61/57.45 Derived: power_power(complex) = hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(nat,complex)),hAPP(complex,fun(fun(complex,fun(complex,complex)),fun(complex,fun(nat,complex))),power_1(complex),one_one(complex)),times_times(complex)). [resolve(5673,a,5662,a)]. 57.61/57.45 Derived: -zero_neq_one(complex) | -no_zero_divisors(complex) | -mult_zero(complex) | zero_zero(complex) != hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) | zero_zero(nat) != B. [resolve(5673,a,5663,a)]. 57.61/57.45 Derived: -zero_neq_one(complex) | -no_zero_divisors(complex) | -mult_zero(complex) | zero_zero(complex) != hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) | zero_zero(complex) = ti(complex,A). [resolve(5673,a,5664,a)]. 57.61/57.45 Derived: -zero_neq_one(complex) | -no_zero_divisors(complex) | -mult_zero(complex) | zero_zero(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) | zero_zero(nat) = B | zero_zero(complex) != ti(complex,A). [resolve(5673,a,5665,a)]. 57.61/57.45 Derived: -semiring_0(complex) | zero_zero(nat) = A | zero_zero(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A). [resolve(5673,a,5666,a)]. 57.61/57.45 Derived: -semiring_0(complex) | zero_zero(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(nat,nat,suc,A)). [resolve(5673,a,5668,a)]. 57.61/57.45 Derived: -real_normed_algebra(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(5673,a,5672,b)]. 57.61/57.45 5674 -comm_monoid_add(A) | -power(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(A,fun(nat,A),power_power(A),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) # label(fact_4201_lemma__realpow__rev__sumr) # label(axiom). [clausify(3081)]. 57.61/57.45 Derived: -comm_monoid_add(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(real,fun(nat,real),power_power(real),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5674,b,5652,a)]. 57.61/57.45 Derived: -comm_monoid_add(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(rat,fun(nat,rat),power_power(rat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5674,b,5653,a)]. 57.61/57.45 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5674,b,5657,a)]. 57.73/57.55 Derived: -comm_monoid_add(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(complex,fun(nat,complex),power_power(complex),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5674,b,5673,a)]. 57.73/57.55 5675 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom). [assumption]. 57.73/57.55 Derived: -real_normed_algebra(int) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,int),fun(A,bool),isCont(A,int),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,int),fun(A,bool),isCont(A,int),hAPP(nat,fun(A,int),hAPP(fun(A,fun(nat,int)),fun(nat,fun(A,int)),combc(A,nat,int),hAPP(fun(A,int),fun(A,fun(nat,int)),hAPP(fun(int,fun(nat,int)),fun(fun(A,int),fun(A,fun(nat,int))),combb(int,fun(nat,int),A),power_power(int)),B)),D)),C)). [resolve(5675,a,5651,b)]. 57.73/57.57 Derived: power_power(int) = ti(fun(int,fun(nat,int)),power_power(int)). [resolve(5675,a,5654,a)]. 57.73/57.57 Derived: zero_zero(nat) = A | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A). [resolve(5675,a,5655,a)]. 57.73/57.57 Derived: zero_zero(nat) != A | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A). [resolve(5675,a,5656,a)]. 57.73/57.57 Derived: -semiring_0(int) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)). [resolve(5675,a,5660,b)]. 57.73/57.57 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(5675,a,5661,a)]. 57.73/57.57 Derived: power_power(int) = hAPP(fun(int,fun(int,int)),fun(int,fun(nat,int)),hAPP(int,fun(fun(int,fun(int,int)),fun(int,fun(nat,int))),power_1(int),one_one(int)),times_times(int)). [resolve(5675,a,5662,a)]. 57.73/57.57 Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | zero_zero(int) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) | zero_zero(nat) != B. [resolve(5675,a,5663,a)]. 57.73/57.57 Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | zero_zero(int) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) | zero_zero(int) = ti(int,A). [resolve(5675,a,5664,a)]. 57.73/57.57 Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | zero_zero(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) | zero_zero(nat) = B | zero_zero(int) != ti(int,A). [resolve(5675,a,5665,a)]. 57.73/57.57 Derived: -semiring_0(int) | zero_zero(nat) = A | zero_zero(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A). [resolve(5675,a,5666,a)]. 57.73/57.57 Derived: -semiring_0(int) | zero_zero(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(nat,nat,suc,A)). [resolve(5675,a,5668,a)]. 57.73/57.57 Derived: -real_normed_algebra(int) | -hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(nat,fun(nat,int),hAPP(fun(nat,fun(nat,int)),fun(nat,fun(nat,int)),combc(nat,nat,int),hAPP(fun(nat,int),fun(nat,fun(nat,int)),hAPP(fun(int,fun(nat,int)),fun(fun(nat,int),fun(nat,fun(nat,int))),combb(int,fun(nat,int),nat),power_power(int)),A)),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C)),sequentially)). [resolve(5675,a,5672,b)]. 57.73/57.57 Derived: -comm_monoid_add(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(int,fun(nat,int),power_power(int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5675,a,5674,b)]. 58.11/57.96 5676 power(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Power_Opower) # label(axiom). [assumption]. 58.11/57.96 Derived: -real_normed_algebra(quickcheck_code_int) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,quickcheck_code_int),fun(A,bool),isCont(A,quickcheck_code_int),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,quickcheck_code_int),fun(A,bool),isCont(A,quickcheck_code_int),hAPP(nat,fun(A,quickcheck_code_int),hAPP(fun(A,fun(nat,quickcheck_code_int)),fun(nat,fun(A,quickcheck_code_int)),combc(A,nat,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(nat,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(nat,quickcheck_code_int))),combb(quickcheck_code_int,fun(nat,quickcheck_code_int),A),power_power(quickcheck_code_int)),B)),D)),C)). [resolve(5676,a,5651,b)]. 58.11/57.96 Derived: power_power(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),power_power(quickcheck_code_int)). [resolve(5676,a,5654,a)]. 58.11/57.96 Derived: zero_zero(nat) = A | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A). [resolve(5676,a,5655,a)]. 58.11/57.96 Derived: 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),B),A). [resolve(5676,a,5656,a)]. 58.11/57.96 Derived: -semiring_0(quickcheck_code_int) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),A) | zero_zero(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(5676,a,5660,b)]. 58.11/57.96 Derived: times_times(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),times_times(quickcheck_code_int)). [resolve(5676,a,5661,a)]. 58.11/57.96 Derived: power_power(quickcheck_code_int) = hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),hAPP(quickcheck_code_int,fun(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int))),power_1(quickcheck_code_int),one_one(quickcheck_code_int)),times_times(quickcheck_code_int)). [resolve(5676,a,5662,a)]. 58.11/57.96 Derived: -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -mult_zero(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) | zero_zero(nat) != B. [resolve(5676,a,5663,a)]. 58.11/57.96 Derived: -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -mult_zero(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) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A). [resolve(5676,a,5664,a)]. 58.11/57.96 Derived: -zero_neq_one(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | -mult_zero(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) | zero_zero(nat) = B | zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A). [resolve(5676,a,5665,a)]. 58.11/57.96 Derived: -semiring_0(quickcheck_code_int) | zero_zero(nat) = A | zero_zero(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(5676,a,5666,a)]. 58.11/57.96 Derived: -semiring_0(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),zero_zero(quickcheck_code_int)),hAPP(nat,nat,suc,A)). [resolve(5676,a,5668,a)]. 58.11/57.96 Derived: -real_normed_algebra(quickcheck_code_int) | -hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(quickcheck_code_int,fun(filter(nat),bool),hAPP(fun(nat,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(nat),bool)),tendsto(nat,quickcheck_code_int),hAPP(nat,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(nat,quickcheck_code_int)),fun(nat,fun(nat,quickcheck_code_int)),combc(nat,nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(nat,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(nat,quickcheck_code_int))),combb(quickcheck_code_int,fun(nat,quickcheck_code_int),nat),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)),sequentially)). [resolve(5676,a,5672,b)]. 58.11/57.96 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5676,a,5674,b)]. 58.11/57.99 5677 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom). [assumption]. 58.11/57.99 Derived: -real_normed_algebra(nat) | -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,nat),fun(A,bool),isCont(A,nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,nat),fun(A,bool),isCont(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),power_power(nat)),B)),D)),C)). [resolve(5677,a,5651,b)]. 58.11/57.99 Derived: power_power(nat) = ti(fun(nat,fun(nat,nat)),power_power(nat)). [resolve(5677,a,5654,a)]. 58.11/57.99 Derived: zero_zero(nat) = A | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A). [resolve(5677,a,5655,a)]. 58.11/57.99 Derived: zero_zero(nat) != A | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A). [resolve(5677,a,5656,a)]. 58.11/57.99 Derived: -semiring_0(nat) | zero_zero(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)). [resolve(5677,a,5660,b)]. 58.11/57.99 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(5677,a,5661,a)]. 58.11/57.99 Derived: power_power(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),power_1(nat),one_one(nat)),times_times(nat)). [resolve(5677,a,5662,a)]. 58.11/57.99 Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) | zero_zero(nat) != B. [resolve(5677,a,5663,a)]. 58.11/57.99 Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) | zero_zero(nat) = ti(nat,A). [resolve(5677,a,5664,a)]. 58.11/57.99 Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) | zero_zero(nat) = B | zero_zero(nat) != ti(nat,A). [resolve(5677,a,5665,a)]. 58.11/57.99 Derived: -semiring_0(nat) | zero_zero(nat) = A | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A). [resolve(5677,a,5666,a)]. 58.11/57.99 Derived: -semiring_0(nat) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(nat,nat,suc,A)). [resolve(5677,a,5668,a)]. 58.11/57.99 Derived: -real_normed_algebra(nat) | -hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(nat,fun(filter(nat),bool),hAPP(fun(nat,nat),fun(nat,fun(filter(nat),bool)),tendsto(nat,nat),hAPP(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),power_power(nat)),A)),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)),sequentially)). [resolve(5677,a,5672,b)]. 58.11/57.99 Derived: -comm_monoid_add(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,nat),power_power(nat),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B))). [resolve(5677,a,5674,b)]. 58.43/58.32 5678 -power(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_1371_power__Suc) # label(axiom). [clausify(3998)]. 58.43/58.32 5679 -real_normed_algebra(A) | -power(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(nat,fun(B,A),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),hAPP(fun(B,A),fun(B,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(B,A),fun(B,fun(nat,A))),combb(A,fun(nat,A),B),power_power(A)),C)),F)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),F)),hAPP(B,filter(B),at(B),E))) # label(fact_4585_LIM__power) # label(axiom). [clausify(4188)]. 58.43/58.32 Derived: -real_normed_algebra(real) | -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(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(5679,b,5652,a)]. 58.43/58.32 Derived: -real_normed_algebra(rat) | -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(rat,fun(filter(A),bool),hAPP(fun(A,rat),fun(rat,fun(filter(A),bool)),tendsto(A,rat),B),C),hAPP(A,filter(A),at(A),D))) | 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(nat,fun(A,rat),hAPP(fun(A,fun(nat,rat)),fun(nat,fun(A,rat)),combc(A,nat,rat),hAPP(fun(A,rat),fun(A,fun(nat,rat)),hAPP(fun(rat,fun(nat,rat)),fun(fun(A,rat),fun(A,fun(nat,rat))),combb(rat,fun(nat,rat),A),power_power(rat)),B)),E)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5679,b,5653,a)]. 58.43/58.32 Derived: -real_normed_algebra(code_code_numeral) | -topological_space(A) | -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),B),C),hAPP(A,filter(A),at(A),D))) | 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(nat,fun(A,code_code_numeral),hAPP(fun(A,fun(nat,code_code_numeral)),fun(nat,fun(A,code_code_numeral)),combc(A,nat,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(nat,code_code_numeral)),hAPP(fun(code_code_numeral,fun(nat,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(nat,code_code_numeral))),combb(code_code_numeral,fun(nat,code_code_numeral),A),power_power(code_code_numeral)),B)),E)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5679,b,5657,a)]. 58.43/58.32 Derived: -real_normed_algebra(complex) | -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(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(5679,b,5673,a)]. 61.23/61.09 Derived: -real_normed_algebra(int) | -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(int,fun(filter(A),bool),hAPP(fun(A,int),fun(int,fun(filter(A),bool)),tendsto(A,int),B),C),hAPP(A,filter(A),at(A),D))) | 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(nat,fun(A,int),hAPP(fun(A,fun(nat,int)),fun(nat,fun(A,int)),combc(A,nat,int),hAPP(fun(A,int),fun(A,fun(nat,int)),hAPP(fun(int,fun(nat,int)),fun(fun(A,int),fun(A,fun(nat,int))),combb(int,fun(nat,int),A),power_power(int)),B)),E)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5679,b,5675,a)]. 61.23/61.09 Derived: -real_normed_algebra(quickcheck_code_int) | -topological_space(A) | -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),B),C),hAPP(A,filter(A),at(A),D))) | 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(nat,fun(A,quickcheck_code_int),hAPP(fun(A,fun(nat,quickcheck_code_int)),fun(nat,fun(A,quickcheck_code_int)),combc(A,nat,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(nat,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(nat,quickcheck_code_int))),combb(quickcheck_code_int,fun(nat,quickcheck_code_int),A),power_power(quickcheck_code_int)),B)),E)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5679,b,5676,a)]. 61.23/61.09 Derived: -real_normed_algebra(nat) | -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(nat,fun(filter(A),bool),hAPP(fun(A,nat),fun(nat,fun(filter(A),bool)),tendsto(A,nat),B),C),hAPP(A,filter(A),at(A),D))) | 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),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),power_power(nat)),B)),E)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5679,b,5677,a)]. 61.23/61.09 5680 sgn_if(int) # label(arity_Int_Oint___Groups_Osgn__if) # label(axiom). [assumption]. 61.23/61.09 5681 -sgn_if(A) | sgn_sgn(A) = ti(fun(A,A),sgn_sgn(A)) # label(tsy_c_Groups_Osgn__class_Osgn_1_res) # label(axiom). [clausify(54)]. 61.23/61.09 5682 -sgn_if(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2315_sgn__if) # label(axiom). [clausify(228)]. 61.23/61.09 5683 -sgn_if(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2315_sgn__if) # label(axiom). [clausify(228)]. 61.23/61.09 5684 -sgn_if(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2315_sgn__if) # label(axiom). [clausify(228)]. 61.23/61.09 Derived: sgn_sgn(int) = ti(fun(int,int),sgn_sgn(int)). [resolve(5680,a,5681,a)]. 61.23/61.09 5685 sgn_if(real) # label(arity_RealDef_Oreal___Groups_Osgn__if) # label(axiom). [assumption]. 61.23/61.09 Derived: sgn_sgn(real) = ti(fun(real,real),sgn_sgn(real)). [resolve(5685,a,5681,a)]. 65.22/65.10 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,sgn_sgn(real),A). [resolve(5685,a,5682,a)]. 65.22/65.10 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,uminus_uminus(real),one_one(real)). [resolve(5685,a,5683,a)]. 65.22/65.10 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | one_one(real) = hAPP(real,real,sgn_sgn(real),A). [resolve(5685,a,5684,a)]. 65.22/65.10 5686 -sgn_if(A) | zero_zero(A) = hAPP(A,A,sgn_sgn(A),zero_zero(A)) # label(fact_2260_sgn0) # label(axiom). [clausify(2491)]. 65.22/65.10 Derived: zero_zero(int) = hAPP(int,int,sgn_sgn(int),zero_zero(int)). [resolve(5686,a,5680,a)]. 65.22/65.10 Derived: zero_zero(real) = hAPP(real,real,sgn_sgn(real),zero_zero(real)). [resolve(5686,a,5685,a)]. 65.22/65.10 5687 sgn_if(rat) # label(arity_Rat_Orat___Groups_Osgn__if) # label(axiom). [assumption]. 65.22/65.10 Derived: sgn_sgn(rat) = ti(fun(rat,rat),sgn_sgn(rat)). [resolve(5687,a,5681,a)]. 65.22/65.10 Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5687,a,5682,a)]. 65.22/65.10 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,sgn_sgn(rat),A) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)). [resolve(5687,a,5683,a)]. 65.22/65.10 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | one_one(rat) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5687,a,5684,a)]. 65.22/65.10 Derived: zero_zero(rat) = hAPP(rat,rat,sgn_sgn(rat),zero_zero(rat)). [resolve(5687,a,5686,a)]. 65.22/65.10 5688 comm_ring_1(int) # label(arity_Int_Oint___Rings_Ocomm__ring__1) # label(axiom). [assumption]. 65.22/65.10 5689 -comm_ring_1(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(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_2493_minus__one__even__power) # label(axiom). [clausify(55)]. 65.22/65.10 5690 -comm_ring_1(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_2480_neg__power__if) # label(axiom). [clausify(131)]. 65.22/65.10 5691 -comm_ring_1(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_2480_neg__power__if) # label(axiom). [clausify(131)]. 65.22/65.10 5692 -comm_ring_1(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(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_2494_minus__one__even__odd__power) # label(axiom). [clausify(486)]. 65.22/65.10 5693 -comm_ring_1(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_2494_minus__one__even__odd__power) # label(axiom). [clausify(486)]. 65.22/65.10 5694 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = 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,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_1481_realpow__two__diff) # label(axiom). [clausify(1019)]. 65.22/65.10 5695 -comm_ring_1(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_2478_power__minus__odd) # label(axiom). [clausify(1744)]. 65.22/65.10 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,uminus_uminus(int),one_one(int))),A). [resolve(5688,a,5689,a)]. 65.45/65.30 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),B)),A). [resolve(5688,a,5690,a)]. 65.45/65.30 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A). [resolve(5688,a,5691,a)]. 65.45/65.30 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A). [resolve(5688,a,5693,a)]. 65.45/65.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = 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,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))). [resolve(5688,a,5694,a)]. 65.45/65.30 5696 -comm_ring_1(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(A,A,uminus_uminus(A),one_one(A)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_2492_minus__one__odd__power) # label(axiom). [clausify(1775)]. 65.45/65.30 5697 -comm_ring_1(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_2479_Parity_Opower__minus__even) # label(axiom). [clausify(1834)]. 65.45/65.30 5698 -comm_ring_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),minus_minus(A),C),D))) # label(fact_711_dvd__diff) # label(axiom). [clausify(2101)]. 65.45/65.30 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),minus_minus(int),B),C))). [resolve(5698,a,5688,a)]. 65.45/65.30 5699 -comm_ring_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(A,A,uminus_uminus(A),B)),C)) # label(fact_1919_minus__dvd__iff) # label(axiom). [clausify(2139)]. 65.45/65.30 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(int,int,uminus_uminus(int),A)),B)). [resolve(5699,a,5688,a)]. 65.45/65.30 5700 -comm_ring_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(A,A,uminus_uminus(A),B)),C)) # label(fact_1919_minus__dvd__iff) # label(axiom). [clausify(2139)]. 65.45/65.30 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(int,int,uminus_uminus(int),A)),B)). [resolve(5700,a,5688,a)]. 65.45/65.30 5701 comm_ring_1(rat) # label(arity_Rat_Orat___Rings_Ocomm__ring__1) # label(axiom). [assumption]. 65.45/65.30 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(rat,rat,uminus_uminus(rat),one_one(rat))),A). [resolve(5701,a,5689,a)]. 65.45/65.30 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(rat,rat,uminus_uminus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A). [resolve(5701,a,5690,a)]. 65.45/65.30 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A). [resolve(5701,a,5691,a)]. 65.45/65.30 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),A). [resolve(5701,a,5693,a)]. 66.04/65.85 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(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),A),B)) = 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,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))). [resolve(5701,a,5694,a)]. 66.04/65.85 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),minus_minus(rat),B),C))). [resolve(5701,a,5698,a)]. 66.04/65.85 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(rat,rat,uminus_uminus(rat),A)),B)). [resolve(5701,a,5699,a)]. 66.04/65.85 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(rat,rat,uminus_uminus(rat),A)),B)). [resolve(5701,a,5700,a)]. 66.04/65.85 5702 comm_ring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__ring__1) # label(axiom). [assumption]. 66.04/65.85 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(real,real,uminus_uminus(real),one_one(real))),A). [resolve(5702,a,5689,a)]. 66.04/65.85 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),B)),A). [resolve(5702,a,5690,a)]. 66.04/65.85 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A). [resolve(5702,a,5691,a)]. 66.04/65.85 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),one_one(real))),A). [resolve(5702,a,5693,a)]. 66.04/65.85 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(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),A),B)) = 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,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))). [resolve(5702,a,5694,a)]. 66.04/65.85 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),minus_minus(real),B),C))). [resolve(5702,a,5698,a)]. 66.04/65.85 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(real,real,uminus_uminus(real),A)),B)). [resolve(5702,a,5699,a)]. 66.04/65.85 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(real,real,uminus_uminus(real),A)),B)). [resolve(5702,a,5700,a)]. 66.04/65.85 5703 -comm_ring_1(A) | -real_normed_algebra(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f594(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_4682_LIMSEQ__setprod) # label(axiom). [clausify(3321)]. 66.04/65.85 Derived: -real_normed_algebra(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f594(A,int,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(A,bool),fun(nat,int),hAPP(fun(nat,fun(fun(A,bool),int)),fun(fun(A,bool),fun(nat,int)),combc(nat,fun(A,bool),int),hAPP(fun(nat,fun(A,int)),fun(nat,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(nat,fun(A,int)),fun(nat,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),nat),big_co302546470etprod(A,int)),hAPP(fun(A,fun(nat,int)),fun(nat,fun(A,int)),combc(A,nat,int),B))),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)),sequentially)). [resolve(5703,a,5688,a)]. 66.04/65.85 Derived: -real_normed_algebra(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f594(A,rat,B,C,D)),D)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(A,bool),fun(nat,rat),hAPP(fun(nat,fun(fun(A,bool),rat)),fun(fun(A,bool),fun(nat,rat)),combc(nat,fun(A,bool),rat),hAPP(fun(nat,fun(A,rat)),fun(nat,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(nat,fun(A,rat)),fun(nat,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),nat),big_co302546470etprod(A,rat)),hAPP(fun(A,fun(nat,rat)),fun(nat,fun(A,rat)),combc(A,nat,rat),B))),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D)),sequentially)). [resolve(5703,a,5701,a)]. 66.04/65.85 Derived: -real_normed_algebra(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f594(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(5703,a,5702,a)]. 66.04/65.85 5704 -comm_ring_1(A) | -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),hAPP(B,fun(nat,A),C,f594(B,A,C,D,E))),hAPP(B,A,D,f594(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_4682_LIMSEQ__setprod) # label(axiom). [clausify(3321)]. 66.04/65.85 Derived: -real_normed_algebra(int) | -hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(A,fun(nat,int),B,f594(A,int,B,C,D))),hAPP(A,int,C,f594(A,int,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(int,fun(filter(nat),bool),hAPP(fun(nat,int),fun(int,fun(filter(nat),bool)),tendsto(nat,int),hAPP(fun(A,bool),fun(nat,int),hAPP(fun(nat,fun(fun(A,bool),int)),fun(fun(A,bool),fun(nat,int)),combc(nat,fun(A,bool),int),hAPP(fun(nat,fun(A,int)),fun(nat,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(nat,fun(A,int)),fun(nat,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),nat),big_co302546470etprod(A,int)),hAPP(fun(A,fun(nat,int)),fun(nat,fun(A,int)),combc(A,nat,int),B))),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)),sequentially)). [resolve(5704,a,5688,a)]. 66.34/66.17 Derived: -real_normed_algebra(rat) | -hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(A,fun(nat,rat),B,f594(A,rat,B,C,D))),hAPP(A,rat,C,f594(A,rat,B,C,D))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(rat,fun(filter(nat),bool),hAPP(fun(nat,rat),fun(rat,fun(filter(nat),bool)),tendsto(nat,rat),hAPP(fun(A,bool),fun(nat,rat),hAPP(fun(nat,fun(fun(A,bool),rat)),fun(fun(A,bool),fun(nat,rat)),combc(nat,fun(A,bool),rat),hAPP(fun(nat,fun(A,rat)),fun(nat,fun(fun(A,bool),rat)),hAPP(fun(fun(A,rat),fun(fun(A,bool),rat)),fun(fun(nat,fun(A,rat)),fun(nat,fun(fun(A,bool),rat))),combb(fun(A,rat),fun(fun(A,bool),rat),nat),big_co302546470etprod(A,rat)),hAPP(fun(A,fun(nat,rat)),fun(nat,fun(A,rat)),combc(A,nat,rat),B))),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),D)),sequentially)). [resolve(5704,a,5701,a)]. 66.34/66.17 Derived: -real_normed_algebra(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,f594(A,real,B,C,D))),hAPP(A,real,C,f594(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(5704,a,5702,a)]. 66.34/66.17 5705 comm_ring_1(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__ring__1) # label(axiom). [assumption]. 66.34/66.17 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(complex,complex,uminus_uminus(complex),one_one(complex))),A). [resolve(5705,a,5689,a)]. 66.34/66.17 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),B)),A). [resolve(5705,a,5690,a)]. 66.34/66.17 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),B)),A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A). [resolve(5705,a,5691,a)]. 66.34/66.17 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(complex,complex,uminus_uminus(complex),one_one(complex)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),A). [resolve(5705,a,5693,a)]. 66.34/66.17 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),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),B)) = 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,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))). [resolve(5705,a,5694,a)]. 66.50/66.32 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),minus_minus(complex),B),C))). [resolve(5705,a,5698,a)]. 66.50/66.32 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(complex,complex,uminus_uminus(complex),A)),B)). [resolve(5705,a,5699,a)]. 66.50/66.32 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(complex,complex,uminus_uminus(complex),A)),B)). [resolve(5705,a,5700,a)]. 66.50/66.32 Derived: -real_normed_algebra(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f594(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(5705,a,5703,a)]. 66.50/66.32 Derived: -real_normed_algebra(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,f594(A,complex,B,C,D))),hAPP(A,complex,C,f594(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(5705,a,5704,a)]. 66.50/66.32 5706 -comm_ring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_1920_dvd__minus__iff) # label(axiom). [clausify(3883)]. 66.50/66.32 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5706,a,5688,a)]. 66.50/66.32 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5706,a,5701,a)]. 66.50/66.32 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,uminus_uminus(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5706,a,5702,a)]. 66.50/66.32 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,uminus_uminus(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)). [resolve(5706,a,5705,a)]. 69.40/69.22 5707 -comm_ring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_1920_dvd__minus__iff) # label(axiom). [clausify(3883)]. 69.40/69.22 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5707,a,5688,a)]. 69.40/69.22 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,uminus_uminus(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5707,a,5701,a)]. 69.40/69.22 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,uminus_uminus(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5707,a,5702,a)]. 69.40/69.22 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(complex,complex,uminus_uminus(complex),B))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)). [resolve(5707,a,5705,a)]. 69.40/69.22 5708 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_1966_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom). [clausify(4428)]. 69.40/69.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A) = hAPP(int,int,uminus_uminus(int),A). [resolve(5708,a,5688,a)]. 69.40/69.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),one_one(rat))),A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5708,a,5701,a)]. 69.40/69.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),one_one(real))),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5708,a,5702,a)]. 69.40/69.22 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),one_one(complex))),A) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(5708,a,5705,a)]. 69.40/69.22 5709 -comm_ring_1(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_1969_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom). [clausify(4731)]. 69.40/69.22 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(5709,a,5688,a)]. 69.40/69.22 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(5709,a,5701,a)]. 69.40/69.22 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(5709,a,5702,a)]. 69.40/69.22 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(5709,a,5705,a)]. 69.40/69.22 5710 t2_space(complex) # label(arity_Complex_Ocomplex___RealVector_Ot2__space) # label(axiom). [assumption]. 69.40/69.22 5711 -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_4119_summable__sums) # label(axiom). [clausify(58)]. 69.40/69.22 5712 -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_4792_tendsto__unique) # label(axiom). [clausify(323)]. 69.40/69.22 5713 -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_4120_sums__iff) # label(axiom). [clausify(475)]. 69.44/69.26 5714 -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_4120_sums__iff) # label(axiom). [clausify(475)]. 69.44/69.26 5715 -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) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) # label(fact_4120_sums__iff) # label(axiom). [clausify(475)]. 69.44/69.26 5716 -t2_space(A) | -comm_monoid_add(A) | zero_zero(A) = hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))) # label(fact_3995_suminf__zero) # label(axiom). [clausify(835)]. 69.44/69.26 5717 -comm_monoid_add(A) | -t2_space(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f244(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_4318_series__zero) # label(axiom). [clausify(1492)]. 69.44/69.26 5718 -comm_monoid_add(A) | -t2_space(A) | zero_zero(A) != hAPP(nat,A,B,f244(A,B,C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)))) # label(fact_4318_series__zero) # label(axiom). [clausify(1492)]. 69.44/69.26 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(5710,a,5711,b)]. 69.44/69.26 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(5710,a,5712,a)]. 69.44/69.26 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(5710,a,5713,b)]. 69.44/69.26 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(5710,a,5714,b)]. 69.44/69.26 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) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)). [resolve(5710,a,5715,b)]. 69.44/69.26 Derived: -comm_monoid_add(complex) | zero_zero(complex) = hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))). [resolve(5710,a,5716,a)]. 69.44/69.26 Derived: -comm_monoid_add(complex) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f244(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(5710,a,5717,b)]. 69.44/69.26 Derived: -comm_monoid_add(complex) | zero_zero(complex) != hAPP(nat,complex,A,f244(complex,A,B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5710,a,5718,b)]. 69.44/69.26 5719 -comm_monoid_add(A) | -t2_space(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_4521_summable__sumr__LIMSEQ__suminf) # label(axiom). [clausify(1924)]. 71.14/70.96 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(5719,b,5710,a)]. 71.14/70.96 5720 -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_4116_sums__unique) # label(axiom). [clausify(4400)]. 71.14/70.96 5721 t2_space(real) # label(arity_RealDef_Oreal___RealVector_Ot2__space) # label(axiom). [assumption]. 71.14/70.96 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(5721,a,5711,b)]. 71.14/70.96 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(5721,a,5712,a)]. 71.14/70.96 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(5721,a,5713,b)]. 71.14/70.96 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(5721,a,5714,b)]. 71.14/70.96 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) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)). [resolve(5721,a,5715,b)]. 71.14/70.96 Derived: -comm_monoid_add(real) | zero_zero(real) = hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))). [resolve(5721,a,5716,a)]. 71.14/70.96 Derived: -comm_monoid_add(real) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f244(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(5721,a,5717,b)]. 71.14/70.96 Derived: -comm_monoid_add(real) | zero_zero(real) != hAPP(nat,real,A,f244(real,A,B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(5721,a,5718,b)]. 71.14/70.96 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(5721,a,5719,b)]. 73.36/73.17 5722 comm_monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 73.36/73.17 5723 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f13(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_4797_setprod__1_H) # label(axiom). [clausify(60)]. 73.36/73.17 5724 -comm_monoid_mult(A) | one_one(A) != hAPP(B,A,C,f13(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_4797_setprod__1_H) # label(axiom). [clausify(60)]. 73.36/73.17 5725 -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_3978_setprod__infinite) # label(axiom). [clausify(172)]. 73.36/73.18 5726 -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_394_power__mult__distrib) # label(axiom). [clausify(397)]. 73.36/73.18 5727 -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_3983_setprod__delta_H) # label(axiom). [clausify(633)]. 73.36/73.18 5728 -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_3983_setprod__delta_H) # label(axiom). [clausify(633)]. 73.36/73.18 5729 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_392_mult_Ocomm__neutral) # label(axiom). [clausify(942)]. 73.36/73.18 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5722,a,5723,a)]. 73.36/73.18 Derived: one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,B,f13(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(5722,a,5724,a)]. 73.36/73.18 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(5722,a,5725,a)]. 73.36/73.18 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(5722,a,5727,a)]. 73.36/73.20 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)) | 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(5722,a,5728,a)]. 73.36/73.20 5730 -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),f172(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_4794_setprod_Ocong) # label(axiom). [clausify(1072)]. 73.36/73.20 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),f172(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(5730,a,5722,a)]. 73.36/73.20 5731 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f172(B,A,E,D,C)) != hAPP(B,A,E,f172(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_4794_setprod_Ocong) # label(axiom). [clausify(1072)]. 73.36/73.20 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f172(A,quickcheck_code_int,D,C,B)) != hAPP(A,quickcheck_code_int,D,f172(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(5731,a,5722,a)]. 73.36/73.24 5732 -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_3982_setprod__delta) # label(axiom). [clausify(1309)]. 73.36/73.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5732,a,5722,a)]. 73.36/73.24 5733 -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_3982_setprod__delta) # label(axiom). [clausify(1309)]. 73.36/73.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),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(5733,a,5722,a)]. 73.45/73.27 5734 comm_monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 73.45/73.27 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5734,a,5723,a)]. 73.45/73.27 Derived: one_one(complex) != hAPP(A,complex,B,f13(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(5734,a,5724,a)]. 73.45/73.27 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(5734,a,5725,a)]. 73.45/73.27 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),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(5734,a,5727,a)]. 73.45/73.27 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),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(5734,a,5728,a)]. 73.45/73.27 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),f172(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(5734,a,5730,a)]. 73.45/73.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f172(A,complex,D,C,B)) != hAPP(A,complex,D,f172(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(5734,a,5731,a)]. 73.45/73.27 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),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(5734,a,5732,a)]. 73.54/73.39 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(5734,a,5733,a)]. 73.54/73.39 5735 -ring_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,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_3956_of__int__setprod) # label(axiom). [clausify(1624)]. 73.54/73.39 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(5735,b,5722,a)]. 73.54/73.39 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(5735,b,5734,a)]. 73.54/73.39 5736 -comm_monoid_mult(A) | -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) # label(fact_3971_transfer__nat__int__sum__prod_I2_J) # label(axiom). [clausify(1889)]. 73.54/73.40 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5736,a,5722,a)]. 73.60/73.44 Derived: -comm_monoid_add(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5736,a,5734,a)]. 73.60/73.44 5737 -comm_monoid_mult(A) | -semiring_1(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_3955_of__nat__setprod) # label(axiom). [clausify(1905)]. 73.60/73.44 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(5737,a,5722,a)]. 73.60/73.44 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(5737,a,5734,a)]. 73.60/73.44 5738 -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),f328(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_3988_setprod__mono__one__left) # label(axiom). [clausify(1965)]. 73.60/73.44 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),f328(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(5738,a,5722,a)]. 73.60/73.44 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),f328(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(5738,a,5734,a)]. 73.66/73.47 5739 -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,f328(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_3988_setprod__mono__one__left) # label(axiom). [clausify(1965)]. 73.66/73.47 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,f328(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(5739,a,5722,a)]. 73.66/73.47 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,f328(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(5739,a,5734,a)]. 73.66/73.47 5740 -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_3979_setprod_Oinfinite) # label(axiom). [clausify(1999)]. 73.66/73.47 5741 -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_3974_setprod__1) # label(axiom). [clausify(2021)]. 73.66/73.47 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(5741,a,5722,a)]. 73.66/73.47 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(5741,a,5734,a)]. 73.66/73.47 5742 -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_3986_setprod__constant) # label(axiom). [clausify(2026)]. 73.66/73.47 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(5742,a,5722,a)]. 73.66/73.47 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(5742,a,5734,a)]. 73.66/73.47 5743 -dvd(A) | -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f342(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_4452_setprod__dvd__setprod) # label(axiom). [clausify(2027)]. 73.66/73.49 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5743,b,5722,a)]. 73.66/73.49 Derived: -dvd(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5743,b,5734,a)]. 73.66/73.49 5744 -dvd(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,C,f342(B,A,C,D,E))),hAPP(B,A,D,f342(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_4452_setprod__dvd__setprod) # label(axiom). [clausify(2027)]. 73.66/73.49 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,f342(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f342(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(5744,b,5722,a)]. 73.66/73.49 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,B,f342(A,complex,B,C,D))),hAPP(A,complex,C,f342(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(5744,b,5734,a)]. 73.66/73.49 5745 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),f351(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) # label(fact_3989_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(2080)]. 73.66/73.49 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)),f351(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),B). [resolve(5745,a,5722,a)]. 73.66/73.49 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)),f351(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),B). [resolve(5745,a,5734,a)]. 73.85/73.66 5746 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f351(A,E,D,C,B)) != hAPP(int,A,E,f351(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),C) # label(fact_3989_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(2080)]. 73.85/73.66 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,f351(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f351(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),D),B). [resolve(5746,a,5722,a)]. 73.85/73.66 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f351(complex,D,C,B,A)) != hAPP(int,complex,D,f351(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),D),B). [resolve(5746,a,5734,a)]. 73.85/73.66 5747 comm_monoid_mult(rat) # label(arity_Rat_Orat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 73.85/73.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5747,a,5723,a)]. 73.85/73.66 Derived: one_one(rat) != hAPP(A,rat,B,f13(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(5747,a,5724,a)]. 73.85/73.66 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(5747,a,5725,a)]. 73.85/73.66 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(5747,a,5727,a)]. 73.85/73.66 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(5747,a,5728,a)]. 73.85/73.67 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),f172(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(5747,a,5730,a)]. 73.85/73.67 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f172(A,rat,D,C,B)) != hAPP(A,rat,D,f172(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(5747,a,5731,a)]. 73.85/73.67 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(5747,a,5732,a)]. 73.85/73.67 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(5747,a,5733,a)]. 73.85/73.67 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(5747,a,5735,b)]. 73.85/73.67 Derived: -comm_monoid_add(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5747,a,5736,a)]. 73.85/73.67 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(5747,a,5737,a)]. 73.85/73.67 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),f328(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(5747,a,5738,a)]. 73.85/73.72 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,f328(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(5747,a,5739,a)]. 73.85/73.72 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(5747,a,5741,a)]. 73.85/73.72 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(5747,a,5742,a)]. 73.85/73.72 Derived: -dvd(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5747,a,5743,b)]. 73.85/73.72 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,B,f342(A,rat,B,C,D))),hAPP(A,rat,C,f342(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(5747,a,5744,b)]. 73.85/73.72 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)),f351(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),B). [resolve(5747,a,5745,a)]. 73.85/73.72 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f351(rat,D,C,B,A)) != hAPP(int,rat,D,f351(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),D),B). [resolve(5747,a,5746,a)]. 73.85/73.72 5748 -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),f457(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_4175_setprod_Oneutral) # label(axiom). [clausify(2643)]. 73.85/73.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(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(5748,a,5722,a)]. 73.85/73.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(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(5748,a,5734,a)]. 73.85/73.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f457(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(5748,a,5747,a)]. 73.85/73.72 5749 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) != hAPP(B,A,D,f457(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_4175_setprod_Oneutral) # label(axiom). [clausify(2643)]. 73.96/73.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f457(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(5749,a,5722,a)]. 73.96/73.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(complex) != hAPP(A,complex,C,f457(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(5749,a,5734,a)]. 73.96/73.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(rat) != hAPP(A,rat,C,f457(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(5749,a,5747,a)]. 73.96/73.76 5750 -comm_monoid_mult(A) | -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),C) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) # label(fact_4291_transfer__nat__int__sum__prod_I1_J) # label(axiom). [clausify(2678)]. 73.96/73.76 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),B) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5750,a,5722,a)]. 73.96/73.76 Derived: -comm_monoid_add(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),B) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5750,a,5734,a)]. 73.96/73.76 Derived: -comm_monoid_add(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),B) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5750,a,5747,a)]. 73.96/73.76 5751 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_389_mult__1) # label(axiom). [clausify(2706)]. 73.96/73.76 5752 -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),f471(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_3987_setprod__mono__one__right) # label(axiom). [clausify(2739)]. 73.96/73.79 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),f471(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(5752,a,5722,a)]. 73.96/73.79 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),f471(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(5752,a,5734,a)]. 73.96/73.79 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),f471(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(5752,a,5747,a)]. 73.96/73.79 5753 -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,f471(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_3987_setprod__mono__one__right) # label(axiom). [clausify(2739)]. 73.96/73.79 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,f471(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(5753,a,5722,a)]. 73.96/73.79 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,f471(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(5753,a,5734,a)]. 73.96/73.79 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,f471(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(5753,a,5747,a)]. 73.96/73.79 5754 comm_monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 73.96/73.79 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5754,a,5723,a)]. 73.96/73.80 Derived: one_one(code_code_numeral) != hAPP(A,code_code_numeral,B,f13(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(5754,a,5724,a)]. 73.96/73.80 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(5754,a,5725,a)]. 73.96/73.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5754,a,5727,a)]. 73.96/73.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5754,a,5728,a)]. 73.96/73.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f172(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(5754,a,5730,a)]. 73.96/73.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f172(A,code_code_numeral,D,C,B)) != hAPP(A,code_code_numeral,D,f172(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(5754,a,5731,a)]. 73.96/73.81 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(5754,a,5732,a)]. 73.96/73.81 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(5754,a,5733,a)]. 73.96/73.81 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(5754,a,5735,b)]. 73.96/73.81 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5754,a,5736,a)]. 73.96/73.82 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(5754,a,5737,a)]. 73.96/73.82 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),f328(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(5754,a,5738,a)]. 73.96/73.82 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)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,D,f328(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(5754,a,5739,a)]. 73.96/73.82 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(5754,a,5741,a)]. 73.96/73.82 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(5754,a,5742,a)]. 73.96/73.82 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5754,a,5743,b)]. 73.96/73.82 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,f342(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f342(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(5754,a,5744,b)]. 73.96/73.82 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)),f351(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),B). [resolve(5754,a,5745,a)]. 74.22/74.06 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,f351(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f351(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),D),B). [resolve(5754,a,5746,a)]. 74.22/74.06 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),f457(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(5754,a,5748,a)]. 74.22/74.06 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,C,f457(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(5754,a,5749,a)]. 74.22/74.06 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),B) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5754,a,5750,a)]. 74.22/74.06 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),f471(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(5754,a,5752,a)]. 74.22/74.06 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,f471(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(5754,a,5753,a)]. 74.22/74.06 5755 -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,f547(C,A,D,E,F,B)),f549(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),f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.06 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,f547(B,quickcheck_code_int,C,D,E,A)),f549(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),f550(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(5755,a,5722,a)]. 74.26/74.06 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,f547(B,complex,C,D,E,A)),f549(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),f550(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(5755,a,5734,a)]. 74.26/74.06 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,f547(B,rat,C,D,E,A)),f549(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),f550(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(5755,a,5747,a)]. 74.26/74.06 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,f547(B,code_code_numeral,C,D,E,A)),f549(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),f550(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(5755,a,5754,a)]. 74.26/74.07 5756 -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,f547(C,A,D,E,F,B)),f549(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,f550(C,A,D,E,F,B))),hAPP(C,A,E,f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.07 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,f547(B,quickcheck_code_int,C,D,E,A)),f549(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,f550(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f550(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(5756,a,5722,a)]. 74.26/74.07 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,f547(B,complex,C,D,E,A)),f549(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,f550(B,complex,C,D,E,A))),hAPP(B,complex,D,f550(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(5756,a,5734,a)]. 74.26/74.07 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,f547(B,rat,C,D,E,A)),f549(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,f550(B,rat,C,D,E,A))),hAPP(B,rat,D,f550(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(5756,a,5747,a)]. 74.26/74.07 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,f547(B,code_code_numeral,C,D,E,A)),f549(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,f550(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f550(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(5756,a,5754,a)]. 74.26/74.07 5757 -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,f546(C,A,D,E,F,B)),f548(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),f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.07 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,f546(B,quickcheck_code_int,C,D,E,A)),f548(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),f550(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(5757,a,5722,a)]. 74.26/74.08 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,f546(B,complex,C,D,E,A)),f548(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),f550(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(5757,a,5734,a)]. 74.26/74.08 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,f546(B,rat,C,D,E,A)),f548(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),f550(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(5757,a,5747,a)]. 74.26/74.08 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,f546(B,code_code_numeral,C,D,E,A)),f548(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),f550(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(5757,a,5754,a)]. 74.26/74.08 5758 -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,f546(C,A,D,E,F,B)),f548(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,f550(C,A,D,E,F,B))),hAPP(C,A,E,f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.08 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,f546(B,quickcheck_code_int,C,D,E,A)),f548(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,f550(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f550(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(5758,a,5722,a)]. 74.26/74.08 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,f546(B,complex,C,D,E,A)),f548(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,f550(B,complex,C,D,E,A))),hAPP(B,complex,D,f550(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(5758,a,5734,a)]. 74.26/74.08 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,f546(B,rat,C,D,E,A)),f548(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,f550(B,rat,C,D,E,A))),hAPP(B,rat,D,f550(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(5758,a,5747,a)]. 74.26/74.08 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,f546(B,code_code_numeral,C,D,E,A)),f548(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,f550(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f550(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(5758,a,5754,a)]. 74.26/74.08 5759 -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),f546(C,A,D,E,F,B)),f547(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f548(C,A,D,E,F,B)),f549(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),f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.08 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),f546(B,quickcheck_code_int,C,D,E,A)),f547(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),f548(B,quickcheck_code_int,C,D,E,A)),f549(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),f550(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(5759,a,5722,a)]. 74.26/74.08 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),f546(B,complex,C,D,E,A)),f547(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f548(B,complex,C,D,E,A)),f549(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),f550(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(5759,a,5734,a)]. 74.26/74.08 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),f546(B,rat,C,D,E,A)),f547(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f548(B,rat,C,D,E,A)),f549(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),f550(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(5759,a,5747,a)]. 74.26/74.08 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),f546(B,code_code_numeral,C,D,E,A)),f547(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),f548(B,code_code_numeral,C,D,E,A)),f549(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),f550(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(5759,a,5754,a)]. 74.26/74.08 5760 -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),f546(C,A,D,E,F,B)),f547(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f548(C,A,D,E,F,B)),f549(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,f550(C,A,D,E,F,B))),hAPP(C,A,E,f550(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_4804_setprod_Orelated) # label(axiom). [clausify(3106)]. 74.26/74.09 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),f546(B,quickcheck_code_int,C,D,E,A)),f547(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),f548(B,quickcheck_code_int,C,D,E,A)),f549(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,f550(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f550(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(5760,a,5722,a)]. 74.26/74.09 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),f546(B,complex,C,D,E,A)),f547(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f548(B,complex,C,D,E,A)),f549(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,f550(B,complex,C,D,E,A))),hAPP(B,complex,D,f550(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(5760,a,5734,a)]. 74.26/74.09 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),f546(B,rat,C,D,E,A)),f547(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f548(B,rat,C,D,E,A)),f549(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,f550(B,rat,C,D,E,A))),hAPP(B,rat,D,f550(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(5760,a,5747,a)]. 74.26/74.09 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),f546(B,code_code_numeral,C,D,E,A)),f547(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),f548(B,code_code_numeral,C,D,E,A)),f549(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,f550(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f550(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(5760,a,5754,a)]. 74.38/74.23 5761 -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(3244)]. 74.38/74.23 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(5761,a,5722,a)]. 74.38/74.23 Derived: big_co302546470etprod(A,complex) = ti(fun(fun(A,complex),fun(fun(A,bool),complex)),big_co302546470etprod(A,complex)). [resolve(5761,a,5734,a)]. 74.38/74.23 Derived: big_co302546470etprod(A,rat) = ti(fun(fun(A,rat),fun(fun(A,bool),rat)),big_co302546470etprod(A,rat)). [resolve(5761,a,5747,a)]. 74.38/74.23 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(5761,a,5754,a)]. 74.38/74.23 5762 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 74.38/74.23 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5762,a,5723,a)]. 74.38/74.23 Derived: one_one(nat) != hAPP(A,nat,B,f13(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(5762,a,5724,a)]. 74.38/74.23 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(5762,a,5725,a)]. 74.38/74.23 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(5762,a,5727,a)]. 74.38/74.23 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(5762,a,5728,a)]. 74.38/74.23 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),f172(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(5762,a,5730,a)]. 74.38/74.23 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f172(A,nat,D,C,B)) != hAPP(A,nat,D,f172(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(5762,a,5731,a)]. 74.38/74.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5762,a,5732,a)]. 74.38/74.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_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(5762,a,5733,a)]. 74.38/74.24 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(5762,a,5735,b)]. 74.38/74.24 Derived: -comm_monoid_add(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5762,a,5736,a)]. 74.38/74.24 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(5762,a,5737,a)]. 74.38/74.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f328(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(5762,a,5738,a)]. 74.38/74.24 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f328(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(5762,a,5739,a)]. 74.44/74.25 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(5762,a,5741,a)]. 74.44/74.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_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(5762,a,5742,a)]. 74.44/74.25 Derived: -dvd(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5762,a,5743,b)]. 74.44/74.25 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,B,f342(A,nat,B,C,D))),hAPP(A,nat,C,f342(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(5762,a,5744,b)]. 74.44/74.25 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)),f351(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),B). [resolve(5762,a,5745,a)]. 74.44/74.25 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f351(nat,D,C,B,A)) != hAPP(int,nat,D,f351(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),D),B). [resolve(5762,a,5746,a)]. 74.44/74.25 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),f457(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(5762,a,5748,a)]. 74.44/74.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) != hAPP(A,nat,C,f457(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(5762,a,5749,a)]. 74.44/74.25 Derived: -comm_monoid_add(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),B) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5762,a,5750,a)]. 74.44/74.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f471(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(5762,a,5752,a)]. 74.44/74.25 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f471(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(5762,a,5753,a)]. 74.44/74.26 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,f547(B,nat,C,D,E,A)),f549(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),f550(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(5762,a,5755,a)]. 74.44/74.26 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,f547(B,nat,C,D,E,A)),f549(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,f550(B,nat,C,D,E,A))),hAPP(B,nat,D,f550(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(5762,a,5756,a)]. 74.44/74.26 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,f546(B,nat,C,D,E,A)),f548(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),f550(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(5762,a,5757,a)]. 74.44/74.26 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,f546(B,nat,C,D,E,A)),f548(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,f550(B,nat,C,D,E,A))),hAPP(B,nat,D,f550(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(5762,a,5758,a)]. 74.44/74.26 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),f546(B,nat,C,D,E,A)),f547(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f548(B,nat,C,D,E,A)),f549(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),f550(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(5762,a,5759,a)]. 74.44/74.26 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),f546(B,nat,C,D,E,A)),f547(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f548(B,nat,C,D,E,A)),f549(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,f550(B,nat,C,D,E,A))),hAPP(B,nat,D,f550(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(5762,a,5760,a)]. 74.44/74.26 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(5762,a,5761,a)]. 74.84/74.65 5763 -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_3973_setprod__timesf) # label(axiom). [clausify(3819)]. 74.84/74.65 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(5763,a,5722,a)]. 74.84/74.65 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(5763,a,5734,a)]. 74.84/74.65 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(5763,a,5747,a)]. 74.84/74.65 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(5763,a,5754,a)]. 74.84/74.73 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(5763,a,5762,a)]. 74.84/74.73 5764 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 74.84/74.73 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5764,a,5723,a)]. 74.84/74.73 Derived: one_one(int) != hAPP(A,int,B,f13(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(5764,a,5724,a)]. 74.84/74.73 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(5764,a,5725,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),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(5764,a,5727,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5764,a,5728,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f172(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(5764,a,5730,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f172(A,int,D,C,B)) != hAPP(A,int,D,f172(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(5764,a,5731,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5764,a,5732,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),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(5764,a,5733,a)]. 74.84/74.73 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(5764,a,5735,b)]. 74.84/74.73 Derived: -comm_monoid_add(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5764,a,5736,a)]. 74.84/74.73 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(5764,a,5737,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f328(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(5764,a,5738,a)]. 74.84/74.73 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f328(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(5764,a,5739,a)]. 74.84/74.73 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(5764,a,5741,a)]. 74.84/74.73 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(5764,a,5742,a)]. 74.84/74.73 Derived: -dvd(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5764,a,5743,b)]. 74.93/74.74 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,B,f342(A,int,B,C,D))),hAPP(A,int,C,f342(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(5764,a,5744,b)]. 74.93/74.74 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)),f351(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),B). [resolve(5764,a,5745,a)]. 74.93/74.74 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f351(int,D,C,B,A)) != hAPP(int,int,D,f351(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),D),B). [resolve(5764,a,5746,a)]. 74.93/74.74 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),f457(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(5764,a,5748,a)]. 74.93/74.74 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) != hAPP(A,int,C,f457(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(5764,a,5749,a)]. 74.93/74.74 Derived: -comm_monoid_add(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),B) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5764,a,5750,a)]. 74.93/74.74 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),f471(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(5764,a,5752,a)]. 74.93/74.74 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)) | one_one(int) != hAPP(A,int,D,f471(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(5764,a,5753,a)]. 74.93/74.74 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,f547(B,int,C,D,E,A)),f549(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),f550(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(5764,a,5755,a)]. 74.93/74.75 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,f547(B,int,C,D,E,A)),f549(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,f550(B,int,C,D,E,A))),hAPP(B,int,D,f550(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(5764,a,5756,a)]. 74.93/74.75 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,f546(B,int,C,D,E,A)),f548(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),f550(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(5764,a,5757,a)]. 74.93/74.75 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,f546(B,int,C,D,E,A)),f548(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,f550(B,int,C,D,E,A))),hAPP(B,int,D,f550(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(5764,a,5758,a)]. 74.93/74.75 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),f546(B,int,C,D,E,A)),f547(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f548(B,int,C,D,E,A)),f549(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),f550(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(5764,a,5759,a)]. 74.93/74.75 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),f546(B,int,C,D,E,A)),f547(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f548(B,int,C,D,E,A)),f549(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,f550(B,int,C,D,E,A))),hAPP(B,int,D,f550(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(5764,a,5760,a)]. 74.93/74.75 Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)). [resolve(5764,a,5761,a)]. 74.93/74.75 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(5764,a,5763,a)]. 75.11/74.92 5765 -comm_monoid_add(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),C),B) # label(fact_4293_transfer__int__nat__sum__prod_I1_J) # label(axiom). [clausify(4161)]. 75.11/74.92 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),B),A). [resolve(5765,b,5722,a)]. 75.11/74.92 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),B),A). [resolve(5765,b,5734,a)]. 75.11/74.92 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),B),A). [resolve(5765,b,5747,a)]. 75.11/74.92 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),B),A). [resolve(5765,b,5754,a)]. 75.11/74.92 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),B),A). [resolve(5765,b,5762,a)]. 75.11/74.92 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),B),A). [resolve(5765,b,5764,a)]. 75.28/75.09 5766 -comm_monoid_mult(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),C),B) # label(fact_3972_transfer__int__nat__sum__prod_I2_J) # label(axiom). [clausify(4396)]. 75.28/75.09 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),B),A). [resolve(5766,a,5722,a)]. 75.28/75.09 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),B),A). [resolve(5766,a,5734,a)]. 75.28/75.09 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),B),A). [resolve(5766,a,5747,a)]. 75.28/75.09 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),B),A). [resolve(5766,a,5754,a)]. 75.28/75.09 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),B),A). [resolve(5766,a,5762,a)]. 75.28/75.09 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),B),A). [resolve(5766,a,5764,a)]. 75.28/75.14 5767 -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)),f772(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) # label(fact_4324_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4464)]. 75.28/75.14 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)),f772(quickcheck_code_int,C,D,B,A))) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),B). [resolve(5767,b,5722,a)]. 75.28/75.14 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)),f772(complex,C,D,B,A))) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),B). [resolve(5767,b,5734,a)]. 75.28/75.14 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)),f772(rat,C,D,B,A))) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),B). [resolve(5767,b,5747,a)]. 75.28/75.14 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)),f772(code_code_numeral,C,D,B,A))) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),B). [resolve(5767,b,5754,a)]. 75.28/75.14 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)),f772(nat,C,D,B,A))) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),B). [resolve(5767,b,5762,a)]. 75.28/75.14 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)),f772(int,C,D,B,A))) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),B). [resolve(5767,b,5764,a)]. 75.28/75.14 5768 -comm_monoid_add(A) | -comm_monoid_mult(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f772(A,E,D,C,B)) != hAPP(int,A,E,f772(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),C) # label(fact_4324_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(4464)]. 75.28/75.15 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,f772(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f772(quickcheck_code_int,D,C,B,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),C),A) = hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),D),B). [resolve(5768,b,5722,a)]. 75.28/75.15 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f772(complex,D,C,B,A)) != hAPP(int,complex,D,f772(complex,D,C,B,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),C),A) = hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),D),B). [resolve(5768,b,5734,a)]. 75.28/75.15 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f772(rat,D,C,B,A)) != hAPP(int,rat,D,f772(rat,D,C,B,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),C),A) = hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),D),B). [resolve(5768,b,5747,a)]. 75.28/75.15 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,f772(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f772(code_code_numeral,D,C,B,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),C),A) = hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),D),B). [resolve(5768,b,5754,a)]. 75.28/75.15 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f772(nat,D,C,B,A)) != hAPP(int,nat,D,f772(nat,D,C,B,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),C),A) = hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),D),B). [resolve(5768,b,5762,a)]. 75.28/75.15 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f772(int,D,C,B,A)) != hAPP(int,int,D,f772(int,D,C,B,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),C),A) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),D),B). [resolve(5768,b,5764,a)]. 75.28/75.15 5769 -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_3963_setprod__gen__delta) # label(axiom). [clausify(4483)]. 75.28/75.15 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),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(5769,a,5722,a)]. 75.28/75.16 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(5769,a,5734,a)]. 75.28/75.16 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(5769,a,5747,a)]. 75.28/75.16 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(5769,a,5754,a)]. 75.37/75.16 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(5769,a,5762,a)]. 75.37/75.16 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(5769,a,5764,a)]. 75.37/75.16 5770 -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_3963_setprod__gen__delta) # label(axiom). [clausify(4483)]. 75.37/75.16 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(5770,a,5722,a)]. 75.37/75.16 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(5770,a,5734,a)]. 75.37/75.16 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(5770,a,5747,a)]. 75.37/75.16 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(5770,a,5754,a)]. 75.54/75.34 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(5770,a,5762,a)]. 75.54/75.34 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(5770,a,5764,a)]. 75.54/75.34 5771 -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_3985_setprod__dvd__setprod__subset) # label(axiom). [clausify(4729)]. 75.54/75.34 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(5771,a,5722,a)]. 75.54/75.34 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(5771,a,5734,a)]. 75.67/75.46 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(5771,a,5747,a)]. 75.67/75.46 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(5771,a,5754,a)]. 75.67/75.46 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(5771,a,5762,a)]. 75.67/75.46 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(5771,a,5764,a)]. 75.67/75.46 5772 -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_3981_setprod_Odistrib) # label(axiom). [clausify(4815)]. 75.67/75.46 5773 comm_monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 75.67/75.46 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f13(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(5773,a,5723,a)]. 75.67/75.46 Derived: one_one(real) != hAPP(A,real,B,f13(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(5773,a,5724,a)]. 75.67/75.46 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(5773,a,5725,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5773,a,5727,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5773,a,5728,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f172(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(5773,a,5730,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f172(A,real,D,C,B)) != hAPP(A,real,D,f172(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(5773,a,5731,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5773,a,5732,a)]. 75.67/75.46 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5773,a,5733,a)]. 75.67/75.46 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(5773,a,5735,b)]. 75.67/75.46 Derived: -comm_monoid_add(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5773,a,5736,a)]. 75.67/75.47 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(5773,a,5737,a)]. 75.67/75.47 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),f328(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(5773,a,5738,a)]. 75.67/75.47 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,f328(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(5773,a,5739,a)]. 75.67/75.47 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(5773,a,5741,a)]. 75.67/75.47 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(5773,a,5742,a)]. 75.67/75.47 Derived: -dvd(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f342(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(5773,a,5743,b)]. 75.67/75.47 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,B,f342(A,real,B,C,D))),hAPP(A,real,C,f342(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(5773,a,5744,b)]. 75.67/75.47 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)),f351(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),B). [resolve(5773,a,5745,a)]. 75.67/75.47 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f351(real,D,C,B,A)) != hAPP(int,real,D,f351(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),D),B). [resolve(5773,a,5746,a)]. 75.67/75.47 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),f457(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(5773,a,5748,a)]. 75.67/75.47 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(real) != hAPP(A,real,C,f457(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(5773,a,5749,a)]. 75.67/75.47 Derived: -comm_monoid_add(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),B) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)). [resolve(5773,a,5750,a)]. 75.67/75.47 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),f471(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(5773,a,5752,a)]. 75.67/75.47 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,f471(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(5773,a,5753,a)]. 75.67/75.47 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,f547(B,real,C,D,E,A)),f549(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),f550(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(5773,a,5755,a)]. 75.67/75.47 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,f547(B,real,C,D,E,A)),f549(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,f550(B,real,C,D,E,A))),hAPP(B,real,D,f550(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(5773,a,5756,a)]. 75.67/75.47 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,f546(B,real,C,D,E,A)),f548(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),f550(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(5773,a,5757,a)]. 75.67/75.47 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,f546(B,real,C,D,E,A)),f548(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,f550(B,real,C,D,E,A))),hAPP(B,real,D,f550(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(5773,a,5758,a)]. 75.67/75.48 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),f546(B,real,C,D,E,A)),f547(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f548(B,real,C,D,E,A)),f549(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),f550(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(5773,a,5759,a)]. 75.67/75.48 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),f546(B,real,C,D,E,A)),f547(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f548(B,real,C,D,E,A)),f549(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,f550(B,real,C,D,E,A))),hAPP(B,real,D,f550(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(5773,a,5760,a)]. 75.67/75.48 Derived: big_co302546470etprod(A,real) = ti(fun(fun(A,real),fun(fun(A,bool),real)),big_co302546470etprod(A,real)). [resolve(5773,a,5761,a)]. 75.67/75.48 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(5773,a,5763,a)]. 75.67/75.48 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),B),A). [resolve(5773,a,5765,b)]. 75.67/75.48 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),B),A). [resolve(5773,a,5766,a)]. 75.67/75.48 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)),f772(real,C,D,B,A))) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),B). [resolve(5773,a,5767,b)]. 75.67/75.48 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f772(real,D,C,B,A)) != hAPP(int,real,D,f772(real,D,C,B,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),C),A) = hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),D),B). [resolve(5773,a,5768,b)]. 77.85/77.65 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(5773,a,5769,a)]. 77.85/77.65 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(5773,a,5770,a)]. 77.85/77.65 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(5773,a,5771,a)]. 77.85/77.65 5774 linord20386208strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 77.85/77.65 5775 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_480_mult__le__less__imp__less) # label(axiom). [clausify(61)]. 77.85/77.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(5774,a,5775,a)]. 77.95/77.81 5776 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_445_mult__pos__neg) # label(axiom). [clausify(254)]. 77.95/77.81 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),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),A),B)),zero_zero(code_code_numeral))). [resolve(5776,a,5774,a)]. 77.95/77.81 5777 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 77.95/77.81 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),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5777,a,5775,a)]. 77.95/77.81 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),times_times(real),A),B)),zero_zero(real))). [resolve(5777,a,5776,a)]. 77.95/77.81 5778 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_474_mult__left__le__imp__le) # label(axiom). [clausify(995)]. 77.95/77.81 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),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(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(5778,a,5774,a)]. 77.95/77.81 5779 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_453_mult__strict__left__mono) # label(axiom). [clausify(1477)]. 77.95/77.81 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B))). [resolve(5779,a,5774,a)]. 78.18/78.01 5780 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_478_mult__less__imp__less__right) # label(axiom). [clausify(1529)]. 78.18/78.01 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(5780,a,5774,a)]. 78.18/78.01 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(5780,a,5777,a)]. 78.18/78.01 5781 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 78.18/78.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(5781,a,5775,a)]. 78.18/78.01 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(5781,a,5780,a)]. 78.18/78.01 5782 linord20386208strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 78.18/78.01 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5782,a,5775,a)]. 78.18/78.01 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),times_times(rat),A),B)),zero_zero(rat))). [resolve(5782,a,5776,a)]. 78.18/78.01 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(5782,a,5780,a)]. 78.25/78.10 5783 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 78.25/78.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5783,a,5775,a)]. 78.25/78.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))). [resolve(5783,a,5776,a)]. 78.25/78.10 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(5783,a,5780,a)]. 78.25/78.10 5784 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_450_mult__neg__pos) # label(axiom). [clausify(2231)]. 78.25/78.10 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),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),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(5784,a,5774,a)]. 78.25/78.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(5784,a,5777,a)]. 78.25/78.10 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),zero_zero(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),A),B)),zero_zero(rat))). [resolve(5784,a,5782,a)]. 78.25/78.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))). [resolve(5784,a,5783,a)]. 78.25/78.10 5785 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_475_mult__right__le__imp__le) # label(axiom). [clausify(2333)]. 78.25/78.10 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),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(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),C)). [resolve(5785,a,5774,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5785,a,5777,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5785,a,5782,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5785,a,5783,a)]. 78.47/78.27 5786 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_447_zero__less__mult__pos) # label(axiom). [clausify(2649)]. 78.47/78.27 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)). [resolve(5786,a,5774,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5786,a,5777,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). [resolve(5786,a,5781,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5786,a,5782,a)]. 78.47/78.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). [resolve(5786,a,5783,a)]. 78.47/78.27 5787 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_476_mult__less__imp__less__left) # label(axiom). [clausify(2722)]. 78.69/78.51 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(5787,a,5774,a)]. 78.69/78.51 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(5787,a,5777,a)]. 78.69/78.51 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(5787,a,5782,a)]. 78.69/78.51 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(5787,a,5783,a)]. 78.69/78.51 5788 linord20386208strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 78.69/78.51 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(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(5788,a,5775,a)]. 78.69/78.51 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)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(5788,a,5776,a)]. 78.69/78.51 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),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(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(5788,a,5778,a)]. 78.69/78.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(5788,a,5779,a)]. 78.69/78.52 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),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(5788,a,5780,a)]. 78.69/78.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),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),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(5788,a,5784,a)]. 78.69/78.52 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),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(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),C)). [resolve(5788,a,5785,a)]. 78.69/78.52 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)). [resolve(5788,a,5786,a)]. 79.01/78.86 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(5788,a,5787,a)]. 79.01/78.86 5789 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_452_mult__strict__right__mono) # label(axiom). [clausify(3054)]. 79.01/78.86 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),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(5789,a,5774,a)]. 79.01/78.86 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),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(5789,a,5788,a)]. 79.01/78.86 5790 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_444_mult__pos__pos) # label(axiom). [clausify(3404)]. 79.01/78.86 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(5790,a,5774,a)]. 79.01/78.86 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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),times_times(real),A),B))). [resolve(5790,a,5777,a)]. 79.01/78.86 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(5790,a,5781,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(5790,a,5782,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(5790,a,5783,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(5790,a,5788,a)]. 79.07/78.90 5791 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_448_zero__less__mult__pos2) # label(axiom). [clausify(3449)]. 79.07/78.90 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)). [resolve(5791,a,5774,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5791,a,5777,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(5791,a,5781,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5791,a,5782,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5791,a,5783,a)]. 79.07/78.90 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)). [resolve(5791,a,5788,a)]. 79.19/79.01 5792 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_481_mult__less__le__imp__less) # label(axiom). [clausify(3606)]. 79.19/79.01 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),D))). [resolve(5792,a,5774,a)]. 79.19/79.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5792,a,5777,a)]. 79.19/79.01 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(5792,a,5781,a)]. 79.19/79.01 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_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5792,a,5782,a)]. 79.19/79.01 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5792,a,5783,a)]. 79.19/79.01 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(5792,a,5788,a)]. 79.85/79.69 5793 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_446_mult__pos__neg2) # label(axiom). [clausify(4065)]. 79.85/79.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(5793,a,5781,a)]. 79.85/79.69 5794 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_483_mult__strict__mono) # label(axiom). [clausify(4544)]. 79.85/79.69 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),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(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(5794,a,5774,a)]. 79.85/79.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5794,a,5777,a)]. 79.85/79.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(5794,a,5781,a)]. 80.11/79.96 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),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(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(5794,a,5782,a)]. 80.11/79.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5794,a,5783,a)]. 80.11/79.96 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),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(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(5794,a,5788,a)]. 80.11/79.96 5795 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_482_mult__strict__mono_H) # label(axiom). [clausify(4886)]. 80.11/79.96 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_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(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(5795,a,5774,a)]. 80.11/79.96 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5795,a,5777,a)]. 82.41/82.26 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(5795,a,5781,a)]. 82.41/82.26 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_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(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(5795,a,5782,a)]. 82.41/82.26 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5795,a,5783,a)]. 82.41/82.26 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_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(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(5795,a,5788,a)]. 82.41/82.26 5796 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption]. 82.41/82.26 5797 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,sgn_sgn(A),B)) # label(fact_2283_abs__sgn) # label(axiom). [clausify(67)]. 82.41/82.26 5798 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2317_sgn__1__neg) # label(axiom). [clausify(309)]. 82.41/82.26 5799 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) != hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2317_sgn__1__neg) # label(axiom). [clausify(309)]. 82.41/82.26 5800 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(A) != ti(A,C) | zero_zero(nat) = B | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5801 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | zero_zero(nat) = C | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5802 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5803 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5804 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5805 -linordered_idom(A) | zero_zero(nat) != B | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),zero_zero(A))) # label(fact_2508_power__le__zero__eq) # label(axiom). [clausify(385)]. 82.41/82.26 5806 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C))) # label(fact_1012_zero__le__power__abs) # label(axiom). [clausify(393)]. 82.41/82.26 5807 -linordered_idom(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_155_linorder__neqE__linordered__idom) # label(axiom). [clausify(435)]. 82.41/82.26 5808 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) # label(fact_3822_Ints__odd__less__0) # label(axiom). [clausify(465)]. 82.41/82.26 5809 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),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),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) # label(fact_3822_Ints__odd__less__0) # label(axiom). [clausify(465)]. 82.41/82.26 5810 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_100_sum__power2__gt__zero__iff) # label(axiom). [clausify(496)]. 82.41/82.26 5811 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_100_sum__power2__gt__zero__iff) # label(axiom). [clausify(496)]. 82.41/82.26 5812 -linordered_idom(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_100_sum__power2__gt__zero__iff) # label(axiom). [clausify(496)]. 82.41/82.26 5813 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3627_of__int__0__le__iff) # label(axiom). [clausify(546)]. 82.41/82.26 5814 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3627_of__int__0__le__iff) # label(axiom). [clausify(546)]. 82.41/82.26 5815 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))) # label(fact_652_zero__le__even__power_H) # label(axiom). [clausify(593)]. 82.41/82.26 5816 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2280_sgn__greater) # label(axiom). [clausify(669)]. 82.41/82.26 5817 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,sgn_sgn(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2280_sgn__greater) # label(axiom). [clausify(669)]. 82.41/82.26 5818 -linordered_idom(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_333_sum__power2__le__zero__iff) # label(axiom). [clausify(765)]. 82.41/82.26 5819 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_333_sum__power2__le__zero__iff) # label(axiom). [clausify(765)]. 82.41/82.26 5820 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_333_sum__power2__le__zero__iff) # label(axiom). [clausify(765)]. 82.41/82.26 5821 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_651_even__power__le__0__imp__0) # label(axiom). [clausify(824)]. 82.41/82.26 5822 -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_106_of__nat__less__two__power) # label(axiom). [clausify(930)]. 82.41/82.26 5823 -linordered_idom(A) | zero_zero(nat) != B | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.41/82.26 5824 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.47/82.28 5825 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.47/82.28 5826 -linordered_idom(A) | zero_zero(nat) = B | zero_zero(A) != ti(A,C) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.47/82.28 5827 -linordered_idom(A) | zero_zero(nat) = B | zero_zero(A) != ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.47/82.28 5828 -linordered_idom(A) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2509_zero__less__power__eq) # label(axiom). [clausify(947)]. 82.47/82.28 Derived: hAPP(int,int,abs_abs(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,sgn_sgn(int),A)). [resolve(5796,a,5797,a)]. 82.47/82.28 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,sgn_sgn(int),A) = hAPP(int,int,uminus_uminus(int),one_one(int)). [resolve(5796,a,5798,a)]. 82.47/82.28 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,sgn_sgn(int),A) != hAPP(int,int,uminus_uminus(int),one_one(int)). [resolve(5796,a,5799,a)]. 82.47/82.28 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(int) != ti(int,B) | zero_zero(nat) = 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),B),A)),zero_zero(int))). [resolve(5796,a,5800,a)]. 82.47/82.28 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(nat) = B | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))). [resolve(5796,a,5801,a)]. 82.47/82.28 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),zero_zero(int))). [resolve(5796,a,5802,a)]. 82.47/82.28 Derived: zero_zero(int) = ti(int,A) | 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(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))). [resolve(5796,a,5803,a)]. 82.47/82.28 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))). [resolve(5796,a,5804,a)]. 82.47/82.28 Derived: zero_zero(nat) != 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),B),A)),zero_zero(int))). [resolve(5796,a,5805,a)]. 82.47/82.28 Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5796,a,5810,a)]. 82.47/82.28 Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5796,a,5811,a)]. 82.47/82.30 Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5796,a,5812,a)]. 82.47/82.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5796,a,5813,a)]. 82.47/82.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5796,a,5814,a)]. 82.47/82.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(5796,a,5815,a)]. 82.47/82.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5796,a,5816,a)]. 82.47/82.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,sgn_sgn(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5796,a,5817,a)]. 82.47/82.30 Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))). [resolve(5796,a,5818,a)]. 82.47/82.30 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))). [resolve(5796,a,5819,a)]. 82.47/82.30 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))). [resolve(5796,a,5820,a)]. 82.47/82.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(5796,a,5821,a)]. 82.47/82.30 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5796,a,5822,b)]. 82.47/82.30 Derived: zero_zero(nat) != A | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5796,a,5823,a)]. 82.56/82.38 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(5796,a,5824,a)]. 82.56/82.38 Derived: zero_zero(nat) = A | zero_zero(int) != ti(int,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5796,a,5826,a)]. 82.56/82.38 Derived: zero_zero(nat) = A | zero_zero(int) != ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5796,a,5827,a)]. 82.56/82.38 Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5796,a,5828,a)]. 82.56/82.38 5829 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_982_abs__of__nat) # label(axiom). [clausify(1047)]. 82.56/82.38 Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(5829,a,5796,a)]. 82.56/82.38 5830 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_973_abs__mult__self) # label(axiom). [clausify(1050)]. 82.56/82.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(5830,a,5796,a)]. 82.56/82.38 5831 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_2481_power__even__abs) # label(axiom). [clausify(1102)]. 82.56/82.38 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),B)),A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A). [resolve(5831,a,5796,a)]. 82.56/82.38 5832 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_235_le__special_I3_J) # label(axiom). [clausify(1223)]. 82.56/82.38 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5832,a,5796,a)]. 82.56/82.38 5833 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) # label(fact_235_le__special_I3_J) # label(axiom). [clausify(1223)]. 82.56/82.38 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5833,a,5796,a)]. 82.56/82.38 5834 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_44_even__less__0__iff) # label(axiom). [clausify(1354)]. 82.56/82.38 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(5834,a,5796,a)]. 82.64/82.48 5835 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_44_even__less__0__iff) # label(axiom). [clausify(1354)]. 82.64/82.48 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(5835,a,5796,a)]. 82.64/82.48 5836 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_315_zero__le__power2) # label(axiom). [clausify(1652)]. 82.64/82.48 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5836,a,5796,a)]. 82.64/82.48 5837 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2491_power__less__zero__eq) # label(axiom). [clausify(1668)]. 82.64/82.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5837,a,5796,a)]. 82.64/82.48 5838 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2491_power__less__zero__eq) # label(axiom). [clausify(1668)]. 82.64/82.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5838,a,5796,a)]. 82.64/82.48 5839 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2491_power__less__zero__eq) # label(axiom). [clausify(1668)]. 82.64/82.48 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5839,a,5796,a)]. 82.64/82.48 5840 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_1138_abs__diff__less__iff) # label(axiom). [clausify(1752)]. 82.64/82.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(5840,a,5796,a)]. 82.64/82.48 5841 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) # label(fact_1138_abs__diff__less__iff) # label(axiom). [clausify(1752)]. 82.64/82.48 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)). [resolve(5841,a,5796,a)]. 82.64/82.48 5842 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)),B)) # label(fact_1138_abs__diff__less__iff) # label(axiom). [clausify(1752)]. 82.71/82.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)),A)). [resolve(5842,a,5796,a)]. 82.71/82.56 5843 -linordered_idom(A) | one_one(A) = hAPP(A,A,abs_abs(A),one_one(A)) # label(fact_976_abs__one) # label(axiom). [clausify(1771)]. 82.71/82.56 Derived: one_one(int) = hAPP(int,int,abs_abs(int),one_one(int)). [resolve(5843,a,5796,a)]. 82.71/82.56 5844 -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3626_of__int__less__0__iff) # label(axiom). [clausify(1786)]. 82.71/82.56 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,ring_1_of_int(int),A)),zero_zero(int))). [resolve(5844,a,5796,a)]. 82.71/82.56 5845 -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3626_of__int__less__0__iff) # label(axiom). [clausify(1786)]. 82.71/82.56 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,ring_1_of_int(int),A)),zero_zero(int))). [resolve(5845,a,5796,a)]. 82.71/82.56 5846 -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_49_less__special_I3_J) # label(axiom). [clausify(1901)]. 82.71/82.56 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5846,b,5796,a)]. 82.71/82.56 5847 -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_49_less__special_I3_J) # label(axiom). [clausify(1901)]. 82.71/82.56 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))). [resolve(5847,b,5796,a)]. 82.71/82.56 5848 -number_ring(A) | -linordered_idom(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)),B)) # label(fact_1029_abs__power__minus__one) # label(axiom). [clausify(1906)]. 82.71/82.56 Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min)),A)). [resolve(5848,b,5796,a)]. 82.71/82.56 5849 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3625_of__int__0__less__iff) # label(axiom). [clausify(1973)]. 82.71/82.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5849,a,5796,a)]. 82.71/82.56 5850 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3625_of__int__0__less__iff) # label(axiom). [clausify(1973)]. 82.91/82.71 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,ring_1_of_int(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5850,a,5796,a)]. 82.91/82.71 5851 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2490_zero__le__odd__power) # label(axiom). [clausify(2001)]. 82.91/82.71 5852 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2490_zero__le__odd__power) # label(axiom). [clausify(2001)]. 82.91/82.71 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5852,a,5796,a)]. 82.91/82.71 5853 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_1511_odd__0__le__power__imp__0__le) # label(axiom). [clausify(2008)]. 82.91/82.71 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5853,a,5796,a)]. 82.91/82.71 5854 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C) # label(fact_978_power__abs) # label(axiom). [clausify(2225)]. 82.91/82.71 Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B). [resolve(5854,a,5796,a)]. 82.91/82.71 5855 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) # label(fact_2264_sgn__times) # label(axiom). [clausify(2253)]. 82.91/82.71 Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,sgn_sgn(int),B)). [resolve(5855,a,5796,a)]. 82.91/82.71 5856 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_207_le__number__of) # label(axiom). [clausify(2353)]. 82.91/82.71 5857 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_207_le__number__of) # label(axiom). [clausify(2353)]. 82.91/82.71 5858 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(A) = ti(A,B) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom). [clausify(2417)]. 83.02/82.82 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(int) = ti(int,A). [resolve(5858,a,5796,a)]. 83.02/82.82 5859 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(A) = ti(A,C) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom). [clausify(2417)]. 83.02/82.82 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(int) = ti(int,B). [resolve(5859,a,5796,a)]. 83.02/82.82 5860 -linordered_idom(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom). [clausify(2417)]. 83.02/82.82 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(5860,a,5796,a)]. 83.02/82.82 5861 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) # label(fact_2279_sgn__less) # label(axiom). [clausify(2593)]. 83.02/82.82 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,sgn_sgn(int),A)),zero_zero(int))). [resolve(5861,a,5796,a)]. 83.02/82.82 5862 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) # label(fact_2279_sgn__less) # label(axiom). [clausify(2593)]. 83.02/82.82 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,sgn_sgn(int),A)),zero_zero(int))). [resolve(5862,a,5796,a)]. 83.02/82.82 5863 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2495_power__mono__even) # label(axiom). [clausify(2669)]. 83.02/82.82 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),B)),hAPP(int,int,abs_abs(int),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(5863,a,5796,a)]. 83.02/82.82 5864 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2303_sgn__pos) # label(axiom). [clausify(2694)]. 83.06/82.87 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | one_one(int) = hAPP(int,int,sgn_sgn(int),A). [resolve(5864,a,5796,a)]. 83.06/82.87 5865 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_241_le__special_I2_J) # label(axiom). [clausify(2733)]. 83.06/82.87 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5865,b,5796,a)]. 83.06/82.87 5866 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_241_le__special_I2_J) # label(axiom). [clausify(2733)]. 83.06/82.87 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5866,b,5796,a)]. 83.06/82.87 5867 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_63_less__special_I2_J) # label(axiom). [clausify(2752)]. 83.06/82.87 Derived: -number_ring(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(5867,a,5796,a)]. 83.06/82.87 5868 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_63_less__special_I2_J) # label(axiom). [clausify(2752)]. 83.06/82.87 Derived: -number_ring(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(5868,a,5796,a)]. 83.06/82.87 5869 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) != hAPP(A,A,abs_abs(A),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_979_dvd__if__abs__eq) # label(axiom). [clausify(2769)]. 83.06/82.87 Derived: hAPP(int,int,abs_abs(int),A) != hAPP(int,int,abs_abs(int),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5869,a,5796,a)]. 83.06/82.87 5870 -linordered_idom(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.06/82.87 5871 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.06/82.87 5872 -linordered_idom(A) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.06/82.87 5873 -linordered_idom(A) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.26/83.08 5874 -linordered_idom(A) | zero_zero(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.26/83.08 5875 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2519_zero__less__power__eq__number__of) # label(axiom). [clausify(2809)]. 83.26/83.08 5876 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1051_abs__power2) # label(axiom). [clausify(2843)]. 83.26/83.08 Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5876,a,5796,a)]. 83.26/83.08 5877 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_980_abs__dvd__iff) # label(axiom). [clausify(2871)]. 83.26/83.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5877,a,5796,a)]. 83.26/83.08 5878 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_980_abs__dvd__iff) # label(axiom). [clausify(2871)]. 83.26/83.08 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5878,a,5796,a)]. 83.26/83.08 5879 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2316_sgn__neg) # label(axiom). [clausify(2891)]. 83.26/83.08 5880 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2476_power__mono__odd) # label(axiom). [clausify(2941)]. 83.26/83.08 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A))). [resolve(5880,a,5796,a)]. 83.26/83.08 5881 -linordered_idom(A) | zero_zero(A) != hAPP(A,A,sgn_sgn(A),B) | zero_zero(A) = ti(A,B) # label(fact_2261_sgn__0__0) # label(axiom). [clausify(3049)]. 83.26/83.08 Derived: zero_zero(int) != hAPP(int,int,sgn_sgn(int),A) | zero_zero(int) = ti(int,A). [resolve(5881,a,5796,a)]. 83.26/83.08 5882 -linordered_idom(A) | zero_zero(A) = hAPP(A,A,sgn_sgn(A),B) | zero_zero(A) != ti(A,B) # label(fact_2261_sgn__0__0) # label(axiom). [clausify(3049)]. 83.37/83.20 Derived: zero_zero(int) = hAPP(int,int,sgn_sgn(int),A) | zero_zero(int) != ti(int,A). [resolve(5882,a,5796,a)]. 83.37/83.20 5883 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5884 -linordered_idom(A) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5885 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5886 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | zero_zero(A) = ti(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),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5887 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5888 -linordered_idom(A) | zero_zero(nat) != hAPP(int,nat,number_number_of(nat),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2518_power__le__zero__eq__number__of) # label(axiom). [clausify(3208)]. 83.37/83.20 5889 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)) # label(fact_2499_power__even__abs__number__of) # label(axiom). [clausify(3229)]. 83.37/83.20 5890 -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_18_less__number__of) # label(axiom). [clausify(3241)]. 83.37/83.20 5891 -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_18_less__number__of) # label(axiom). [clausify(3241)]. 83.37/83.20 5892 -linordered_idom(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,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_1981_abs__less__iff) # label(axiom). [clausify(3255)]. 83.37/83.20 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,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)). [resolve(5892,a,5796,a)]. 83.58/83.42 5893 -linordered_idom(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,abs_abs(A),B)),C)) # label(fact_1981_abs__less__iff) # label(axiom). [clausify(3255)]. 83.58/83.42 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,abs_abs(int),A)),B)). [resolve(5893,a,5796,a)]. 83.58/83.42 5894 -linordered_idom(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,abs_abs(A),B)),C)) # label(fact_1981_abs__less__iff) # label(axiom). [clausify(3255)]. 83.58/83.42 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,abs_abs(int),A)),B)). [resolve(5894,a,5796,a)]. 83.58/83.42 5895 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2510_zero__le__power__eq__number__of) # label(axiom). [clausify(3409)]. 83.58/83.42 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5895,a,5796,a)]. 83.58/83.42 5896 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2510_zero__le__power__eq__number__of) # label(axiom). [clausify(3409)]. 83.58/83.42 5897 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2510_zero__le__power__eq__number__of) # label(axiom). [clausify(3409)]. 83.58/83.42 5898 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B)) # label(fact_491_mult__left__le__one__le) # label(axiom). [clausify(3447)]. 83.58/83.42 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A)). [resolve(5898,a,5796,a)]. 83.58/83.42 5899 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3604_of__int__le__iff) # label(axiom). [clausify(3465)]. 83.58/83.42 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5899,a,5796,a)]. 83.58/83.42 5900 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_3604_of__int__le__iff) # label(axiom). [clausify(3465)]. 83.58/83.42 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5900,a,5796,a)]. 83.77/83.56 5901 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))) # label(fact_99_power2__less__0) # label(axiom). [clausify(3528)]. 83.77/83.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(int))). [resolve(5901,a,5796,a)]. 83.77/83.56 5902 -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_62_less__special_I4_J) # label(axiom). [clausify(3534)]. 83.77/83.56 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5902,b,5796,a)]. 83.77/83.56 5903 -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_62_less__special_I4_J) # label(axiom). [clausify(3534)]. 83.77/83.56 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,bit1,pls))). [resolve(5903,b,5796,a)]. 83.77/83.56 5904 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),C)),B) # label(fact_1010_abs__mult__pos) # label(axiom). [clausify(3551)]. 83.77/83.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B)),A). [resolve(5904,a,5796,a)]. 83.77/83.56 5905 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_2488_zero__le__power__iff) # label(axiom). [clausify(3635)]. 83.77/83.56 5906 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2488_zero__le__power__iff) # label(axiom). [clausify(3635)]. 83.77/83.56 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5906,a,5796,a)]. 83.77/83.56 5907 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_2488_zero__le__power__iff) # label(axiom). [clausify(3635)]. 83.77/83.56 5908 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2511_power__less__zero__eq__number__of) # label(axiom). [clausify(3676)]. 83.77/83.56 5909 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2511_power__less__zero__eq__number__of) # label(axiom). [clausify(3676)]. 83.83/83.61 5910 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2511_power__less__zero__eq__number__of) # label(axiom). [clausify(3676)]. 83.83/83.61 5911 linordered_idom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__idom) # label(axiom). [assumption]. 83.83/83.61 Derived: hAPP(real,real,abs_abs(real),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,sgn_sgn(real),A)). [resolve(5911,a,5797,a)]. 83.83/83.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,uminus_uminus(real),one_one(real)). [resolve(5911,a,5798,a)]. 83.83/83.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,sgn_sgn(real),A) != hAPP(real,real,uminus_uminus(real),one_one(real)). [resolve(5911,a,5799,a)]. 83.83/83.61 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(real) != ti(real,B) | zero_zero(nat) = 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),B),A)),zero_zero(real))). [resolve(5911,a,5800,a)]. 83.83/83.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(nat) = B | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))). [resolve(5911,a,5801,a)]. 83.83/83.61 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),zero_zero(real))). [resolve(5911,a,5802,a)]. 83.83/83.61 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))). [resolve(5911,a,5803,a)]. 83.83/83.61 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))). [resolve(5911,a,5804,a)]. 83.83/83.61 Derived: zero_zero(nat) != 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),B),A)),zero_zero(real))). [resolve(5911,a,5805,a)]. 83.83/83.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B))). [resolve(5911,a,5806,a)]. 83.83/83.61 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))). [resolve(5911,a,5808,a)]. 83.83/83.61 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))). [resolve(5911,a,5809,a)]. 83.83/83.61 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5911,a,5810,a)]. 83.83/83.62 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5911,a,5811,a)]. 83.83/83.62 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5911,a,5812,a)]. 83.83/83.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5911,a,5813,a)]. 83.83/83.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5911,a,5814,a)]. 83.83/83.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(5911,a,5815,a)]. 83.83/83.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5911,a,5816,a)]. 83.83/83.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sgn_sgn(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5911,a,5817,a)]. 83.83/83.62 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) != ti(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(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))). [resolve(5911,a,5818,a)]. 83.83/83.62 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))). [resolve(5911,a,5819,a)]. 83.83/83.62 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))). [resolve(5911,a,5820,a)]. 83.83/83.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(5911,a,5821,a)]. 83.83/83.64 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5911,a,5822,b)]. 83.83/83.64 Derived: zero_zero(nat) != A | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5823,a)]. 83.83/83.64 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(5911,a,5824,a)]. 83.83/83.64 Derived: zero_zero(nat) = A | zero_zero(real) != ti(real,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5826,a)]. 83.83/83.64 Derived: zero_zero(nat) = A | zero_zero(real) != ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5827,a)]. 83.83/83.64 Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5828,a)]. 83.83/83.64 Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,semiring_1_of_nat(real),A)) = hAPP(nat,real,semiring_1_of_nat(real),A). [resolve(5911,a,5829,a)]. 83.83/83.64 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(5911,a,5830,a)]. 83.83/83.64 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),B)),A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A). [resolve(5911,a,5831,a)]. 83.83/83.64 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5911,a,5832,a)]. 83.83/83.64 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5911,a,5833,a)]. 83.83/83.64 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(5911,a,5834,a)]. 83.83/83.64 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(5911,a,5835,a)]. 83.83/83.64 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5911,a,5836,a)]. 83.83/83.64 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5911,a,5837,a)]. 83.83/83.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5911,a,5838,a)]. 83.83/83.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5911,a,5839,a)]. 83.83/83.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(5911,a,5840,a)]. 83.83/83.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)). [resolve(5911,a,5841,a)]. 83.83/83.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),A)). [resolve(5911,a,5842,a)]. 83.83/83.65 Derived: one_one(real) = hAPP(real,real,abs_abs(real),one_one(real)). [resolve(5911,a,5843,a)]. 83.83/83.65 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))). [resolve(5911,a,5844,a)]. 83.83/83.65 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))). [resolve(5911,a,5845,a)]. 83.83/83.65 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5911,a,5846,b)]. 83.83/83.65 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))). [resolve(5911,a,5847,b)]. 83.83/83.65 Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min)),A)). [resolve(5911,a,5848,b)]. 83.83/83.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5911,a,5849,a)]. 83.83/83.65 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,ring_1_of_int(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5911,a,5850,a)]. 83.83/83.65 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5852,a)]. 83.83/83.65 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5911,a,5853,a)]. 83.88/83.66 Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B). [resolve(5911,a,5854,a)]. 83.88/83.66 Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,sgn_sgn(real),B)). [resolve(5911,a,5855,a)]. 83.88/83.66 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5911,a,5856,a)]. 83.88/83.66 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5911,a,5857,a)]. 83.88/83.66 Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(real) = ti(real,A). [resolve(5911,a,5858,a)]. 83.88/83.66 Derived: zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(real) = ti(real,B). [resolve(5911,a,5859,a)]. 83.88/83.66 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(5911,a,5860,a)]. 83.88/83.66 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,sgn_sgn(real),A)),zero_zero(real))). [resolve(5911,a,5861,a)]. 83.88/83.66 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,sgn_sgn(real),A)),zero_zero(real))). [resolve(5911,a,5862,a)]. 83.88/83.66 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(5911,a,5863,a)]. 83.88/83.66 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | one_one(real) = hAPP(real,real,sgn_sgn(real),A). [resolve(5911,a,5864,a)]. 83.88/83.66 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5911,a,5865,b)]. 83.88/83.66 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5911,a,5866,b)]. 83.88/83.69 Derived: -number_ring(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(5911,a,5867,a)]. 83.88/83.69 Derived: -number_ring(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(5911,a,5868,a)]. 83.88/83.69 Derived: hAPP(real,real,abs_abs(real),A) != hAPP(real,real,abs_abs(real),B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5911,a,5869,a)]. 83.88/83.69 Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5911,a,5876,a)]. 83.88/83.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5911,a,5877,a)]. 83.88/83.69 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5911,a,5878,a)]. 83.88/83.69 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),A))). [resolve(5911,a,5880,a)]. 83.88/83.69 Derived: zero_zero(real) != hAPP(real,real,sgn_sgn(real),A) | zero_zero(real) = ti(real,A). [resolve(5911,a,5881,a)]. 83.88/83.69 Derived: -number_ring(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(5911,a,5890,a)]. 83.88/83.69 Derived: -number_ring(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(5911,a,5891,a)]. 83.88/83.69 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,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)). [resolve(5911,a,5892,a)]. 83.88/83.69 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,abs_abs(real),A)),B)). [resolve(5911,a,5893,a)]. 83.88/83.69 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,abs_abs(real),A)),B)). [resolve(5911,a,5894,a)]. 83.88/83.69 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5911,a,5895,a)]. 83.88/83.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),A)). [resolve(5911,a,5898,a)]. 83.88/83.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5911,a,5899,a)]. 83.88/83.72 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5911,a,5900,a)]. 83.88/83.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(real))). [resolve(5911,a,5901,a)]. 83.88/83.72 Derived: -number_ring(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(5911,a,5902,b)]. 83.88/83.72 Derived: -number_ring(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(5911,a,5903,b)]. 83.88/83.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),B)),A). [resolve(5911,a,5904,a)]. 83.88/83.72 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5911,a,5906,a)]. 83.88/83.72 5912 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B)) # label(fact_490_mult__right__le__one__le) # label(axiom). [clausify(3745)]. 83.88/83.72 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A)). [resolve(5912,a,5796,a)]. 83.88/83.72 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_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),A)). [resolve(5912,a,5911,a)]. 83.88/83.72 5913 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1952_less__minus__self__iff) # label(axiom). [clausify(3772)]. 83.88/83.72 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5913,a,5796,a)]. 83.88/83.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5913,a,5911,a)]. 83.88/83.72 5914 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_1952_less__minus__self__iff) # label(axiom). [clausify(3772)]. 83.88/83.72 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5914,a,5796,a)]. 84.14/83.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,uminus_uminus(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5914,a,5911,a)]. 84.14/83.95 5915 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2487_zero__le__power__eq) # label(axiom). [clausify(4026)]. 84.14/83.95 5916 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2487_zero__le__power__eq) # label(axiom). [clausify(4026)]. 84.14/83.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5916,a,5796,a)]. 84.14/83.95 5917 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2487_zero__le__power__eq) # label(axiom). [clausify(4026)]. 84.14/83.95 5918 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_981_dvd__abs__iff) # label(axiom). [clausify(4032)]. 84.14/83.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5918,a,5796,a)]. 84.14/83.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5918,a,5911,a)]. 84.14/83.95 5919 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,abs_abs(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_981_dvd__abs__iff) # label(axiom). [clausify(4032)]. 84.14/83.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,abs_abs(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(5919,a,5796,a)]. 84.14/83.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(real,real,abs_abs(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)). [resolve(5919,a,5911,a)]. 84.14/83.95 5920 -linordered_idom(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,abs_abs(A),B)) # label(fact_2282_mult__sgn__abs) # label(axiom). [clausify(4046)]. 84.14/83.95 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A)),hAPP(int,int,abs_abs(int),A)). [resolve(5920,a,5796,a)]. 84.14/83.95 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),A)),hAPP(real,real,abs_abs(real),A)). [resolve(5920,a,5911,a)]. 84.14/83.95 5921 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_974_abs__mult) # label(axiom). [clausify(4081)]. 84.14/83.95 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)). [resolve(5921,a,5796,a)]. 84.14/83.95 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)). [resolve(5921,a,5911,a)]. 84.14/83.95 5922 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_101_not__sum__power2__lt__zero) # label(axiom). [clausify(4091)]. 84.26/84.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(int))). [resolve(5922,a,5796,a)]. 84.26/84.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(real))). [resolve(5922,a,5911,a)]. 84.26/84.07 5923 -linordered_idom(A) | one_one(A) != hAPP(A,A,sgn_sgn(A),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2304_sgn__1__pos) # label(axiom). [clausify(4180)]. 84.26/84.07 Derived: one_one(int) != hAPP(int,int,sgn_sgn(int),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5923,a,5796,a)]. 84.26/84.07 Derived: one_one(real) != hAPP(real,real,sgn_sgn(real),A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5923,a,5911,a)]. 84.26/84.07 5924 -linordered_idom(A) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2304_sgn__1__pos) # label(axiom). [clausify(4180)]. 84.26/84.07 5925 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),C)) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_1983_abs__power__minus) # label(axiom). [clausify(4198)]. 84.26/84.07 Derived: hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A)),B)) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5925,a,5796,a)]. 84.26/84.07 Derived: hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,uminus_uminus(real),A)),B)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5925,a,5911,a)]. 84.26/84.07 5926 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_3605_of__int__less__iff) # label(axiom). [clausify(4261)]. 84.26/84.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5926,a,5796,a)]. 84.26/84.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5926,a,5911,a)]. 84.26/84.07 5927 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_3605_of__int__less__iff) # label(axiom). [clausify(4261)]. 84.26/84.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5927,a,5796,a)]. 84.29/84.10 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5927,a,5911,a)]. 84.29/84.10 5928 -number_ring(A) | -linordered_idom(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),min)) # label(fact_1015_abs__minus__one) # label(axiom). [clausify(4265)]. 84.29/84.10 Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),min)). [resolve(5928,b,5796,a)]. 84.29/84.10 Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),min)). [resolve(5928,b,5911,a)]. 84.29/84.10 5929 -linordered_idom(A) | zero_zero(A) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(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_98_zero__less__power2) # label(axiom). [clausify(4293)]. 84.29/84.10 Derived: zero_zero(int) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5929,a,5796,a)]. 84.29/84.10 Derived: zero_zero(real) = ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5929,a,5911,a)]. 84.29/84.10 5930 -linordered_idom(A) | zero_zero(A) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_98_zero__less__power2) # label(axiom). [clausify(4293)]. 84.29/84.10 Derived: zero_zero(int) != ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5930,a,5796,a)]. 84.29/84.10 Derived: zero_zero(real) != ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5930,a,5911,a)]. 84.29/84.10 5931 -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_240_le__special_I4_J) # label(axiom). [clausify(4301)]. 84.29/84.10 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5931,a,5796,a)]. 84.29/84.10 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5931,a,5911,a)]. 84.29/84.10 5932 -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_240_le__special_I4_J) # label(axiom). [clausify(4301)]. 84.29/84.10 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5932,a,5796,a)]. 84.29/84.10 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5932,a,5911,a)]. 84.48/84.27 5933 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_334_sum__power2__ge__zero) # label(axiom). [clausify(4411)]. 84.48/84.27 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5933,a,5796,a)]. 84.48/84.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5933,a,5911,a)]. 84.48/84.27 5934 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,sgn_sgn(A),B)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2257_sgn__sgn) # label(axiom). [clausify(4415)]. 84.48/84.27 Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,sgn_sgn(int),A)) = hAPP(int,int,sgn_sgn(int),A). [resolve(5934,a,5796,a)]. 84.48/84.27 Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),A). [resolve(5934,a,5911,a)]. 84.48/84.27 5935 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1050_power2__abs) # label(axiom). [clausify(4446)]. 84.48/84.27 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5935,a,5796,a)]. 84.48/84.27 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5935,a,5911,a)]. 84.48/84.27 5936 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))),zero_zero(A))) # label(fact_1512_odd__power__less__zero) # label(axiom). [clausify(4540)]. 84.48/84.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(int))). [resolve(5936,a,5796,a)]. 84.48/84.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(real))). [resolve(5936,a,5911,a)]. 84.56/84.36 5937 -linordered_idom(A) | -number_ring(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_236_le__special_I1_J) # label(axiom). [clausify(4541)]. 84.56/84.36 Derived: -number_ring(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(5937,a,5796,a)]. 84.56/84.36 Derived: -number_ring(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(5937,a,5911,a)]. 84.56/84.36 5938 -linordered_idom(A) | -number_ring(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_236_le__special_I1_J) # label(axiom). [clausify(4541)]. 84.56/84.36 Derived: -number_ring(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(5938,a,5796,a)]. 84.56/84.36 Derived: -number_ring(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(5938,a,5911,a)]. 84.56/84.36 5939 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),D)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_992_abs__mult__less) # label(axiom). [clausify(4545)]. 84.56/84.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),C)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(5939,a,5796,a)]. 84.56/84.36 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5939,a,5911,a)]. 84.56/84.36 5940 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) # label(fact_3628_of__int__le__0__iff) # label(axiom). [clausify(4654)]. 84.56/84.36 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5940,a,5796,a)]. 84.56/84.36 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5940,a,5911,a)]. 84.56/84.36 5941 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) # label(fact_3628_of__int__le__0__iff) # label(axiom). [clausify(4654)]. 84.56/84.36 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5941,a,5796,a)]. 84.70/84.50 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5941,a,5911,a)]. 84.70/84.50 5942 -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_2027_abs__number__of) # label(axiom). [clausify(4805)]. 84.70/84.50 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,number_number_of(int),A). [resolve(5942,b,5796,a)]. 84.70/84.50 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(int,real,number_number_of(real),A). [resolve(5942,b,5911,a)]. 84.70/84.50 5943 -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(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2027_abs__number__of) # label(axiom). [clausify(4805)]. 84.70/84.50 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),A)). [resolve(5943,b,5796,a)]. 84.70/84.50 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),A)). [resolve(5943,b,5911,a)]. 84.70/84.50 5944 -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_50_less__special_I1_J) # label(axiom). [clausify(4813)]. 84.70/84.50 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5944,b,5796,a)]. 84.70/84.50 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5944,b,5911,a)]. 84.70/84.50 5945 -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_50_less__special_I1_J) # label(axiom). [clausify(4813)]. 84.70/84.50 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5945,b,5796,a)]. 84.70/84.50 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5945,b,5911,a)]. 84.70/84.50 5946 linordered_idom(rat) # label(arity_Rat_Orat___Rings_Olinordered__idom) # label(axiom). [assumption]. 84.70/84.50 Derived: hAPP(rat,rat,abs_abs(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,sgn_sgn(rat),A)). [resolve(5946,a,5797,a)]. 84.70/84.50 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,sgn_sgn(rat),A) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)). [resolve(5946,a,5798,a)]. 84.70/84.51 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,sgn_sgn(rat),A) != hAPP(rat,rat,uminus_uminus(rat),one_one(rat)). [resolve(5946,a,5799,a)]. 84.70/84.51 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | zero_zero(rat) != ti(rat,B) | zero_zero(nat) = 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),B),A)),zero_zero(rat))). [resolve(5946,a,5800,a)]. 84.70/84.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | zero_zero(nat) = B | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))). [resolve(5946,a,5801,a)]. 84.70/84.51 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),zero_zero(rat))). [resolve(5946,a,5802,a)]. 84.70/84.51 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))). [resolve(5946,a,5803,a)]. 84.70/84.51 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))). [resolve(5946,a,5804,a)]. 84.70/84.51 Derived: zero_zero(nat) != 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),B),A)),zero_zero(rat))). [resolve(5946,a,5805,a)]. 84.70/84.51 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B))). [resolve(5946,a,5806,a)]. 84.70/84.51 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))). [resolve(5946,a,5808,a)]. 84.70/84.51 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))). [resolve(5946,a,5809,a)]. 84.70/84.51 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5946,a,5810,a)]. 84.70/84.51 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5946,a,5811,a)]. 84.70/84.51 Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5946,a,5812,a)]. 84.70/84.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5946,a,5813,a)]. 84.70/84.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5946,a,5814,a)]. 84.70/84.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))). [resolve(5946,a,5815,a)]. 84.70/84.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5946,a,5816,a)]. 84.70/84.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,sgn_sgn(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5946,a,5817,a)]. 84.70/84.52 Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(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(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))). [resolve(5946,a,5818,a)]. 84.70/84.52 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))). [resolve(5946,a,5819,a)]. 84.70/84.52 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))). [resolve(5946,a,5820,a)]. 84.70/84.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),zero_zero(rat))) | zero_zero(rat) = ti(rat,A). [resolve(5946,a,5821,a)]. 84.70/84.52 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A))). [resolve(5946,a,5822,b)]. 84.70/84.52 Derived: zero_zero(nat) != A | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5823,a)]. 84.70/84.52 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))). [resolve(5946,a,5824,a)]. 84.70/84.52 Derived: zero_zero(nat) = A | zero_zero(rat) != ti(rat,B) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5826,a)]. 84.74/84.53 Derived: zero_zero(nat) = A | zero_zero(rat) != ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5827,a)]. 84.74/84.53 Derived: zero_zero(nat) = A | hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5828,a)]. 84.74/84.53 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)) = hAPP(nat,rat,semiring_1_of_nat(rat),A). [resolve(5946,a,5829,a)]. 84.74/84.53 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(5946,a,5830,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),B)),A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A). [resolve(5946,a,5831,a)]. 84.74/84.53 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5946,a,5832,a)]. 84.74/84.53 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5946,a,5833,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(5946,a,5834,a)]. 84.74/84.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(5946,a,5835,a)]. 84.74/84.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5946,a,5836,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5946,a,5837,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5946,a,5838,a)]. 84.74/84.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5946,a,5839,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))). [resolve(5946,a,5840,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)). [resolve(5946,a,5841,a)]. 84.74/84.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),A)). [resolve(5946,a,5842,a)]. 84.74/84.53 Derived: one_one(rat) = hAPP(rat,rat,abs_abs(rat),one_one(rat)). [resolve(5946,a,5843,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))). [resolve(5946,a,5844,a)]. 84.74/84.53 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))). [resolve(5946,a,5845,a)]. 84.74/84.53 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5946,a,5846,b)]. 84.74/84.53 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))). [resolve(5946,a,5847,b)]. 84.74/84.53 Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min)),A)). [resolve(5946,a,5848,b)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5946,a,5849,a)]. 84.74/84.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,ring_1_of_int(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(5946,a,5850,a)]. 84.74/84.53 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5852,a)]. 84.74/84.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5946,a,5853,a)]. 84.74/84.53 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B). [resolve(5946,a,5854,a)]. 84.74/84.53 Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,sgn_sgn(rat),B)). [resolve(5946,a,5855,a)]. 84.74/84.53 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | 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))). [resolve(5946,a,5856,a)]. 84.74/84.53 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -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))). [resolve(5946,a,5857,a)]. 84.74/84.53 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(rat) = ti(rat,A). [resolve(5946,a,5858,a)]. 84.74/84.53 Derived: zero_zero(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(rat) = ti(rat,B). [resolve(5946,a,5859,a)]. 84.77/84.55 Derived: zero_zero(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | zero_zero(rat) != ti(rat,A) | zero_zero(rat) != ti(rat,B). [resolve(5946,a,5860,a)]. 84.77/84.55 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,sgn_sgn(rat),A)),zero_zero(rat))). [resolve(5946,a,5861,a)]. 84.77/84.55 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,sgn_sgn(rat),A)),zero_zero(rat))). [resolve(5946,a,5862,a)]. 84.77/84.55 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(5946,a,5863,a)]. 84.77/84.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | one_one(rat) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5946,a,5864,a)]. 84.77/84.55 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5946,a,5865,b)]. 84.77/84.55 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5946,a,5866,b)]. 84.77/84.55 Derived: -number_ring(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(5946,a,5867,a)]. 84.77/84.55 Derived: -number_ring(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(5946,a,5868,a)]. 84.77/84.55 Derived: hAPP(rat,rat,abs_abs(rat),A) != hAPP(rat,rat,abs_abs(rat),B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5946,a,5869,a)]. 84.77/84.55 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5946,a,5876,a)]. 84.77/84.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5946,a,5877,a)]. 84.77/84.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5946,a,5878,a)]. 84.77/84.55 Derived: hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),A))). [resolve(5946,a,5880,a)]. 84.77/84.55 Derived: zero_zero(rat) != hAPP(rat,rat,sgn_sgn(rat),A) | zero_zero(rat) = ti(rat,A). [resolve(5946,a,5881,a)]. 84.77/84.56 Derived: -number_ring(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(5946,a,5890,a)]. 84.77/84.56 Derived: -number_ring(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(5946,a,5891,a)]. 84.77/84.56 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,uminus_uminus(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)). [resolve(5946,a,5892,a)]. 84.77/84.56 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,abs_abs(rat),A)),B)). [resolve(5946,a,5893,a)]. 84.77/84.56 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,abs_abs(rat),A)),B)). [resolve(5946,a,5894,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5946,a,5895,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),A)). [resolve(5946,a,5898,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5946,a,5899,a)]. 84.77/84.56 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5946,a,5900,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(rat))). [resolve(5946,a,5901,a)]. 84.77/84.56 Derived: -number_ring(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(5946,a,5902,b)]. 84.77/84.56 Derived: -number_ring(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(5946,a,5903,b)]. 84.77/84.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),B)),A). [resolve(5946,a,5904,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5946,a,5906,a)]. 84.77/84.56 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),A)). [resolve(5946,a,5912,a)]. 84.77/84.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5946,a,5913,a)]. 84.77/84.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5946,a,5914,a)]. 84.77/84.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5946,a,5918,a)]. 84.77/84.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(rat,rat,abs_abs(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)). [resolve(5946,a,5919,a)]. 84.77/84.57 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,sgn_sgn(rat),A)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5946,a,5920,a)]. 84.77/84.57 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)). [resolve(5946,a,5921,a)]. 84.77/84.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(rat))). [resolve(5946,a,5922,a)]. 84.77/84.57 Derived: one_one(rat) != hAPP(rat,rat,sgn_sgn(rat),A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5946,a,5923,a)]. 84.77/84.57 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5946,a,5925,a)]. 84.77/84.57 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5946,a,5926,a)]. 84.77/84.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5946,a,5927,a)]. 84.77/84.57 Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),min)). [resolve(5946,a,5928,b)]. 84.77/84.57 Derived: zero_zero(rat) = ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5946,a,5929,a)]. 84.77/84.57 Derived: zero_zero(rat) != ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5946,a,5930,a)]. 84.77/84.57 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5946,a,5931,a)]. 84.77/84.57 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,bit1,pls))). [resolve(5946,a,5932,a)]. 84.77/84.57 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). [resolve(5946,a,5933,a)]. 87.29/87.08 Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,sgn_sgn(rat),A)) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5946,a,5934,a)]. 87.29/87.08 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5946,a,5935,a)]. 87.29/87.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))),zero_zero(rat))). [resolve(5946,a,5936,a)]. 87.29/87.08 Derived: -number_ring(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(5946,a,5937,a)]. 87.29/87.08 Derived: -number_ring(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(5946,a,5938,a)]. 87.29/87.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),C)),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),C))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(5946,a,5939,a)]. 87.29/87.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5946,a,5940,a)]. 87.29/87.08 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(5946,a,5941,a)]. 87.29/87.08 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(int,rat,number_number_of(rat),A). [resolve(5946,a,5942,b)]. 87.29/87.08 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(5946,a,5943,b)]. 87.29/87.08 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5946,a,5944,b)]. 87.29/87.08 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(5946,a,5945,b)]. 87.29/87.08 5947 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 87.29/87.08 5948 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hAPP(A,A,abs_abs(A),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2000_abs__of__nonpos) # label(axiom). [clausify(81)]. 87.29/87.08 5949 -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_2001_abs__minus__le__zero) # label(axiom). [clausify(122)]. 87.29/87.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hAPP(int,int,abs_abs(int),A) = hAPP(int,int,uminus_uminus(int),A). [resolve(5947,a,5948,a)]. 87.43/87.20 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(5947,a,5949,a)]. 87.43/87.20 5950 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) != ti(A,B) # label(fact_990_zero__less__abs__iff) # label(axiom). [clausify(185)]. 87.43/87.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) != ti(int,A). [resolve(5950,a,5947,a)]. 87.43/87.20 5951 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) = ti(A,B) # label(fact_990_zero__less__abs__iff) # label(axiom). [clausify(185)]. 87.43/87.20 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) = ti(int,A). [resolve(5951,a,5947,a)]. 87.43/87.20 5952 -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(214)]. 87.43/87.20 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(5952,a,5947,a)]. 87.43/87.20 5953 -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_975_abs__add__abs) # label(axiom). [clausify(464)]. 87.43/87.20 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(5953,a,5947,a)]. 87.43/87.20 5954 -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_1013_abs__triangle__ineq4) # label(axiom). [clausify(772)]. 87.43/87.20 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(5954,a,5947,a)]. 87.43/87.20 5955 -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_1979_abs__le__D2) # label(axiom). [clausify(994)]. 87.43/87.20 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(5955,a,5947,a)]. 87.43/87.20 5956 -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_971_abs__ge__self) # label(axiom). [clausify(1076)]. 87.43/87.20 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(5956,a,5947,a)]. 87.43/87.20 5957 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_996_abs__triangle__ineq3) # label(axiom). [clausify(1195)]. 87.43/87.20 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(5957,a,5947,a)]. 87.43/87.20 5958 -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_1943_abs__minus__cancel) # label(axiom). [clausify(1280)]. 87.67/87.44 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(5958,a,5947,a)]. 87.67/87.44 5959 -ordere142940540dd_abs(A) | zero_zero(A) != ti(A,B) | 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_987_abs__le__zero__iff) # label(axiom). [clausify(1297)]. 87.67/87.44 Derived: zero_zero(int) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(5959,a,5947,a)]. 87.67/87.44 5960 -ordere142940540dd_abs(A) | zero_zero(A) = ti(A,B) | -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_987_abs__le__zero__iff) # label(axiom). [clausify(1297)]. 87.67/87.44 Derived: zero_zero(int) = ti(int,A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(5960,a,5947,a)]. 87.67/87.44 5961 -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_1976_abs__ge__minus__self) # label(axiom). [clausify(1368)]. 87.67/87.44 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(5961,a,5947,a)]. 87.67/87.44 5962 -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_995_abs__triangle__ineq2) # label(axiom). [clausify(1580)]. 87.67/87.44 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(5962,a,5947,a)]. 87.67/87.44 5963 -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_988_abs__of__nonneg) # label(axiom). [clausify(1808)]. 87.67/87.44 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(5963,a,5947,a)]. 87.67/87.44 5964 -ordere142940540dd_abs(A) | zero_zero(A) = hAPP(A,A,abs_abs(A),zero_zero(A)) # label(fact_970_abs__zero) # label(axiom). [clausify(1882)]. 87.67/87.44 Derived: zero_zero(int) = hAPP(int,int,abs_abs(int),zero_zero(int)). [resolve(5964,a,5947,a)]. 87.67/87.44 5965 -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_989_abs__of__pos) # label(axiom). [clausify(1969)]. 87.67/87.44 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(5965,a,5947,a)]. 87.67/87.44 5966 -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_4192_setsum__abs) # label(axiom). [clausify(1992)]. 87.67/87.44 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(5966,a,5947,a)]. 87.67/87.44 5967 -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_991_abs__not__less__zero) # label(axiom). [clausify(2152)]. 87.67/87.44 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(5967,a,5947,a)]. 88.57/88.37 5968 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,abs_abs(A),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2002_abs__of__neg) # label(axiom). [clausify(2174)]. 88.57/88.37 5969 -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_965_abs__idempotent) # label(axiom). [clausify(2237)]. 88.57/88.37 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(5969,a,5947,a)]. 88.57/88.37 5970 -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_977_abs__minus__commute) # label(axiom). [clausify(2258)]. 88.57/88.37 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(5970,a,5947,a)]. 88.57/88.37 5971 -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_993_abs__triangle__ineq) # label(axiom). [clausify(3110)]. 88.57/88.37 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(5971,a,5947,a)]. 88.57/88.37 5972 -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_4193_setsum__abs__ge__zero) # label(axiom). [clausify(3251)]. 88.57/88.37 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(5972,a,5947,a)]. 88.57/88.37 5973 -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_972_abs__le__D1) # label(axiom). [clausify(3262)]. 88.57/88.37 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(5973,a,5947,a)]. 88.57/88.37 5974 -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_986_abs__ge__zero) # label(axiom). [clausify(3265)]. 88.57/88.37 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(5974,a,5947,a)]. 88.57/88.37 5975 -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_1014_abs__diff__triangle__ineq) # label(axiom). [clausify(3595)]. 88.57/88.37 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(5975,a,5947,a)]. 88.57/88.37 5976 ordere142940540dd_abs(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 88.63/88.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5976,a,5948,a)]. 88.63/88.39 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(5976,a,5949,a)]. 88.63/88.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | zero_zero(rat) != ti(rat,A). [resolve(5976,a,5950,a)]. 88.63/88.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))) | zero_zero(rat) = ti(rat,A). [resolve(5976,a,5951,a)]. 88.63/88.39 Derived: abs_abs(rat) = ti(fun(rat,rat),abs_abs(rat)). [resolve(5976,a,5952,a)]. 88.63/88.39 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(5976,a,5953,a)]. 88.63/88.39 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(5976,a,5954,a)]. 88.63/88.39 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(5976,a,5955,a)]. 88.63/88.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,abs_abs(rat),A))). [resolve(5976,a,5956,a)]. 88.63/88.39 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,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),A),B)))). [resolve(5976,a,5957,a)]. 88.63/88.39 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5976,a,5958,a)]. 88.63/88.39 Derived: zero_zero(rat) != ti(rat,A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(5976,a,5959,a)]. 88.63/88.39 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(5976,a,5960,a)]. 88.63/88.39 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(5976,a,5961,a)]. 88.63/88.39 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),A),B)))). [resolve(5976,a,5962,a)]. 88.63/88.39 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(5976,a,5963,a)]. 88.63/88.39 Derived: zero_zero(rat) = hAPP(rat,rat,abs_abs(rat),zero_zero(rat)). [resolve(5976,a,5964,a)]. 88.63/88.39 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(5976,a,5965,a)]. 88.63/88.39 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(5976,a,5966,a)]. 88.63/88.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(5976,a,5967,a)]. 88.63/88.39 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,abs_abs(rat),A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(5976,a,5968,a)]. 88.63/88.42 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5976,a,5969,a)]. 88.63/88.42 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(5976,a,5970,a)]. 88.63/88.42 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(5976,a,5971,a)]. 88.63/88.42 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(5976,a,5972,a)]. 88.63/88.42 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),A),B)). [resolve(5976,a,5973,a)]. 88.63/88.42 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(5976,a,5974,a)]. 88.63/88.42 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),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(5976,a,5975,a)]. 88.63/88.42 5977 -ordere142940540dd_abs(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),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_1977_abs__le__iff) # label(axiom). [clausify(3788)]. 88.63/88.42 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),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)). [resolve(5977,a,5947,a)]. 88.63/88.42 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),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),B)). [resolve(5977,a,5976,a)]. 88.63/88.42 5978 -ordere142940540dd_abs(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,abs_abs(A),B)),C)) # label(fact_1977_abs__le__iff) # label(axiom). [clausify(3788)]. 88.63/88.42 5979 -ordere142940540dd_abs(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,abs_abs(A),B)),C)) # label(fact_1977_abs__le__iff) # label(axiom). [clausify(3788)]. 88.63/88.42 5980 ordere142940540dd_abs(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 88.63/88.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hAPP(real,real,abs_abs(real),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5980,a,5948,a)]. 88.63/88.42 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(5980,a,5949,a)]. 88.63/88.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) != ti(real,A). [resolve(5980,a,5950,a)]. 88.63/88.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) = ti(real,A). [resolve(5980,a,5951,a)]. 88.63/88.44 Derived: abs_abs(real) = ti(fun(real,real),abs_abs(real)). [resolve(5980,a,5952,a)]. 88.63/88.44 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(5980,a,5953,a)]. 88.63/88.44 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(5980,a,5954,a)]. 88.63/88.44 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(5980,a,5955,a)]. 88.63/88.44 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,abs_abs(real),A))). [resolve(5980,a,5956,a)]. 88.63/88.44 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,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(5980,a,5957,a)]. 88.63/88.44 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(5980,a,5958,a)]. 88.63/88.44 Derived: zero_zero(real) != ti(real,A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(5980,a,5959,a)]. 88.63/88.44 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(5980,a,5960,a)]. 88.63/88.44 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(5980,a,5961,a)]. 88.63/88.44 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(5980,a,5962,a)]. 88.63/88.44 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(5980,a,5963,a)]. 88.63/88.44 Derived: zero_zero(real) = hAPP(real,real,abs_abs(real),zero_zero(real)). [resolve(5980,a,5964,a)]. 88.63/88.44 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(5980,a,5965,a)]. 88.63/88.44 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(5980,a,5966,a)]. 88.63/88.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(5980,a,5967,a)]. 88.63/88.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,abs_abs(real),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(5980,a,5968,a)]. 88.63/88.44 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(5980,a,5969,a)]. 88.63/88.44 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(5980,a,5970,a)]. 89.17/88.99 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(5980,a,5971,a)]. 89.17/88.99 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(5980,a,5972,a)]. 89.17/88.99 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),A),B)). [resolve(5980,a,5973,a)]. 89.17/88.99 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(5980,a,5974,a)]. 89.17/88.99 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(5980,a,5975,a)]. 89.17/88.99 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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,abs_abs(real),A)),B)). [resolve(5980,a,5977,a)]. 89.17/88.99 5981 -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_994_abs__triangle__ineq2__sym) # label(axiom). [clausify(4251)]. 89.17/88.99 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(5981,a,5947,a)]. 89.17/88.99 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(5981,a,5976,a)]. 89.17/88.99 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(5981,a,5980,a)]. 89.17/88.99 5982 -ordere142940540dd_abs(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),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_1978_abs__leI) # label(axiom). [clausify(4570)]. 89.17/88.99 5983 -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_4246_abs__setsum__abs) # label(axiom). [clausify(4601)]. 89.17/88.99 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(5983,a,5947,a)]. 92.03/91.85 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),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(5983,a,5976,a)]. 92.03/91.85 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(5983,a,5980,a)]. 92.03/91.85 5984 -ordere142940540dd_abs(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,abs_abs(A),B) # label(fact_969_abs__eq__0) # label(axiom). [clausify(4625)]. 92.03/91.85 Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,abs_abs(int),A). [resolve(5984,a,5947,a)]. 92.03/91.85 Derived: zero_zero(rat) != ti(rat,A) | zero_zero(rat) = hAPP(rat,rat,abs_abs(rat),A). [resolve(5984,a,5976,a)]. 92.03/91.85 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,abs_abs(real),A). [resolve(5984,a,5980,a)]. 92.03/91.85 5985 -ordere142940540dd_abs(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != hAPP(A,A,abs_abs(A),B) # label(fact_969_abs__eq__0) # label(axiom). [clausify(4625)]. 92.03/91.85 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != hAPP(int,int,abs_abs(int),A). [resolve(5985,a,5947,a)]. 92.03/91.85 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) != hAPP(rat,rat,abs_abs(rat),A). [resolve(5985,a,5976,a)]. 92.03/91.85 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) != hAPP(real,real,abs_abs(real),A). [resolve(5985,a,5980,a)]. 92.03/91.85 5986 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 92.03/91.85 5987 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_439_split__mult__neg__le) # label(axiom). [clausify(82)]. 92.03/91.85 5988 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_439_split__mult__neg__le) # label(axiom). [clausify(82)]. 92.03/91.85 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(5986,a,5987,a)]. 92.03/91.85 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(5986,a,5988,a)]. 92.03/91.85 5989 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_427_mult__nonneg__nonpos) # label(axiom). [clausify(1458)]. 93.24/93.03 5990 ordere453448008miring(rat) # label(arity_Rat_Orat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 93.24/93.03 5991 ordere453448008miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 93.24/93.03 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(5991,a,5987,a)]. 93.24/93.03 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),zero_zero(code_code_numeral))). [resolve(5991,a,5988,a)]. 93.24/93.03 5992 ordere453448008miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 93.24/93.03 5993 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_429_mult__nonpos__nonneg) # label(axiom). [clausify(3457)]. 93.24/93.03 5994 ordere453448008miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 93.24/93.03 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(5994,a,5987,a)]. 93.24/93.03 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),zero_zero(quickcheck_code_int))). [resolve(5994,a,5988,a)]. 93.24/93.03 5995 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_426_mult__nonneg__nonneg) # label(axiom). [clausify(3918)]. 96.41/96.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(5995,a,5986,a)]. 96.41/96.17 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(5995,a,5991,a)]. 96.41/96.17 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B))). [resolve(5995,a,5994,a)]. 96.41/96.17 5996 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 96.41/96.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(5996,a,5995,a)]. 96.41/96.17 5997 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_428_mult__nonneg__nonpos2) # label(axiom). [clausify(4413)]. 96.41/96.17 5998 real_vector(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__vector) # label(axiom). [assumption]. 96.41/96.17 5999 -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_4755_scaleR__left_Osetsum) # label(axiom). [clausify(88)]. 96.41/96.17 6000 -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_4713_scaleR__left__commute) # label(axiom). [clausify(398)]. 96.41/96.17 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(5998,a,5999,a)]. 96.41/96.25 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(5998,a,6000,a)]. 96.41/96.25 6001 -real_vector(A) | 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)) = 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)) # label(fact_4701_scaleR__right_Odiff) # label(axiom). [clausify(427)]. 96.41/96.25 Derived: 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)) = 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)). [resolve(6001,a,5998,a)]. 96.41/96.25 6002 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4695_scaleR__left_Oadd) # label(axiom). [clausify(488)]. 96.41/96.25 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(6002,a,5998,a)]. 96.41/96.25 6003 -real_vector(A) | 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)) = 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)) # label(fact_4700_scaleR__right_Oadd) # label(axiom). [clausify(534)]. 96.41/96.25 Derived: 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)) = 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)). [resolve(6003,a,5998,a)]. 96.41/96.25 6004 -real_vector(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) # label(fact_4728_scaleR__cancel__left) # label(axiom). [clausify(888)]. 96.41/96.25 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B). [resolve(6004,a,5998,a)]. 96.41/96.25 6005 -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) # label(fact_4728_scaleR__cancel__left) # label(axiom). [clausify(888)]. 96.41/96.25 Derived: zero_zero(real) != A | 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). [resolve(6005,a,5998,a)]. 96.41/96.25 6006 -real_vector(A) | ti(A,B) = ti(A,C) | zero_zero(real) = D | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),C) # label(fact_4728_scaleR__cancel__left) # label(axiom). [clausify(888)]. 96.41/96.25 Derived: ti(complex,A) = ti(complex,B) | zero_zero(real) = C | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),A) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),B). [resolve(6006,a,5998,a)]. 96.41/96.25 6007 -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_4756_scaleR__right_Osetsum) # label(axiom). [clausify(1105)]. 96.51/96.28 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(6007,a,5998,a)]. 96.51/96.28 6008 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4739_scaleR__left_Ominus) # label(axiom). [clausify(1167)]. 96.51/96.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)). [resolve(6008,a,5998,a)]. 96.51/96.28 6009 real_vector(real) # label(arity_RealDef_Oreal___RealVector_Oreal__vector) # label(axiom). [assumption]. 96.51/96.28 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(6009,a,5999,a)]. 96.51/96.28 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(6009,a,6000,a)]. 96.51/96.28 Derived: 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)) = 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)). [resolve(6009,a,6001,a)]. 96.51/96.28 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(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),scaleR_scaleR(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(6009,a,6002,a)]. 96.51/96.28 Derived: 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)) = 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)). [resolve(6009,a,6003,a)]. 96.51/96.28 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B). [resolve(6009,a,6004,a)]. 96.51/96.28 Derived: zero_zero(real) != A | 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). [resolve(6009,a,6005,a)]. 96.51/96.28 Derived: ti(real,A) = ti(real,B) | zero_zero(real) = C | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),A) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),B). [resolve(6009,a,6006,a)]. 96.84/96.60 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(6009,a,6007,a)]. 96.84/96.60 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)). [resolve(6009,a,6008,a)]. 96.84/96.60 6010 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4698_scaleR__left__diff__distrib) # label(axiom). [clausify(1616)]. 96.84/96.60 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C)),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),C)). [resolve(6010,a,5998,a)]. 96.84/96.60 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(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),scaleR_scaleR(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)). [resolve(6010,a,6009,a)]. 96.84/96.60 6011 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4734_scaleR__minus__right) # label(axiom). [clausify(1920)]. 96.84/96.60 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)). [resolve(6011,a,5998,a)]. 96.84/96.60 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)). [resolve(6011,a,6009,a)]. 96.84/96.60 6012 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),zero_zero(real)),B) # label(fact_4737_scaleR__left_Ozero) # label(axiom). [clausify(2215)]. 96.84/96.60 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),zero_zero(real)),A). [resolve(6012,a,5998,a)]. 96.84/96.60 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),zero_zero(real)),A). [resolve(6012,a,6009,a)]. 96.84/96.60 6013 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4693_real__vector_Oscale__left__distrib) # label(axiom). [clausify(2330)]. 96.84/96.60 6014 -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(2360)]. 96.84/96.60 Derived: scaleR_scaleR(complex) = ti(fun(real,fun(complex,complex)),scaleR_scaleR(complex)). [resolve(6014,a,5998,a)]. 96.84/96.60 Derived: scaleR_scaleR(real) = ti(fun(real,fun(real,real)),scaleR_scaleR(real)). [resolve(6014,a,6009,a)]. 96.84/96.60 6015 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) # label(fact_4740_scaleR__minus__left) # label(axiom). [clausify(2412)]. 97.11/96.88 6016 -real_vector(A) | zero_zero(real) != B | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) # label(fact_4736_scaleR__eq__0__iff) # label(axiom). [clausify(2483)]. 97.11/96.88 Derived: zero_zero(real) != A | zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B). [resolve(6016,a,5998,a)]. 97.11/96.88 Derived: zero_zero(real) != A | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B). [resolve(6016,a,6009,a)]. 97.11/96.88 6017 -real_vector(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) # label(fact_4736_scaleR__eq__0__iff) # label(axiom). [clausify(2483)]. 97.11/96.88 Derived: zero_zero(complex) != ti(complex,A) | zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A). [resolve(6017,a,5998,a)]. 97.11/96.88 Derived: zero_zero(real) != ti(real,A) | zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A). [resolve(6017,a,6009,a)]. 97.11/96.89 6018 -real_vector(A) | zero_zero(real) = B | zero_zero(A) = ti(A,C) | zero_zero(A) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) # label(fact_4736_scaleR__eq__0__iff) # label(axiom). [clausify(2483)]. 97.11/96.89 Derived: zero_zero(real) = A | zero_zero(complex) = ti(complex,B) | zero_zero(complex) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B). [resolve(6018,a,5998,a)]. 97.11/96.89 Derived: zero_zero(real) = A | zero_zero(real) = ti(real,B) | zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B). [resolve(6018,a,6009,a)]. 97.11/96.89 6019 -real_vector(A) | zero_zero(A) != ti(A,B) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) # label(fact_4732_scaleR__cancel__right) # label(axiom). [clausify(2630)]. 97.11/96.89 Derived: zero_zero(complex) != ti(complex,A) | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),A). [resolve(6019,a,5998,a)]. 97.11/96.89 Derived: zero_zero(real) != ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),A). [resolve(6019,a,6009,a)]. 97.11/96.89 6020 -real_vector(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),C),D) # label(fact_4732_scaleR__cancel__right) # label(axiom). [clausify(2630)]. 97.11/96.89 Derived: 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),B),C). [resolve(6020,a,5998,a)]. 97.11/96.89 Derived: 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),B),C). [resolve(6020,a,6009,a)]. 97.11/96.89 6021 -real_vector(A) | zero_zero(A) = ti(A,B) | C = D | 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) # label(fact_4732_scaleR__cancel__right) # label(axiom). [clausify(2630)]. 97.11/96.89 Derived: zero_zero(complex) = ti(complex,A) | B = C | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),C),A). [resolve(6021,a,5998,a)]. 97.11/96.89 Derived: zero_zero(real) = ti(real,A) | B = C | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),C),A). [resolve(6021,a,6009,a)]. 97.11/96.89 6022 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4696_scaleR__left_Odiff) # label(axiom). [clausify(2856)]. 97.11/96.89 6023 -real_vector(A) | ti(A,B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),one_one(real)),B) # label(fact_4703_real__vector_Oscale__one) # label(axiom). [clausify(2930)]. 101.00/100.76 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),one_one(real)),A). [resolve(6023,a,5998,a)]. 101.00/100.76 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),one_one(real)),A). [resolve(6023,a,6009,a)]. 101.00/100.76 6024 -real_vector(A) | zero_zero(A) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),zero_zero(A)) # label(fact_4730_scaleR__right_Ozero) # label(axiom). [clausify(3546)]. 101.00/100.76 Derived: zero_zero(complex) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),zero_zero(complex)). [resolve(6024,a,5998,a)]. 101.00/100.76 Derived: zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),zero_zero(real)). [resolve(6024,a,6009,a)]. 101.00/100.76 6025 -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_4716_real__vector_Oscale__scale) # label(axiom). [clausify(3855)]. 101.00/100.76 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(6025,a,5998,a)]. 101.00/100.76 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(6025,a,6009,a)]. 101.00/100.76 6026 -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_4729_scaleR__left__imp__eq) # label(axiom). [clausify(4216)]. 101.00/100.76 6027 -real_vector(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) | C = D # label(fact_4733_scaleR__right__imp__eq) # label(axiom). [clausify(4453)]. 101.00/100.76 6028 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(int,real,number_number_of(real),min)),B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_4690_scaleR__minus1__left) # label(axiom). [clausify(4712)]. 101.00/100.76 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(int,real,number_number_of(real),min)),A) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(6028,a,5998,a)]. 101.00/100.76 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(int,real,number_number_of(real),min)),A) = hAPP(real,real,uminus_uminus(real),A). [resolve(6028,a,6009,a)]. 101.00/100.76 6029 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1117_div__add__self2) # label(axiom). [clausify(181)]. 101.00/100.76 6030 semiring_div(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Divides_Osemiring__div) # label(axiom). [assumption]. 101.00/100.76 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(6029,a,6030,a)]. 101.00/100.76 6031 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_1356_dvd__imp__mod__0) # label(axiom). [clausify(205)]. 101.00/100.77 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A). [resolve(6031,a,6030,a)]. 101.00/100.77 6032 -semiring_div(A) | zero_zero(A) = ti(A,B) | -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_1119_dvd__div__eq__mult) # label(axiom). [clausify(320)]. 101.00/100.77 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | 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(6032,a,6030,a)]. 101.00/100.77 6033 -semiring_div(A) | zero_zero(A) = ti(A,B) | -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_1119_dvd__div__eq__mult) # label(axiom). [clausify(320)]. 101.00/100.77 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | 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(6033,a,6030,a)]. 101.00/100.77 6034 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) # label(fact_1120_dvd__div__div__eq__mult) # label(axiom). [clausify(326)]. 101.00/100.77 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) | 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),A),D). [resolve(6034,a,6030,a)]. 101.00/100.77 6035 -semiring_div(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E) # label(fact_1120_dvd__div__div__eq__mult) # label(axiom). [clausify(326)]. 101.03/100.82 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,B) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),D),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A) | 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),A),D). [resolve(6035,a,6030,a)]. 101.03/100.82 6036 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),zero_zero(A)),B) # label(fact_1282_mod__0) # label(axiom). [clausify(608)]. 101.03/100.82 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(6036,a,6030,a)]. 101.03/100.82 6037 -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_1092_div__mult__swap) # label(axiom). [clausify(693)]. 101.03/100.82 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(6037,a,6030,a)]. 101.03/100.82 6038 -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_1093_dvd__div__mult__self) # label(axiom). [clausify(833)]. 101.03/100.82 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(6038,a,6030,a)]. 101.03/100.82 6039 -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_1293_mod__add__eq) # label(axiom). [clausify(857)]. 101.03/100.82 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(6039,a,6030,a)]. 101.03/100.84 6040 -semiring_div(A) | zero_zero(A) = ti(A,B) | 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_1088_div__mult__self2__is__id) # label(axiom). [clausify(876)]. 101.03/100.84 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | 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(6040,a,6030,a)]. 101.03/100.84 6041 -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_1289_mod__mult__cong) # label(axiom). [clausify(956)]. 101.03/100.84 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(6041,a,6030,a)]. 101.03/100.84 6042 -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_1303_dvd__mod) # label(axiom). [clausify(968)]. 101.03/100.84 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))). [resolve(6042,a,6030,a)]. 101.03/100.84 6043 -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_1292_zmod__simps_I2_J) # label(axiom). [clausify(1010)]. 101.03/100.84 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(6043,a,6030,a)]. 101.11/100.91 6044 -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_1296_mod__add__self1) # label(axiom). [clausify(1140)]. 101.11/100.91 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(6044,a,6030,a)]. 101.11/100.91 6045 -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_1294_mod__add__left__eq) # label(axiom). [clausify(1281)]. 101.11/100.91 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(6045,a,6030,a)]. 101.11/100.91 6046 -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_1412_mod__div__equality) # label(axiom). [clausify(1347)]. 101.11/100.91 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),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(6046,a,6030,a)]. 101.11/100.91 6047 -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_1305_dvd__mod__iff) # label(axiom). [clausify(1357)]. 101.11/100.91 6048 -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_1305_dvd__mod__iff) # label(axiom). [clausify(1357)]. 101.11/100.91 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(6048,a,6030,a)]. 101.21/101.00 6049 -semiring_div(A) | zero_zero(A) = ti(A,B) | 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_1087_div__mult__self1__is__id) # label(axiom). [clausify(1400)]. 101.21/101.00 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | 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(6049,a,6030,a)]. 101.21/101.00 6050 -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_1295_mod__add__right__eq) # label(axiom). [clausify(1520)]. 101.21/101.00 6051 -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_1411_mod__div__equality2) # label(axiom). [clausify(1554)]. 101.21/101.00 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(6051,a,6030,a)]. 101.21/101.00 6052 -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_1304_mod__mod__cancel) # label(axiom). [clausify(1648)]. 101.21/101.00 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(6052,a,6030,a)]. 101.21/101.00 6053 -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(1690)]. 101.21/101.00 Derived: div_div(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_div(quickcheck_code_int)). [resolve(6053,a,6030,a)]. 101.21/101.00 6054 -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_1095_div__mult__div__if__dvd) # label(axiom). [clausify(1730)]. 101.41/101.17 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(6054,a,6030,a)]. 101.41/101.17 6055 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1115_div__mult__self2) # label(axiom). [clausify(1939)]. 101.41/101.17 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(6055,a,6030,a)]. 101.41/101.17 6056 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),zero_zero(A)) # label(fact_1074_div__by__0) # label(axiom). [clausify(1955)]. 101.41/101.17 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),zero_zero(quickcheck_code_int)). [resolve(6056,a,6030,a)]. 101.41/101.17 6057 -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_1354_mod__mult__self2) # label(axiom). [clausify(2159)]. 101.41/101.17 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(6057,a,6030,a)]. 101.41/101.17 6058 -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_1286_mod__mult__mult1) # label(axiom). [clausify(2331)]. 101.41/101.17 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(6058,a,6030,a)]. 101.41/101.18 6059 -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_1413_div__mod__equality2) # label(axiom). [clausify(2332)]. 101.41/101.18 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(6059,a,6030,a)]. 101.41/101.18 6060 semiring_div(int) # label(arity_Int_Oint___Divides_Osemiring__div) # label(axiom). [assumption]. 101.41/101.18 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(6060,a,6029,a)]. 101.41/101.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A). [resolve(6060,a,6031,a)]. 101.41/101.18 Derived: zero_zero(int) = ti(int,A) | -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(6060,a,6032,a)]. 101.41/101.18 Derived: zero_zero(int) = ti(int,A) | -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(6060,a,6033,a)]. 101.41/101.18 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D). [resolve(6060,a,6034,a)]. 101.41/101.18 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D). [resolve(6060,a,6035,a)]. 101.41/101.21 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),A). [resolve(6060,a,6036,a)]. 101.41/101.21 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(6060,a,6037,a)]. 101.41/101.21 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(6060,a,6038,a)]. 101.41/101.21 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(6060,a,6039,a)]. 101.41/101.21 Derived: zero_zero(int) = ti(int,A) | 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(6060,a,6040,a)]. 101.41/101.21 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(6060,a,6041,a)]. 101.41/101.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))). [resolve(6060,a,6042,a)]. 101.41/101.21 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(6060,a,6043,a)]. 101.41/101.21 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(6060,a,6044,a)]. 101.41/101.21 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(6060,a,6045,a)]. 101.41/101.21 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(6060,a,6046,a)]. 101.41/101.21 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(6060,a,6048,a)]. 101.41/101.21 Derived: zero_zero(int) = ti(int,A) | 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(6060,a,6049,a)]. 101.41/101.21 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(6060,a,6052,a)]. 101.41/101.21 Derived: div_div(int) = ti(fun(int,fun(int,int)),div_div(int)). [resolve(6060,a,6053,a)]. 101.41/101.21 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(6060,a,6054,a)]. 101.47/101.25 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6060,a,6055,a)]. 101.47/101.25 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),zero_zero(int)). [resolve(6060,a,6056,a)]. 101.47/101.25 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(6060,a,6057,a)]. 101.47/101.25 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(6060,a,6058,a)]. 101.47/101.25 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),A),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C). [resolve(6060,a,6059,a)]. 101.47/101.25 6061 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),B) # label(fact_1280_mod__self) # label(axiom). [clausify(2357)]. 101.47/101.25 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),A). [resolve(6061,a,6030,a)]. 101.47/101.25 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),A). [resolve(6061,a,6060,a)]. 101.47/101.25 6062 -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_1285_mod__mult__eq) # label(axiom). [clausify(2373)]. 101.47/101.25 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(6062,a,6030,a)]. 101.47/101.25 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(6062,a,6060,a)]. 101.47/101.25 6063 -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_1414_div__mod__equality) # label(axiom). [clausify(2444)]. 101.72/101.50 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(6063,a,6030,a)]. 101.72/101.50 6064 -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(2494)]. 101.72/101.50 Derived: div_mod(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_mod(quickcheck_code_int)). [resolve(6064,a,6030,a)]. 101.72/101.50 Derived: div_mod(int) = ti(fun(int,fun(int,int)),div_mod(int)). [resolve(6064,a,6060,a)]. 101.72/101.50 6065 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),one_one(A)) # label(fact_1353_mod__by__1) # label(axiom). [clausify(2570)]. 101.72/101.50 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),one_one(quickcheck_code_int)). [resolve(6065,a,6030,a)]. 101.72/101.50 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),one_one(int)). [resolve(6065,a,6060,a)]. 101.72/101.50 6066 -semiring_div(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),B) # label(fact_1090_div__self) # label(axiom). [clausify(2621)]. 101.72/101.50 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | one_one(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),A). [resolve(6066,a,6030,a)]. 101.72/101.50 Derived: zero_zero(int) = ti(int,A) | one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),A). [resolve(6066,a,6060,a)]. 101.72/101.50 6067 -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_1520_mod__div__decomp) # label(axiom). [clausify(2711)]. 101.72/101.50 6068 -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_1290_mod__add__cong) # label(axiom). [clausify(2896)]. 101.72/101.50 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(6068,a,6030,a)]. 101.86/101.62 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(6068,a,6060,a)]. 101.86/101.62 6069 -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_1287_mod__mult__mult2) # label(axiom). [clausify(2959)]. 101.86/101.62 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(6069,a,6030,a)]. 101.86/101.62 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(6069,a,6060,a)]. 101.86/101.62 6070 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_1086_div__mult__mult2) # label(axiom). [clausify(3031)]. 101.86/101.62 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(6070,a,6030,a)]. 101.86/101.62 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(6070,a,6060,a)]. 101.86/101.62 6071 -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_1288_zmod__simps_I4_J) # label(axiom). [clausify(3140)]. 101.86/101.62 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(6071,a,6030,a)]. 102.09/101.89 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(6071,a,6060,a)]. 102.09/101.89 6072 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),zero_zero(A)) # label(fact_1281_mod__by__0) # label(axiom). [clausify(3412)]. 102.09/101.89 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(6072,a,6030,a)]. 102.09/101.89 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),zero_zero(int)). [resolve(6072,a,6060,a)]. 102.09/101.89 6073 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_1085_div__mult__mult1) # label(axiom). [clausify(3453)]. 102.09/101.89 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(6073,a,6030,a)]. 102.09/101.89 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(6073,a,6060,a)]. 102.09/101.89 6074 -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_1097_div__power) # label(axiom). [clausify(3462)]. 102.09/101.89 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(6074,a,6030,a)]. 102.09/101.89 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(6074,a,6060,a)]. 102.23/101.98 6075 -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),C),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))) # label(fact_1076_div__dvd__div) # label(axiom). [clausify(3470)]. 102.23/101.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),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))). [resolve(6075,a,6030,a)]. 102.23/101.98 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),B),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))). [resolve(6075,a,6060,a)]. 102.23/101.98 6076 -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),C),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))) # label(fact_1076_div__dvd__div) # label(axiom). [clausify(3470)]. 102.23/101.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),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))). [resolve(6076,a,6030,a)]. 102.23/101.98 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),B),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))). [resolve(6076,a,6060,a)]. 102.23/101.98 6077 -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_1094_dvd__div__mult) # label(axiom). [clausify(3620)]. 102.23/101.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),C). [resolve(6077,a,6030,a)]. 102.32/102.09 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(6077,a,6060,a)]. 102.32/102.09 6078 -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_1284_mod__mult__left__eq) # label(axiom). [clausify(3657)]. 102.32/102.09 6079 -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_1355_mod__mult__self1) # label(axiom). [clausify(3683)]. 102.32/102.09 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(6079,a,6030,a)]. 102.32/102.09 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(6079,a,6060,a)]. 102.32/102.09 6080 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_1089_div__mult__mult1__if) # label(axiom). [clausify(3740)]. 102.32/102.09 6081 -semiring_div(A) | zero_zero(A) != ti(A,B) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_1089_div__mult__mult1__if) # label(axiom). [clausify(3740)]. 102.32/102.09 Derived: zero_zero(quickcheck_code_int) != ti(quickcheck_code_int,A) | zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)). [resolve(6081,a,6030,a)]. 102.32/102.09 Derived: zero_zero(int) != ti(int,A) | zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(6081,a,6060,a)]. 102.32/102.09 6082 -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_1279_mod__mod__trivial) # label(axiom). [clausify(3782)]. 102.32/102.09 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(6082,a,6030,a)]. 102.46/102.22 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(6082,a,6060,a)]. 102.46/102.22 6083 -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_1291_zmod__simps_I1_J) # label(axiom). [clausify(3863)]. 102.46/102.22 6084 -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_1096_div__add) # label(axiom). [clausify(3912)]. 102.46/102.22 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(6084,a,6030,a)]. 102.46/102.22 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(6084,a,6060,a)]. 102.46/102.22 6085 -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_1297_mod__add__self2) # label(axiom). [clausify(3924)]. 102.46/102.22 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(6085,a,6030,a)]. 102.46/102.22 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(6085,a,6060,a)]. 102.46/102.22 6086 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1116_div__mult__self1) # label(axiom). [clausify(3968)]. 102.46/102.22 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(6086,a,6030,a)]. 102.46/102.27 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6086,a,6060,a)]. 102.46/102.27 6087 -semiring_div(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1118_div__add__self1) # label(axiom). [clausify(3991)]. 102.46/102.27 Derived: zero_zero(quickcheck_code_int) = ti(quickcheck_code_int,A) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(6087,a,6030,a)]. 102.46/102.27 Derived: zero_zero(int) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(6087,a,6060,a)]. 102.46/102.27 6088 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_1351_mod__mult__self2__is__0) # label(axiom). [clausify(3995)]. 102.46/102.27 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B). [resolve(6088,a,6030,a)]. 102.46/102.27 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B). [resolve(6088,a,6060,a)]. 102.46/102.27 6089 -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_1091_dvd__mult__div__cancel) # label(axiom). [clausify(4051)]. 102.46/102.27 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(6089,a,6030,a)]. 102.46/102.27 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(6089,a,6060,a)]. 102.91/102.69 6090 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),one_one(A)) # label(fact_1075_div__by__1) # label(axiom). [clausify(4177)]. 102.91/102.69 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),one_one(quickcheck_code_int)). [resolve(6090,a,6030,a)]. 102.91/102.69 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),one_one(int)). [resolve(6090,a,6060,a)]. 102.91/102.69 6091 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) # label(fact_1352_mod__mult__self1__is__0) # label(axiom). [clausify(4194)]. 102.91/102.69 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A). [resolve(6091,a,6030,a)]. 102.91/102.69 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A). [resolve(6091,a,6060,a)]. 102.91/102.69 6092 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),zero_zero(A)),B) # label(fact_1073_div__0) # label(axiom). [clausify(4229)]. 102.91/102.69 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(6092,a,6030,a)]. 102.91/102.69 6093 -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_1302_dvd__mod__imp__dvd) # label(axiom). [clausify(4421)]. 102.91/102.69 6094 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) # label(fact_1358_mod__div__trivial) # label(axiom). [clausify(4494)]. 102.91/102.69 Derived: zero_zero(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B). [resolve(6094,a,6030,a)]. 102.91/102.69 Derived: zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B). [resolve(6094,a,6060,a)]. 102.91/102.69 6095 -semiring_div(A) | zero_zero(A) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)) # label(fact_1357_dvd__eq__mod__eq__0) # label(axiom). [clausify(4568)]. 102.91/102.69 Derived: zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),A)). [resolve(6095,a,6030,a)]. 102.91/102.69 Derived: zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A)). [resolve(6095,a,6060,a)]. 102.91/102.69 6096 -semiring_div(A) | zero_zero(A) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),B)) # label(fact_1357_dvd__eq__mod__eq__0) # label(axiom). [clausify(4568)]. 102.91/102.69 6097 -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_1410_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(4698)]. 102.91/102.69 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),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(6097,a,6030,a)]. 102.98/102.77 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(6097,a,6060,a)]. 102.98/102.77 6098 -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_1283_mod__mult__right__eq) # label(axiom). [clausify(4761)]. 102.98/102.77 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(6098,a,6030,a)]. 102.98/102.77 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(6098,a,6060,a)]. 102.98/102.77 6099 semiring_div(nat) # label(arity_Nat_Onat___Divides_Osemiring__div) # label(axiom). [assumption]. 102.98/102.77 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(6099,a,6029,a)]. 102.98/102.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A). [resolve(6099,a,6031,a)]. 102.98/102.77 Derived: zero_zero(nat) = ti(nat,A) | -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(6099,a,6032,a)]. 102.98/102.77 Derived: zero_zero(nat) = ti(nat,A) | -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(6099,a,6033,a)]. 102.98/102.77 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D). [resolve(6099,a,6034,a)]. 102.98/102.77 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D). [resolve(6099,a,6035,a)]. 102.98/102.78 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),zero_zero(nat)),A). [resolve(6099,a,6036,a)]. 102.98/102.78 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(6099,a,6037,a)]. 102.98/102.78 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(6099,a,6038,a)]. 102.98/102.78 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(6099,a,6039,a)]. 102.98/102.78 Derived: zero_zero(nat) = ti(nat,A) | 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(6099,a,6040,a)]. 102.98/102.78 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(6099,a,6041,a)]. 102.98/102.78 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))). [resolve(6099,a,6042,a)]. 102.98/102.78 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(6099,a,6043,a)]. 102.98/102.78 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(6099,a,6044,a)]. 102.98/102.78 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(6099,a,6045,a)]. 102.98/102.78 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(6099,a,6046,a)]. 102.98/102.78 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(6099,a,6048,a)]. 102.98/102.78 Derived: zero_zero(nat) = ti(nat,A) | 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(6099,a,6049,a)]. 102.98/102.78 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(6099,a,6051,a)]. 102.98/102.78 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(6099,a,6052,a)]. 102.98/102.79 Derived: div_div(nat) = ti(fun(nat,fun(nat,nat)),div_div(nat)). [resolve(6099,a,6053,a)]. 102.98/102.79 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(6099,a,6054,a)]. 102.98/102.79 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(6099,a,6055,a)]. 102.98/102.79 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),zero_zero(nat)). [resolve(6099,a,6056,a)]. 102.98/102.79 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(6099,a,6057,a)]. 102.98/102.79 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(6099,a,6058,a)]. 102.98/102.79 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(6099,a,6059,a)]. 102.98/102.79 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),A). [resolve(6099,a,6061,a)]. 102.98/102.79 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(6099,a,6062,a)]. 102.98/102.79 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(6099,a,6063,a)]. 102.98/102.79 Derived: div_mod(nat) = ti(fun(nat,fun(nat,nat)),div_mod(nat)). [resolve(6099,a,6064,a)]. 102.98/102.79 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),one_one(nat)). [resolve(6099,a,6065,a)]. 102.98/102.79 Derived: zero_zero(nat) = ti(nat,A) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),A). [resolve(6099,a,6066,a)]. 102.98/102.79 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(6099,a,6068,a)]. 102.98/102.79 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(6099,a,6069,a)]. 102.98/102.79 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(6099,a,6070,a)]. 102.98/102.80 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(6099,a,6071,a)]. 102.98/102.80 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),zero_zero(nat)). [resolve(6099,a,6072,a)]. 102.98/102.80 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(6099,a,6073,a)]. 102.98/102.80 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(6099,a,6074,a)]. 102.98/102.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -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),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(6099,a,6075,a)]. 102.98/102.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | 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),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(6099,a,6076,a)]. 102.98/102.80 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(6099,a,6077,a)]. 102.98/102.80 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(6099,a,6079,a)]. 102.98/102.80 Derived: zero_zero(nat) != ti(nat,A) | zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(6099,a,6081,a)]. 102.98/102.80 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(6099,a,6082,a)]. 102.98/102.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),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(6099,a,6084,a)]. 102.98/102.80 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(6099,a,6085,a)]. 102.98/102.80 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(6099,a,6086,a)]. 103.08/102.84 Derived: zero_zero(nat) = ti(nat,A) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(6099,a,6087,a)]. 103.08/102.84 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(6099,a,6088,a)]. 103.08/102.84 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(6099,a,6089,a)]. 103.08/102.84 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),one_one(nat)). [resolve(6099,a,6090,a)]. 103.08/102.84 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A). [resolve(6099,a,6091,a)]. 103.08/102.85 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),zero_zero(nat)),A). [resolve(6099,a,6092,a)]. 103.08/102.85 Derived: zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B). [resolve(6099,a,6094,a)]. 103.08/102.85 Derived: zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A)). [resolve(6099,a,6095,a)]. 103.08/102.85 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(6099,a,6097,a)]. 103.08/102.85 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(6099,a,6098,a)]. 103.08/102.85 6100 semiring_div(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Divides_Osemiring__div) # label(axiom). [assumption]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(6100,a,6029,a)]. 103.08/102.85 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A). [resolve(6100,a,6031,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | 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(6100,a,6032,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | 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(6100,a,6033,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) | 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),A),D). [resolve(6100,a,6034,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | zero_zero(code_code_numeral) = ti(code_code_numeral,B) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),D),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A) | 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),A),D). [resolve(6100,a,6035,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(6100,a,6036,a)]. 103.08/102.85 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(6100,a,6037,a)]. 103.08/102.85 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(6100,a,6038,a)]. 103.08/102.85 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(6100,a,6039,a)]. 103.08/102.85 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | 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(6100,a,6040,a)]. 103.08/102.85 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(6100,a,6041,a)]. 103.08/102.85 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),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))). [resolve(6100,a,6042,a)]. 103.08/102.85 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(6100,a,6043,a)]. 103.08/102.85 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(6100,a,6044,a)]. 103.08/102.85 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(6100,a,6045,a)]. 103.08/102.86 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(6100,a,6046,a)]. 103.08/102.86 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(6100,a,6048,a)]. 103.08/102.86 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | 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(6100,a,6049,a)]. 103.08/102.86 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(6100,a,6051,a)]. 103.08/102.86 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(6100,a,6052,a)]. 103.08/102.86 Derived: div_div(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_div(code_code_numeral)). [resolve(6100,a,6053,a)]. 103.08/102.86 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(6100,a,6054,a)]. 103.08/102.86 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(6100,a,6055,a)]. 103.08/102.86 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),zero_zero(code_code_numeral)). [resolve(6100,a,6056,a)]. 103.08/102.86 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(6100,a,6057,a)]. 103.08/102.86 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(6100,a,6058,a)]. 103.08/102.86 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(6100,a,6059,a)]. 103.08/102.86 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),A). [resolve(6100,a,6061,a)]. 103.08/102.86 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(6100,a,6062,a)]. 103.08/102.87 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(6100,a,6063,a)]. 103.08/102.87 Derived: div_mod(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_mod(code_code_numeral)). [resolve(6100,a,6064,a)]. 103.08/102.87 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),one_one(code_code_numeral)). [resolve(6100,a,6065,a)]. 103.08/102.87 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | one_one(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),A). [resolve(6100,a,6066,a)]. 103.08/102.87 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(6100,a,6068,a)]. 103.08/102.87 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(6100,a,6069,a)]. 103.08/102.87 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(6100,a,6070,a)]. 103.08/102.87 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(6100,a,6071,a)]. 103.08/102.87 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(6100,a,6072,a)]. 103.08/102.87 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(6100,a,6073,a)]. 103.08/102.87 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(6100,a,6074,a)]. 103.08/102.87 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),B),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))). [resolve(6100,a,6075,a)]. 103.08/102.87 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),B),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))). [resolve(6100,a,6076,a)]. 103.08/102.88 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(6100,a,6077,a)]. 103.08/102.88 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(6100,a,6079,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) != ti(code_code_numeral,A) | zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)). [resolve(6100,a,6081,a)]. 103.08/102.88 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(6100,a,6082,a)]. 103.08/102.88 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(6100,a,6084,a)]. 103.08/102.88 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(6100,a,6085,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(6100,a,6086,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = ti(code_code_numeral,A) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(6100,a,6087,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B). [resolve(6100,a,6088,a)]. 103.08/102.88 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(6100,a,6089,a)]. 103.08/102.88 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(6100,a,6090,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A). [resolve(6100,a,6091,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(6100,a,6092,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B). [resolve(6100,a,6094,a)]. 103.08/102.88 Derived: zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),A)). [resolve(6100,a,6095,a)]. 103.08/102.88 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(6100,a,6097,a)]. 106.10/105.88 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(6100,a,6098,a)]. 106.10/105.88 6101 -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_327_add__strict__mono) # label(axiom). [clausify(639)]. 106.10/105.88 6102 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 106.10/105.88 6103 ordere223160158up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 106.10/105.88 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(6103,a,6101,a)]. 106.10/105.88 6104 -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_233_add__le__less__mono) # label(axiom). [clausify(975)]. 106.10/105.88 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(6104,a,6102,a)]. 106.10/105.88 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(6104,a,6103,a)]. 106.10/105.88 6105 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 106.10/105.88 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(6105,a,6101,a)]. 106.10/105.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(6105,a,6104,a)]. 107.07/106.82 6106 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 107.07/106.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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(6106,a,6101,a)]. 107.07/106.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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(6106,a,6104,a)]. 107.07/106.82 6107 -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_328_add__strict__left__mono) # label(axiom). [clausify(2321)]. 107.07/106.82 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(6107,a,6102,a)]. 107.07/106.82 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(6107,a,6103,a)]. 107.07/106.82 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),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(6107,a,6105,a)]. 107.07/106.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(6107,a,6106,a)]. 107.07/106.82 6108 -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_234_add__less__le__mono) # label(axiom). [clausify(3786)]. 107.07/106.82 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(6108,a,6102,a)]. 107.07/106.82 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(6108,a,6103,a)]. 107.12/106.89 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(6108,a,6105,a)]. 107.12/106.89 6109 ordere223160158up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__cancel__ab__semigroup_) # label(axiom). [assumption]. 107.12/106.89 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(6109,a,6101,a)]. 107.12/106.89 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(6109,a,6104,a)]. 107.12/106.89 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(6109,a,6107,a)]. 107.12/106.89 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(6109,a,6108,a)]. 107.12/106.89 6110 -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_329_add__strict__right__mono) # label(axiom). [clausify(3904)]. 107.12/106.89 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(6110,a,6102,a)]. 107.12/106.89 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(6110,a,6103,a)]. 110.41/110.17 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(6110,a,6105,a)]. 110.41/110.17 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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(6110,a,6106,a)]. 110.41/110.17 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(6110,a,6109,a)]. 110.41/110.17 6111 ordere223160158up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 110.41/110.17 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(6111,a,6101,a)]. 110.41/110.17 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(6111,a,6104,a)]. 110.41/110.17 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(6111,a,6107,a)]. 110.41/110.17 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(6111,a,6108,a)]. 110.41/110.17 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(6111,a,6110,a)]. 110.41/110.17 6112 -field(A) | one_one(A) = ti(A,B) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = 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),B),C)),one_one(A))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_4197_geometric__sum) # label(axiom). [clausify(288)]. 110.41/110.17 6113 field(real) # label(arity_RealDef_Oreal___Fields_Ofield) # label(axiom). [assumption]. 110.41/110.17 Derived: one_one(real) = ti(real,A) | 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),A)),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),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(6112,a,6113,a)]. 110.41/110.19 6114 -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_1782_divide__numeral__1) # label(axiom). [clausify(423)]. 110.41/110.19 Derived: -number_ring(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(6114,b,6113,a)]. 110.41/110.19 6115 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(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,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(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),E),C)) # label(fact_1884_diff__frac__eq) # label(axiom). [clausify(509)]. 110.41/110.19 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(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,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(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),D),B)). [resolve(6115,a,6113,a)]. 110.41/110.19 6116 -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_4244_setsum__divide__distrib) # label(axiom). [clausify(578)]. 110.41/110.19 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(6116,a,6113,a)]. 110.41/110.19 6117 field(rat) # label(arity_Rat_Orat___Fields_Ofield) # label(axiom). [assumption]. 110.41/110.19 Derived: one_one(rat) = ti(rat,A) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),one_one(rat))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(6117,a,6112,a)]. 110.41/110.19 Derived: -number_ring(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(6117,a,6114,b)]. 110.41/110.19 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(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))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(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),D),B)). [resolve(6117,a,6115,a)]. 110.63/110.37 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),inverse_divide(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),C). [resolve(6117,a,6116,a)]. 110.63/110.37 6118 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)) # label(fact_1880_add__divide__eq__iff) # label(axiom). [clausify(1196)]. 110.63/110.37 Derived: zero_zero(real) = ti(real,A) | 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,hAPP(real,fun(real,real),times_times(real),A),B)),C)),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)). [resolve(6118,a,6113,a)]. 110.63/110.37 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)). [resolve(6118,a,6117,a)]. 110.63/110.37 6119 -field(A) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) # label(fact_2603_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(1275)]. 110.63/110.37 Derived: hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A). [resolve(6119,a,6113,a)]. 110.63/110.37 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A). [resolve(6119,a,6117,a)]. 110.63/110.37 6120 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D) # label(fact_1878_divide__add__eq__iff) # label(axiom). [clausify(1535)]. 110.63/110.37 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C). [resolve(6120,a,6113,a)]. 110.63/110.37 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C). [resolve(6120,a,6117,a)]. 110.63/110.37 6121 -field(A) | -number_ring(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_2621_inverse__numeral__1) # label(axiom). [clausify(1692)]. 110.63/110.37 Derived: -number_ring(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(6121,a,6113,a)]. 110.63/110.37 Derived: -number_ring(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(6121,a,6117,a)]. 111.23/111.00 6122 -field(A) | -number_ring(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_1783_divide__Numeral1) # label(axiom). [clausify(2317)]. 111.23/111.00 6123 -field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2600_field__divide__inverse) # label(axiom). [clausify(2377)]. 111.23/111.00 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(6123,a,6117,a)]. 111.23/111.00 6124 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D) # label(fact_1883_divide__diff__eq__iff) # label(axiom). [clausify(2542)]. 111.23/111.00 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C). [resolve(6124,a,6113,a)]. 111.23/111.00 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C). [resolve(6124,a,6117,a)]. 111.23/111.00 6125 -field(A) | zero_zero(A) = ti(A,B) | 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),B),C)),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)) # label(fact_1882_diff__divide__eq__iff) # label(axiom). [clausify(3006)]. 111.23/111.00 Derived: zero_zero(real) = ti(real,A) | 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),A),B)),C)),A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)). [resolve(6125,a,6113,a)]. 111.23/111.00 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)). [resolve(6125,a,6117,a)]. 111.23/111.00 6126 field(complex) # label(arity_Complex_Ocomplex___Fields_Ofield) # label(axiom). [assumption]. 111.23/111.00 Derived: one_one(complex) = ti(complex,A) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)) = 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),A),B)),one_one(complex))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),one_one(complex))). [resolve(6126,a,6112,a)]. 111.23/111.00 Derived: -number_ring(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(6126,a,6114,b)]. 111.23/111.00 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(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,hAPP(complex,fun(complex,complex),times_times(complex),C),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),B)). [resolve(6126,a,6115,a)]. 111.40/111.15 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(6126,a,6116,a)]. 111.40/111.15 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C)),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)). [resolve(6126,a,6118,a)]. 111.40/111.15 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A). [resolve(6126,a,6119,a)]. 111.40/111.15 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C). [resolve(6126,a,6120,a)]. 111.40/111.15 Derived: -number_ring(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(6126,a,6121,a)]. 111.40/111.15 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C). [resolve(6126,a,6124,a)]. 111.40/111.15 Derived: zero_zero(complex) = ti(complex,A) | 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),A),B)),C)),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)). [resolve(6126,a,6125,a)]. 111.40/111.15 6127 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),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))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(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),E),C)) # label(fact_1877_add__frac__eq) # label(axiom). [clausify(3401)]. 111.62/111.37 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | 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,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(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),D),B)). [resolve(6127,a,6113,a)]. 111.62/111.37 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),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))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(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),D),B)). [resolve(6127,a,6117,a)]. 111.62/111.37 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),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))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),B)). [resolve(6127,a,6126,a)]. 111.62/111.37 6128 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | 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),inverse_divide(A),D),C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),B) # label(fact_1852_frac__eq__eq) # label(axiom). [clausify(3785)]. 111.62/111.37 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | 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),inverse_divide(real),C),B) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),A). [resolve(6128,a,6113,a)]. 111.62/111.37 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | 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),inverse_divide(rat),C),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),A). [resolve(6128,a,6117,a)]. 111.62/111.37 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | 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),inverse_divide(complex),C),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),A). [resolve(6128,a,6126,a)]. 111.62/111.37 6129 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | 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),inverse_divide(A),D),C) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),E),B) # label(fact_1852_frac__eq__eq) # label(axiom). [clausify(3785)]. 111.62/111.37 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | 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),inverse_divide(real),C),B) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),D),A). [resolve(6129,a,6113,a)]. 112.04/111.82 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | 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),inverse_divide(rat),C),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),D),A). [resolve(6129,a,6117,a)]. 112.04/111.82 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | 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),inverse_divide(complex),C),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),D),A). [resolve(6129,a,6126,a)]. 112.04/111.82 6130 -field(A) | zero_zero(A) = ti(A,B) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) # label(fact_2617_field__inverse) # label(axiom). [clausify(3799)]. 112.04/111.82 Derived: zero_zero(real) = ti(real,A) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),A). [resolve(6130,a,6113,a)]. 112.04/111.82 Derived: zero_zero(rat) = ti(rat,A) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),A). [resolve(6130,a,6117,a)]. 112.04/111.82 Derived: zero_zero(complex) = ti(complex,A) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),A). [resolve(6130,a,6126,a)]. 112.04/111.82 6131 -field(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,inverse_inverse(A),B))),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2612_inverse__add) # label(axiom). [clausify(4109)]. 112.04/111.82 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,inverse_inverse(real),A))),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(6131,a,6113,a)]. 112.04/111.82 Derived: zero_zero(rat) = ti(rat,A) | zero_zero(rat) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,inverse_inverse(rat),A))),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(6131,a,6117,a)]. 112.04/111.82 Derived: zero_zero(complex) = ti(complex,A) | zero_zero(complex) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,inverse_inverse(complex),A))),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(6131,a,6126,a)]. 112.04/111.82 6132 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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),inverse_divide(A),C),B)),D) # label(fact_1764_nonzero__power__divide) # label(axiom). [clausify(4526)]. 112.04/111.82 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),C). [resolve(6132,a,6113,a)]. 112.21/112.00 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),C). [resolve(6132,a,6117,a)]. 112.21/112.00 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),C). [resolve(6132,a,6126,a)]. 112.21/112.00 6133 -field(A) | zero_zero(A) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),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),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,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(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),D),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),D),hAPP(nat,nat,suc,zero_zero(nat)))))) = 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)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_4265_lemma__termdiff2) # label(axiom). [clausify(4802)]. 112.21/112.00 Derived: zero_zero(real) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),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),C),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),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = 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)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6133,a,6113,a)]. 112.21/112.00 Derived: zero_zero(rat) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,fun(nat,bool)),fun(nat,rat),hAPP(fun(fun(nat,bool),rat),fun(fun(nat,fun(nat,bool)),fun(nat,rat)),combb(fun(nat,bool),rat,nat),hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),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),C),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),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A)),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),C))),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,semiring_1_of_nat(rat),C)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6133,a,6117,a)]. 112.21/112.00 Derived: zero_zero(complex) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),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),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),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),C),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),C),hAPP(nat,nat,suc,zero_zero(nat)))))) = 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)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),hAPP(nat,nat,suc,zero_zero(nat)))))). [resolve(6133,a,6126,a)]. 114.84/114.63 6134 -field(A) | zero_zero(A) = ti(A,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(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),B),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),C)) # label(fact_1798_power__diff) # label(axiom). [clausify(4811)]. 114.84/114.63 Derived: zero_zero(real) = ti(real,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(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),A),B)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)). [resolve(6134,a,6113,a)]. 114.84/114.63 Derived: zero_zero(rat) = ti(rat,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(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),A),B)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)). [resolve(6134,a,6117,a)]. 114.84/114.63 Derived: zero_zero(complex) = ti(complex,A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(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),A),B)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)). [resolve(6134,a,6126,a)]. 114.84/114.63 6135 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom). [assumption]. 114.93/114.69 6136 -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_4261_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(138)]. 114.93/114.69 6137 -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_4261_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(138)]. 114.93/114.69 6138 -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_4261_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(138)]. 114.93/114.69 6139 -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_4261_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(138)]. 114.93/114.69 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(6135,a,6136,a)]. 114.93/114.69 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(6135,a,6137,a)]. 114.93/114.69 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(6135,a,6138,a)]. 114.93/114.69 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(6135,a,6139,a)]. 114.93/114.69 6140 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f150(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2858_dense__le) # label(axiom). [clausify(969)]. 114.93/114.69 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f150(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6140,a,6135,a)]. 115.10/114.84 6141 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f150(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2858_dense__le) # label(axiom). [clausify(969)]. 115.10/114.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f150(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(6141,a,6135,a)]. 115.10/114.84 6142 -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_4555_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(1772)]. 115.10/114.84 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(6142,a,6135,a)]. 115.10/114.84 6143 -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_4555_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(1772)]. 115.10/114.84 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(6143,a,6135,a)]. 115.10/114.84 6144 -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_4555_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(1772)]. 115.10/114.84 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(6144,a,6135,a)]. 115.10/114.84 6145 -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),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4555_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(1772)]. 115.10/114.84 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),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6145,a,6135,a)]. 115.89/115.63 6146 -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(2081)]. 115.89/115.63 6147 -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),f418(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2859_dense__le__bounded) # label(axiom). [clausify(2457)]. 115.89/115.63 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),f418(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6147,a,6135,a)]. 115.89/115.63 6148 -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),f418(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2859_dense__le__bounded) # label(axiom). [clausify(2457)]. 115.89/115.63 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),f418(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6148,a,6135,a)]. 115.89/115.63 6149 -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),f418(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_2859_dense__le__bounded) # label(axiom). [clausify(2457)]. 115.89/115.63 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),f418(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6149,a,6135,a)]. 115.89/115.63 6150 dense_linorder(rat) # label(arity_Rat_Orat___Orderings_Odense__linorder) # label(axiom). [assumption]. 115.89/115.63 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(6150,a,6136,a)]. 115.89/115.63 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(6150,a,6137,a)]. 115.89/115.63 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(6150,a,6138,a)]. 115.89/115.63 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(6150,a,6139,a)]. 115.89/115.63 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f150(rat,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6150,a,6140,a)]. 115.89/115.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),f150(rat,A,B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(6150,a,6141,a)]. 115.98/115.77 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(6150,a,6142,a)]. 115.98/115.77 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(6150,a,6143,a)]. 115.98/115.77 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(6150,a,6144,a)]. 115.98/115.77 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),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6150,a,6145,a)]. 115.98/115.77 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),f418(rat,C,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6150,a,6147,a)]. 115.98/115.77 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),f418(rat,C,A,B)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6150,a,6148,a)]. 115.98/115.77 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),f418(rat,C,A,B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6150,a,6149,a)]. 115.98/115.77 6151 -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_4553_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3709)]. 115.98/115.77 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(6151,a,6135,a)]. 115.98/115.77 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(6151,a,6150,a)]. 115.98/115.77 6152 -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_4553_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3709)]. 116.73/116.50 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(6152,a,6135,a)]. 116.73/116.50 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(6152,a,6150,a)]. 116.73/116.50 6153 -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_4553_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3709)]. 116.73/116.50 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(6153,a,6135,a)]. 116.73/116.50 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(6153,a,6150,a)]. 116.73/116.50 6154 -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),D),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4553_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom). [clausify(3709)]. 116.73/116.50 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),C),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(6154,a,6135,a)]. 116.73/116.50 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),C),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(6154,a,6150,a)]. 116.73/116.50 6155 -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_4554_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4853)]. 116.73/116.50 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(6155,a,6135,a)]. 116.73/116.50 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(6155,a,6150,a)]. 116.73/116.50 6156 -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_4554_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4853)]. 116.73/116.50 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(6156,a,6135,a)]. 116.73/116.50 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(6156,a,6150,a)]. 116.73/116.50 6157 -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_4554_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4853)]. 116.73/116.50 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(6157,a,6135,a)]. 116.73/116.50 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(6157,a,6150,a)]. 116.73/116.50 6158 -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_4554_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom). [clausify(4853)]. 119.60/119.35 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(6158,a,6135,a)]. 119.60/119.35 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(6158,a,6150,a)]. 119.60/119.35 6159 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_243_add__neg__nonpos) # label(axiom). [clausify(147)]. 119.60/119.35 6160 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 119.60/119.35 6161 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_200_add__neg__neg) # label(axiom). [clausify(278)]. 119.60/119.35 6162 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_228_add__increasing) # label(axiom). [clausify(449)]. 119.60/119.35 6163 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_244_add__strict__increasing2) # label(axiom). [clausify(1290)]. 119.60/119.35 6164 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 119.60/119.35 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6164,a,6159,a)]. 119.60/119.35 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6164,a,6161,a)]. 119.60/119.35 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6164,a,6162,a)]. 119.60/119.35 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6164,a,6163,a)]. 120.13/119.94 6165 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_247_add__pos__nonneg) # label(axiom). [clausify(2077)]. 120.13/119.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(6165,a,6164,a)]. 120.13/119.94 6166 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_230_add__nonneg__nonneg) # label(axiom). [clausify(2293)]. 120.13/119.94 6167 ordere216010020id_add(rat) # label(arity_Rat_Orat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6167,a,6159,a)]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6167,a,6161,a)]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6167,a,6162,a)]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6167,a,6163,a)]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))). [resolve(6167,a,6165,a)]. 120.13/119.94 6168 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_242_add__nonpos__neg) # label(axiom). [clausify(3148)]. 120.13/119.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6168,a,6164,a)]. 120.13/119.94 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6168,a,6167,a)]. 120.13/119.94 6169 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_245_add__strict__increasing) # label(axiom). [clausify(3153)]. 120.22/119.97 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(6169,a,6160,a)]. 120.22/119.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(6169,a,6164,a)]. 120.22/119.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6169,a,6167,a)]. 120.22/119.97 6170 -ordere216010020id_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f564(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4320_setsum__mono2) # label(axiom). [clausify(3188)]. 120.22/119.97 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),f564(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(6170,a,6160,a)]. 120.22/119.97 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),f564(A,real,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B))). [resolve(6170,a,6164,a)]. 120.22/119.97 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),f564(A,rat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B))). [resolve(6170,a,6167,a)]. 120.22/119.97 6171 -ordere216010020id_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,E,f564(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAAlarm clock 120.32/120.06 Prover9 interrupted 120.32/120.07 EOF